Corporate Finance FlexText™ 3e

7/23/2019 Corporate Finance FlexText™ 3e

http://slidepdf.com/reader/full/corporate-finance-flextext-3e 1/364

1

Corporate Finance

Third Edition FlexTextTM

David J. Moore, Ph.D.

http://www.efficientminds.com



2

Copyright (c) 2010, 2011, 2012, 2013, 2014 By David J. Moore, Ph.D.

All rights reserved.

No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in anyform, or by any means, electronic, mechanical, photocopying, recording, or otherwise, without theprior consent of the author. For more information contact the author viahttp://www.efficientminds.com.



3



4

What is FlexTextTM?

I have taught corporate finance at the introductory undergraduate, intermediate undergraduate, and

introductory MBA levels. While teaching those courses I noticed significant overlap in the materialcovered. For instance, net present value is covered at all levels. To promote efficiency I have combinedmy lecture notes from all three levels into this single text.

This book offers a new approach for multilevel instruction. With this Corporate Finance bookprofessors can choose their own subset of chapters tailored to the level of instruction. In so doingprofessors and students have a consistent text for a sequence of corporate finance courses.

About this book

It is my wish that these notes equip the reader in at least three ways. First, I would like the reader tounderstand ways to improve operating, investing, and financing activities. Second, I would like thereader to learn the tools for project selection, project risk assessment, and project risk management.Third, I would like the reader to become familiar with the implications of debt vs. equity financing.

Throughout the notes you will find questions to check your understanding of the material. These

questions foster classroom interaction. Answers are available at the end of the book. Also, I in-tentionally omitted numerical example details to encourage note taking during class. Numericalexamples will be worked in class so you can fill in the blanks. So, watch for the symbol thatindicates a numerical example is near.

These lecture notes are organized into three parts. Part I covers the fundamental concepts of financial management including the financial manager’s role, corporate governance, the time value



5

of money, bond valuation, stock valuation, and risk and return. Part II utilizes the concepts of PartI to analyze and forecast forecast financial statements, compute the cost of capital, and to increaseawareness of the debt vs. equity choice.

While Part II is focused on broader issues in corporate value, Part III is focused on projectselection concepts. Part III includes detailed discussions on project selection criteria, project riskassessment, and managing project risk using decision trees and real options.

Thank you for purchasing this text. Lets learn how to make our corporations more valuable...

-David J. Moore, Ph.D.

What’s new in the Third Edition?

1. Added answers to embedded questions at the end of the book.

2. Added several appendices to Chapter 4: (1) using the financial calculator, (2) formulas for n,and (3) approximation of i.

3. Updated Discounted Free Cash Flow valuation discussion (Section 5.7).

4. Updated Market Multiple valuation discussion (Section 5.8).

5. Updated CAPM and SML estimation (Section 7.4.3) with reference to CAPM inputs andequation for direct computation of β .



6

6. Added 3 inches of space to the bottom of each page so students may take notes.

7. Corrected equation numbering.

8. Standardized variable notation to capital letter with lowercase subscripts.

9. Miscellaneous typographical error corrections.



Contents

I Fundamental concepts 19

1 Corporate finance introduction 211.1 Financial manager’s role . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221.2 Cash flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251.3 Three fundamental decisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251.4 Legal business forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261.5 Typical corporation organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2 Corporate governance 31

2.1 Stockholder-manager agency conflict . . . . . . . . . . . . . . . . . . . . . . . . . . . 322.2 Stockholder-creditor conflict . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.3 Financial reporting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.4 Are ethics important to business? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372.5 Preventing managerial entrenchment . . . . . . . . . . . . . . . . . . . . . . . . . . . 382.6 The compensation carrot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

7



8 CONTENTS

2.7 Optimal corporate governance structure . . . . . . . . . . . . . . . . . . . . . . . . . 43

3 Time value of money 45

3.1 Why is there a time value of money? . . . . . . . . . . . . . . . . . . . . . . . . . . . 463.2 Future value, simple interest, and compound interest . . . . . . . . . . . . . . . . . . 473.3 Present value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.4 Additional information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.5 Multiple cash flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513.6 Annuities and perpetuities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523.7 Growing annuities and perpetuities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583.8 Five ways to describe interest rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603.9 Three bonus examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4 Bond valuation 654.1 Bond prices and yields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664.2 Sinking fund provisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694.3 Interest and reinvestment rate risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . 704.4 The Malkiel theorems of bond price changes . . . . . . . . . . . . . . . . . . . . . . . 72

4.5 Default risk and bond contract provisions . . . . . . . . . . . . . . . . . . . . . . . . 784.6 Bond ratings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794.7 Bond markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 824.8 Term structure of interest rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 824.9 Real vs. nominal rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 844.10 Market interest rate components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87



CONTENTS 9

4.11 Bond price and duration example . . . . . . . . . . . . . . . . . . . . . . . . . . . . 894.A Financial calculators: behind the scenes . . . . . . . . . . . . . . . . . . . . . . . . . 924.B The elusive n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

4.C The more elusive i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

5 Stock valuation 1055.1 Legal issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1055.2 Common stock markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1075.3 The dividend discount model (DDM) . . . . . . . . . . . . . . . . . . . . . . . . . . 1085.4 The constant growth DDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1115.5 From DDM to expected return . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1145.6 Multiple growth rate DDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1155.7 Discounted FCF approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1155.8 Valuation by market multiple . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1165.9 Preferred stock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1185.A Preemptive right workaround . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1195.B Multi-growth rate DDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

6 Financial options 1256.1 Financial options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1256.2 Binomial option pricing model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1286.3 The Black-Scholes option pricing model . . . . . . . . . . . . . . . . . . . . . . . . . 1376.4 Put options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1416.5 Corporate finance applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142



10 CONTENTS

7 Risk and return 1457.1 Stand alone return and risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1467.2 Portfolio return and risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

7.3 Efficient portfolios and portfolio selection . . . . . . . . . . . . . . . . . . . . . . . . 1577.4 Asset pricing models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1607.5 Tests of the CAPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1637.6 Stock market equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

II Corporate valuation 169

8 Managerial accounting 1718.1 Financial reports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1728.2 Balance sheet (BS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1728.3 Income statement (IS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1788.4 Statement of cash flows (SoCF) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1838.5 Modifying accounting data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1888.6 Free cash flow (FCF) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

8.7 MVA and EVA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1948.8 Federal tax considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

9 Financial statement analysis 2039.1 Why ratio analysis? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2049.2 Liquidity ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204



CONTENTS 11

9.3 Asset management ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2059.4 Debt management ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2099.5 Profitability ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

9.6 Market value ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2139.7 Trend, common size, and percent change analysis . . . . . . . . . . . . . . . . . . . . 2149.8 The DuPont equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2169.9 Benchmarking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2189.10 Closing comments on ratio analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2199.11 Qualitative analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220

10 Financial statement forecasting 22310.1 Financial planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22410.2 Sales forecast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22610.3 Percent of sales forecasting method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22710.4 The AFN formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23810.5 Forecasting with variable balance sheet ratios . . . . . . . . . . . . . . . . . . . . . . 241

11 Cost of capital 245

11.1 The weighted average cost of capital (WACC) . . . . . . . . . . . . . . . . . . . . . . 24611.2 Cost of debt Rd(1 − τ ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24711.3 Cost of preferred stock R ps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24711.4 Cost of common equity Rs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24811.5 WACC factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25511.6 Divisional and project risk adjustments . . . . . . . . . . . . . . . . . . . . . . . . . 256



12 CONTENTS

11.7 Flotation cost adjustments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25711.8 Cost of capital estimation problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 26011.9 Common WACC estimation mistakes . . . . . . . . . . . . . . . . . . . . . . . . . . 260

11.A Example Rs estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261

12 Value based management 26312.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26312.2 Corporate valuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26412.3 The corporate valuation model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26412.4 Value-based Management (VBM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270

13 Capital structure 27713.1 Tax free world . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27813.2 A world with taxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28013.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281

III Project selection 283

14 Project selection criteria 28514.1 Project classifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28514.2 Decision rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28614.3 Implementation of capital budgeting methods . . . . . . . . . . . . . . . . . . . . . . 29514.4 Special applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29914.5 The optimal project mix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300



CONTENTS 13

14.A Another look at IRR vs. MIRR plus incremental IRR . . . . . . . . . . . . . . . . . 302

15 Estimating project cash flows 307

15.1 Who estimates cash flows? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30815.2 Relevant cash flows: incremental free cash flow . . . . . . . . . . . . . . . . . . . . . 30815.3 Tax effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31415.4 Capital budgeting project example . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31615.5 Inflation adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320

16 Equivalent annual cost 32316.1 The AEC procedure and interpretations . . . . . . . . . . . . . . . . . . . . . . . . . 324

16.2 Acme Inc. example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32516.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329

17 Project risk analysis 33117.1 Project (stand-alone) risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33117.2 Incorporating project risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33517.3 Phased decisions and risk management . . . . . . . . . . . . . . . . . . . . . . . . . . 33617.4 Real options introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337

18 Real options 34118.1 Real option valuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34118.2 Investment timing option . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34218.3 Growth option . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34618.4 Use of real options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348



14 CONTENTS

19 Change Log 349

20 Answers to embedded questions 353



List of Tables

4.1 Discount rate interpretations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674.2 Reinvestment rate risk illustration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.3 Bond price sensitivity to market yields and maturity . . . . . . . . . . . . . . . . . . 734.4 Maturity-interest rate change sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . 754.5 Coupon - interest rate sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774.6 Malkiel Theorem Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 784.7 Perspectives and signs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

5.1 DDM definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1105.2 Value vs. years of dividends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

6.1 The long and short of call and put . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

8.1 Balance sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1748.2 Income statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1798.3 Statement of cash flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

15



16 LIST OF TABLES

9.1 ROE interpretations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215

10.1 Forecasted income statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22910.2 Forecasted balance sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23410.3 AFN formula inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239

14.1 Project classifications, analysis, and rewards . . . . . . . . . . . . . . . . . . . . . . . 28614.2 Capital budgeting method matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29614.3 Capital budgeting methods used in industry . . . . . . . . . . . . . . . . . . . . . . . 298



List of Figures

1.1 U.S. Business Forms in 2008. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.1 Interest and principal over time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563.2 Sample QIR and APR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

6.1 Stock price “tree” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1296.2 Call option value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1306.3 Option replicating portfolio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

7.1 Portfolio risk vs. number of securities . . . . . . . . . . . . . . . . . . . . . . . . . . 153

17



18 LIST OF FIGURES



Part I

Fundamental concepts

19



Chapter 1

Corporate finance introduction

Overview

• What is a corporation supposed to do?

• Why would KKR/TPG borrow money and pay a 20% to 27.5% premium for TXU (February2007)? Because they expect to make money!

• How do they expect to make money on the deal?

1. Taking over management and selecting the “right” projects.

2. Choosing the lowest cost (most efficient) means of funding those projects.

3. Improving day-to-day operational efficiency

21



22 CHAPTER 1. CORPORATE FINANCE INTRODUCTION

1.1 Financial manager’s role

• The basic goal of a financial manager or managers of a firm in general is to maximize share-

holder value subject to government-imposed constraints.

QUESTION: What are some of those constraints? What are some laudableself-imposed constraints?1.1

• Inadequate oversight → leaves poor management in place → erosion of shareholder value.Examples: Enron, Worldcom, Satyam (India), current financial crisis, etc.

• Recent gains in oversight: concentrated ownership by institutional investors and regulatory

changes/enforcement.

1.1.1 Societal considerations

How maximizing shareholder value (subject to government-imposed constraints) with a long term

focus can simultaneously maximize social well being:

Benefit to consumers Maximizing profit implies reducing production costs and developing prod-

ucts that add value to consumers. Prices charged to consumers are impacted by competition.

QUESTION: How else does competition benefit consumers?1.2

Benefit to employees Shareholder value maximization is a result of a company’s ability to attract,develop, and retain quality employees.



1.1. FINANCIAL MANAGER’S ROLE 23

Other benefits High stock prices lead to (1) wealthier people (and increased spending) and (2)greater corporate investment via enhanced ability to raise capital.

1.1.2 Managerial actions to maximize shareholder wealth• Firm value is a function of current and future free cash flows (FCFs).

• FCFs are a function of revenues, costs, required new investments.

• The current value of future FCFs related to size, timing, and risk (discount rate) of those FCFs.

QUESTION: Is it clear what managerial actions should accomplish?1.3

• Regarding FCFs, managers can act to

1. Increase sales: develop products people want (an ongoing endeavor).

2. Reduce production costs: be mindful that cheap labor and materials may produce poorquality products or products that consumers do not want.

3. Minimize reinvestment costs: reduce capital requirements (e.g., use just-in-time inventory

management).• An overview of all the considerations of a financial manager):

1. Financing decisions: debt vs. equity, what kind of debt and equity, which project?

2. Reinvestment decision: reinvest earnings, pay dividends, or repurchase stock?




1.1.3 Market vs. intrinsic value

• The intrinsic or fundamental value is based on investor’s estimate of cash flows.

• The market value is the aggregation of cash flow estimates from all investors.

QUESTION: Should financial managers maximize market or intrinsic value?1.4

• Equilibrium is attained when market value equals true fundamental value.

QUESTION: Who knows the true fundamental value?1.5

1.1.4 Short-term vs. long-term price

• The current stock price reflects all [publicly and some privately] available information (short-term price).

QUESTION: Should financial managers maximize short term or long term stockprice?1.6

• Some private information at time t does not become publicly available until time t + n (long-term price).

QUESTION: What types of information take time before public revelation?1.7



1.2. CASH FLOWS 25

1.2 Cash flows

• Financial manager should make decisions to maximize cash flows to shareholders. Thesedecisions should balancing dividend payments, stock repurchases, and reinvestment in thefirm.

• Three board decision categories

1. Capital budgeting

2. Financing

3. Working capital management

• These are the same decisions and analysis KKR and TPG should have done as part of theTXU leveraged buyout.

• Bankruptcy occurs if expenses persistently exceed income.

1.3 Three fundamental decisions




Captial Budgeting Decisions Project selection {includes estimates of future cash flows}, patentsto purchase, machines to purchase, anything that will generate, or contribute in the generationof, cash flows.

Financing Decisions How do you pay for the assets you decided to buy?

Debt Obtain loans or issue bonds

Equity Issue stock or use cash

Capital Structure The mix of debt and equity at a point in time.

Working Capital Decisions The management of working capital including the collection of salesrevenues, repayment of debt, inventory management, etc.

QUESTION: What is the definition of working capital?1.8

1.4 Legal business forms

1.4.1 Sole proprietorship• Owned by one person (hence use of the word “sole”)

• Easy to start

• Unlimited liability exposure



1.4. LEGAL BUSINESS FORMS 27

• Income taxed at normal income tax rate

• Difficult to sell “the business” since there are no shares of stock → must sell off assets

1.4.2 Partnership

• Like a proprietorship but with two or more owners joined together legally

• Legal agreement includes initial investments, management roles and decisions, profit distribu-tion, sale of business, actions after death of partner, etc.

• General Partnership: Everyone has unlimited liability

• Limited Partnership: General partners have unlimited liability.

QUESTION: What kind of liability do limited partners have?1.9

1.4.3 Corporations

• Entity distinct from its owners (stockholders)

• Limited liability for owners: If you were a stockholder of Exxon during the Valdez accident,you could not be sued but could your investment if “Exxon” were sued and lost and wentbankrupt




• Can be publicly held (shares traded on public markets such as NYSE and NASDAQ) orclosely held (smaller number of investors and not publicly traded).

QUESTION: What are some advantages and disadvantages of having a businessin the form of a corporation as opposed to a sole proprietorship?1.10

1.4.4 Hybrid forms

• We are not talking about fuel efficient cars

• LLPs/LLCs have two advantages

– Limited Liability for Partners: If one partner commits malpractice the whole firm is nottaken down.

– Single-taxation.

QUESTION: Can anyone distinguish between single taxation for partnerships and

double taxation for corporations?1.11

Figure 1.1 illustrates that the majority of businesses in the United States are sole proprietorshipswhile most of the income is attributed to corporations.

1 4 LEGAL BUSINESS FORMS 29



1.4. LEGAL BUSINESS FORMS 29

!"#$ &'"(')$*"'+,)(

-./

&0'*1$'+,)(

23/

4"'("'05"1

26/

!"#$%& () *"+,-%++%+!"#$ &'"(')$*"'+,)(

-./

&0'*1$'+,)(23/

4"'("'05"1.6/

!"# %&'()"

Figure 1.1: U.S. Business Forms in 2008.

Source: Table 744, U.S. Census Bureau, Statistical Abstract of the United States: 2012

30 CHAPTER 1 CORPORATE FINANCE INTRODUCTION




1.5 Typical corporation organization

• Lets take a look at a typical org chart...

External Auditor Are the financial statements a fair representation of the firm’s financial position?

QUESTION: Did Arthur Andersen do a good job of this when they were externalauditor for Enron back in the day?1.12

Audit committee A group of board members who oversee the accounting of a firmCompliance and Ethics Director

• Reports to the board’s audit committee to “ensure independence.”

QUESTION: Why might one be skeptical of true independence?1.13

• This position is distinct from the “Internal Auditor.”

QUESTION: How so?1.14



Chapter 2

Corporate governance

Overview

In this chapter we look at some of the issues surrounding corporate governance including

• agency conflicts,

• ethics,

• managerial entrenchment, and

• compensation.

31

32 CHAPTER 2 CORPORATE GOVERNANCE



32 CHAPTER 2. CORPORATE GOVERNANCE

2.1 Stockholder-manager agency conflict

• The principal (owner, stockholder) hires the agent (management) to manage (control) firmsuch that principal’s interests are taken care of, that is, stock price maximization.

• Agency conflict sources:

1. Since agent (manager) does not own 100% of the firm, manager will receive less than100% of the profits → might put in less than 100% effort

2. Agent will bear less than 100% of expenses also → agent can use 100% of the private jetbut using the principal’s money to buy the jet!

3. Ownership is disperse (many shareholders) so it is difficult to get together and disciplineor remove poor management

• Studies suggest that in practice managers are concerned with firm size maximization (Wild-smith, 1974) → more job security (harder to takeover), more compensation, more ego

• Stockholders incur agency costs in order to reduce the agency conflict.

• Two extremes for dealing with agency conflict:

1. Compensate solely on long-run stock performance → near-zero agency costs

– Good: could minimize falsified accounting statements.


2 1 STOCKHOLDER MANAGER AGENCY CONFLICT 33



2.1. STOCKHOLDER-MANAGER AGENCY CONFLICT 33

– Bad: (1) economic events beyond manager’s control could impact stock price; (2)managers need income during the time it takes from good decision to market priceincrease

2. Monitory every managerial action (high agency costs)– Costly (time, money, and inefficient)

– If shareholders have that kind of time they should manage the firm themselves.

• “Optimum” solution is somewhere between the extremes however...

• Tools to align principal (stockholder) and agent (management) interests:

1. Compensation tied to firm performance.

QUESTION: What are some problems with this?2.2

2. Managerial labor market.

Theory: If you do well, other firms will want to pay you big bucks. If you do poorly, noone will want to hire you.

Practice: Poor performance does not appear to stop those who have connections andthe compensation of poor performers comes at the expense of others.

3. Board of directors.

Theory: Hire the best managers, monitor, set compensation fairly, etc. so that share-holder value is maximized.

34 CHAPTER 2 CORPORATE GOVERNANCE




Practice: Hire buddy and pay him as much as possible.

4. Other managers.

Theory: Competition within firm for CEO position will keep everyone on their toes.Practice: Cut-throat and “clique-ish” environment where everyone is pursuing self-interest

which, at times, is at the expense of the firm (and firm’s owners).

5. Large stockholders.

Theory: Have enough “skin in the game” to take the time and attend board meetings andpushing through meaningful management changes to maximize shareholder wealth.

Practice: (1) Maybe large stockholder wants another company they own to acquire thetarget on the cheap. (2) Maybe large stockholder knows nothing about the particularbusiness and will mess it up.

6. The takeover market.

Theory: Management makes bad decisions → stock price drops → firm is taken over →management is fired. Knowing this progression, management gets their act togetherto maximize stock price and save their jobs.

Practice: (1) Sometimes management blocks shareholder wealth-enhancing acquisitionsto hold on to their jobs such as the Microsoft attempted takeover of Yahoo (2)Sometimes management allows acquisitions that reduce shareholder value

7. Legal environment. Can we really legalize Morality?

2.2. STOCKHOLDER-CREDITOR CONFLICT 35



2.2. STOCKHOLDER CREDITOR CONFLICT 35

2.2 Stockholder-creditor conflict

• Creditors lend at a rate based on perceived risk at the time of the loan.

• Stockholders want firms to take risky projects since they will benefit if the projects succeed.Thus, firms could take money from creditors (banks) and invest in risky projects or repurchasesstock (which increases leverage and bankruptcy risk but can enhance gains).

• If creditors sense firms will do a “bait and switch” with borrowed money, they (creditors) willcharger higher rates or impose constraints on how the debt is used.

QUESTION: How well has our government done this with bailout funds?2.3

2.3 Financial reporting

• Market transparency: reliable and accurate information available to all.

• Securities Act of 1933 - Requires companies to register with the SEC

• Securities Exchange Act of 1934 - extends disclosure requirements• 1933 and 1934 Acts include safeguards to ensure transparency (and consequently, efficiency) :

1. Publicly-owned firms (POFs) are supposed to follow GAAP.

2. POFs must have financial statements examined by independent auditors.




3. Accounting industry’s “Public Oversight Board” is supposed to set policy and disciplinethose who do not follow it.

4. POFs must submit financial statements to SEC then SEC makes statements freely avail-

able.5. POFs must release information to all investors simultaneously.

6. Analysts are supposed to form objective opinions based on available information and makehonest recommendations.

7. Violators are supposed to be prosecuted expeditiously with sufficient penalties.

• Late 1990s, early 2000s

→ these safeguards were not in place and/or insufficient (Enron)

Sarbanes-Oxley Act of 2002 (SOX)

• Auditors were complicit because they were not independent.

QUESTION: Why not?2.4

• Analyst recommendations were at times dishonest and not necessarily independent.


• Penalties for these violations were too weak to prevent their recurrence.

2.4. ARE ETHICS IMPORTANT TO BUSINESS? 37



• SOX regulation designed to reduce/eliminate these violations by ensuring that

1. auditors are sufficiently independent,

2. key executive (e.g., CEO) personally certifies completeness and accuracy of financialstatements,

3. audit committee is relatively independent of management,

4. analysts are relatively independent of POFs they analyze, and

5. Companies release all important information publicly and promptly.

2.4 Are ethics important to business?

• Ethics: what is right and what is wrong (set of moral principals)

• Some corporate finance textbooks reference the Golden Rule in the Bible: do unto others asyou wish others to do unto you.

• The capitalist mantra “pursue self-interest” appears to be at odds with considering the impactof your actions on others.

• Read about the “triple bottom line” on Wikipedia (people, planet, profit)

• For historical context, read “Religion, Discipline, and the Economy in Calvin’s Geneva.”




• Is business like poker where you deceive to make a profit? As a result of the accounting scandalspreviously mentioned, $2.3T in stockholder value was lost.

• It is difficult to attract capital in the presence of corruption and investment is needed for

economic growth.

• Agency costs and conflicts of interest are two types of ethical issues in business (see earlierexamples).

• Another is information asymmetry: do you tell someone interested in your used car thefull story?

• Since the legal systems and market forces have proven insufficient mechanisms to ensure ethicalbusiness, the book suggests establishing an ethical business culture.

• This culture is set at the top of the organization. Contrast Enron’s management with Google’s.

QUESTION: Upon graduation would you choose a $50,000 salary at a companywith some obvious ethical problems or $45,000 at a company with solid ethics?2.6

• Ethical failings have serious consequences: in the past you would get a slap on the wrist now

you will go to jail for decades.

2.5 Preventing managerial entrenchment

• A manager is entrenched when conditions exist that impede the ability to remove that manager.

2.5. PREVENTING MANAGERIAL ENTRENCHMENT 39



• Consequences include excess non-pecuniary benefits, empire-building, and reluctance to cancelunderperforming divisions or projects.

2.5.1 Barriers to hostile takeovers

• Microsoft attempted to takeover in Q1 2008 → Yahoo management rejected MSFT’s $33/shareoffer → Yahoo management entrenched and concerned about their egos → stock closed at 12.50on 2008.11.07 after MSFT rejected the begging of Yahoo’s CEO for MSFT to make anotheroffer.

QUESTION: So what is the barrier here?2.7

• Target share repurchases (greenmail): Allows poorly performing firm to repurchase stock fromraider at an elevated price in exchange for agreement to cease takeover attempts for a specifiednumber of years.

• Poison pill (shareholder rights provision): Enables existing shareholders to purchase additionalshares at a bargain price if an acquisition attempt is detected (e.g., once a raider acquires 20%of the firm)

• Restricted voting rights: if you own more than X % of the stock, your voting rights are restrictedto Y % where Y < X . For example, you could own 50% of the firm but only have voting rightsas if you owned 25%.




2.5.2 Monitoring by board members

• Insider: board member who also holds management position within the firm

• Outsider: does not have a management position within the firm• Problems (the “good ’ol boy network”)

1. If the CEO is also chairman of the board disagreement will get you kicked off the boardand/or fired.

2. Outsider is not necessarily independent.


3. Combined effect: entrenched CEO

• The [alleged] improvements in board structure

– Stock and options instead of cash compensation for board members

– More independent outsiders

• Additional entrenchment mechanisms

– Non-cumulative voting plus 51% ownership: you own the board.

QUESTION: What is the difference between cumulative and non-cumulativevoting?2.9

2.6. THE COMPENSATION CARROT 41



– staggered terms: fewer board seats up for election each year

QUESTION: What has caused boards to be more effective in recent times?2.10

2.6 The compensation carrot

• Average package breakdown: 21% salary, 79% “performance-based” bonuses.

QUESTION: Why do I question “performance-based?” 2.11

• Bonus breakdown: 34% short term goals (e.g., current year EPS growth), 20% long term goals,46% stock price

• Can be cash, stock, options, non-pecuniary. May not vest immediately

QUESTION: What does “vesting” mean?2.12

2.6.1 Stock options

• Theory: if executives own options, their interests are in alignment with shareholder interests

• Reality: not so. An important example...

• Additional problems




– Falsified financial statements

– Options are not worth the Black-Scholes value to the recipients even though the companyexpenses them using that value.

QUESTION: Why?2.13

2.6.2 Employee stock ownership plans

• ESOP formation process

1. Issue 500,000 shares @ $100 per share (50M).

2. Form legal entity (ESOP) to purchase newly issued shares with a loan guaranteed (andpaid indirectly) by the parent company (thus, an off-balance sheet liability since debtappears on the books of the ESOP not the parent company).

3. Parent company makes payments to the ESOP sufficient to cover loan payments.

4. Equity builds as the loan is paid off, and this equity is associated with the ESOP partic-ipants (employees).

5. Employees receive pro rata amount of parent company stock at retirement.

• Reasons for ESOPs

1. Motivate employees to be more productive thereby improving shareholder value.

2. More money at retirement.

2.7. OPTIMAL CORPORATE GOVERNANCE STRUCTURE 43



3. Employee retention.

4. Tax benefit for borrower (ultimately the parent company) and lender if ESOP owns ≥ 50%of parent company stock. Dividend payments to ESOP for distribution to participants

or loan repayment are tax deductible by the parent company.5. Makes labor cutbacks as a result of acquisition more difficult (benefits employees, not

shareholders).

QUESTION: What does this sound like?2.14

• In sum, ESOPs can be used to boost employee motivation, retention, and retirement incomebut can also be used to entrench management (i.e., make takeover less attractive)

QUESTION: Are ESOPs more prevalent with privately held companies? Why orwhy not?2.15

2.7 Optimal corporate governance structure

Okay, so we have seen different types of sticks, carrots, monitoring, and take-over prevention mech-

anisms.

QUESTION: What is the optimum mix?2.16




Chapter 3

Time value of money

Overview

• Assume you have plenty of money and are considering the purchase of a new $36,000 car. Yougo to the dealer and are given 2 options:

Option 1: Pay cash and receive a $3,321 discount → sale price = $32,679

Option 2: Finance the car for 3 years @ 0% but pay full price = $36,000

QUESTION: Which option do you choose? What if CD rates were 3%? 7%?3.1

• Understanding this chapter is “critical for your understanding of corporate finance” ( Parrinoand Kidwell, 2010). I would argue this applies to personal finance also.

45

46 CHAPTER 3. TIME VALUE OF MONEY



• Value Creation: From a corporation’s perspective, buying productive assets today at cost $Xwith hopes (belief) future cash flows will be $X.

3.1 Why is there a time value of money?• Simple example (that is similar to our car example): winning the lottery:

Option 1: Receive $60 million today.

Option 2: Receive $100 million spread out evenly over 26 years ($3,846,154 per year)

• Thus we say the “time value of money,” or the market price of 26 annual payments of $3,846,154

is $60,000,000

QUESTION: Why is the lump-sum payment so much less than $100,000,000?3.2

• Since humans are impatient (and risk averse) they must be compensated for deferring con-sumption (and taking risk).

• Problem Solving tool : Time lines...

• Future vs. Present Value:

Future Value is found by compounding cash flows.

Present Value is found by discounting cash flows.

3.2. FUTURE VALUE, SIMPLE INTEREST, AND COMPOUND INTEREST 47



• Use of Financial Calculator: You will need to use a financial calculator to solve problems in theremainder of this course (and when you are sitting at the car dealer or the real estate broker’sdesk).

3.2 Future value, simple interest, and compound interest

• One, two, and n-period calculation

F V 1 = P 0 + (P 0 × i) = P 0 (1 + i) = P V (1 + i) (3.1)

F V 2 = F V 1(1 + i) = (P 0 (1 + i)) (1 + i) = P V (1 + i)2 (3.2)

F V n

= P 0 (1 + i)n = P V (1 + i)n (3.3)

• Simple vs. Compound Interest

Simple: interest gained on principal investment

Compound: interest gained on prior earned interest

• Compound interest in a powerful phenomenon from both a good and bad perspective. Froma good perspective, you will gain interest on top of interest (i.e., on money in excess of whatyou invested).

QUESTION: How can compound interest be a bad thing?3.3

• Another example of the power of compound interest: The Rule of 72...




• Lets work through a few FV, simple interest, and compound interest calculations...

QUESTION: How long will it take for a $100 investment to double @8%?3.4

• Thus far we have discussed annual compounding. What if compounding is quarterly, monthly,daily, or continuous? A simple modification to the FV formula:

F V n = P V

1 +

i

m

m×n

(3.4)

Where n is number of years and m is the number of times per year that interest is compounded.

QUESTION: What is m for semi-annual, quarterly, monthly, and dailycompounding? What about continuous compounding?3.5

• Lets take a look at compounding bank deposit rates and compounding frequency...

• More frequent compounding → more compound interest

3.3 Present value

• Present value = today’s value of a future cash flow.

• Future values are discounted to account for (1) delayed consumption and (2) risk.

3.3. PRESENT VALUE 49



• The discount rate is the rate used to arrive at the present value of future cash flows.

• n-period calculation:

P V = F V n(1 + i)n (3.5)

QUESTION: Look familiar?3.6

• Let’s look at how time n, interest rates i, and future value F V impact the present value P V ...

• Important note when doing PV/FV calculations on your financial calculator: PV is a negativenumber and FV is a positive number.

QUESTION: Why?3.7

• One more discounting example: Lottery payoff options. You have access to a 10% CD if youhave the minimum $1M investment. Fortunately, you won the lottery and have been presentedthe following choices:

Take money today PV=$1,000,000

2 years from now receive F V 2 = $1, 200, 0005 years from now receive F V 5 = $1, 500, 000

8 years from now receive F V 8 = $2, 000, 000

QUESTION: Which option do you choose and why?3.8




3.4 Additional information

• Finding the interest rate. As I write these notes I cannot help but think most students wouldtake the $1,000,000 today without doing a simple calculation. However, there must be some

amount you would be willing to wait for.

QUESTION: What is that amount and what interest rate is associated with thatamount?3.9

• Another example: You want to purchase a $50,000 car, do not have the money now, and areexpecting a bonus in a couple years (or expecting to somehow save with the same mindset usedto buy a car you do not have cash for). You violate a second rule and ask a family member

to loan the down payment of $20,000 and have agreed to pay that family member $28,800 intwo years to settle the debt.

QUESTION: Is that a good deal for the borrower? the lender?3.10

• Money is not the only thing subject to compounding. In the book “Richest Man in Babylon”(I think), the author refers to money as your children and how your children have children andso on.

• Thus, population is something else that compounds.

• Simply use population for PV/FV and call the compound growth rate g

F V n = P V (1 + g)n (3.6)

3.5. MULTIPLE CASH FLOWS 51



• Other examples include sales, GDP, commodities prices, etc.

• An example: U.S. Population in 1970 was 203,211,926. Somehow Wikipedia has 2010 censusdata and puts the number at 309,162,581.

QUESTION: What was the U.S. population growth rate CAGR from 1970 to 2010?3.11

• The computation of sales CAGR is a preliminary step in forecasting financial statements.

QUESTION: Why would you want to forecast financial statements?3.12

• Lets compute Apple’s sales CAGR...

3.5 Multiple cash flows

Example 3.1. Future Value. Simple example: put $1,000 in savings account today, then another$1,000 in your account next year. What is the value (total) of the account in two years if the interestrate is 3%?

QUESTION: What is the first step to solving this problem?3.13

Example 3.2. Future Value. You deposit $3,000 today, $4,000 next year, and $5,000 two yearsfrom now. What is the value in year 3 if the interest rate = 8%?

• Present Value. You have a friend that wants to borrow $3,000 from you today and pay youback $1,000 per year for 3 years.




QUESTION: What are two reasons to reject the loan?3.14

Example 3.3. Lets say your friend does go to a bank and rates for 3 year loans are 7%. We canexamine this problem from two angles: (1) if your friend does not need $3,000, how much will banklend today such that repayment is $1,000 per year for 3 years such that the bank earns 7%? (2)Your friend needs $3,000 today so how much must he/she repay each year for the next 3 years toensure the bank earns 7%? Let’s take a look...

• Cash flows in the previous example were the same in each year, so you could use the N, I,PMT, FV, PV buttons to arrive at the answers.

• You cannot do so when the cash flows are uneven. Rather, you can use the CF 0, C F i, I , N P V buttons. I will redo Ex. 2 using these buttons...

Example 3.4. You go to a car dealer to purchase a car. You can finance $35,000 for 5 years @ 9%or 4 years @ 7%.

QUESTION: Which do you choose and why?3.15

3.6 Annuities and perpetuities

• Both annuities and perpetuities have level cash flows

• Annuities have a finite number of previous while perpetuities are infinite

3.6. ANNUITIES AND PERPETUITIES 53



• The present value of an annuity (PVA) (or perpetuity) is the present value (PV) of all futurecash flows.

P V An = CF 11 + i

+ CF 2(1 + i)2 + · · · + CF n

(1 + i)n

=n

t=1

CF t

(1 + i)t (3.7)

Moreover, we knowCF 1 = C F 2 = · · · = C F n ≡ CF

therefore

P V An = C F

1

1 + i +

1

(1 + i)2 + · · · + 1

(1 + i)n

. (3.8)

This equation simplifies to

P V An = CF

i ×

1 − 1

(1 + i)n

(3.9)

where C F is the cash flow received at the end of the first period.

Example 3.5. How much should you pay (i.e., the maximum you would pay) for an 8% annuitywith 3,500 annual payments for 4 years?

QUESTION: How would you begin this problem?3.16




• You can also find the interest rate of an annuity given (1) the length of the annuity, (2) thesize of the cash flow, and (3) the price of the annuity.

QUESTION: What is the interest rate of 3-year 2,000 per year annuity selling for

5,154.19?3.17

• Perpetuities pay periodic cash flows forever. Recall equation 3.9:

P V An = CF

i ×

1 − 1

(1 + i)n

(3.10)

To determine the value of a perpetuity, take the limit as n approaches ∞

P V A∞ = limn→∞

CF

i ×

1 − 1

(1 + i)n

=

CF

i (1 − 0) =

CF

i (3.11)

• Thus far we have covered ordinary annuities, annuities with cash payments that occur at theend of each period. With an annuity due cash payments occur at the beginning of each period.The simplest way to compute the value of an annuity due is (1) ignore the fact that paymentsare at the beginning and calculate the ordinary annuity value; (2) multiply the ordinary annuity

value by (1+i):

Annuity due value = Ordinary annuity value × (1 + i) (3.12)

Example 3.6. Redo the previous example for an annuity due.




• Monthly Payments. When purchasing a car or home you are typically presented with anannual rate and monthly payments. To ensure you are not being cheated, use this informationto calculate the monthly payments yourself.

Example 3.7. You are about to purchase a new car for $30,000 and have obtained 1.9% annualfinancing for 5 years. What will your monthly payment be?

QUESTION: To begin, what values do you put into N and I? 3.18

• The dealer offers to lower your repayment to 400 by increasing the length of the loan from 60to 111 months.

QUESTION: Do you take the deal?3.19

• Amortization Schedule. By the way, you want an amortizing loan, that is, a loan in whichthe principal balance is reduced with each payment. Please be sure you see “amortized” beforeyou sign. With amortized loans, you pay more principle and less interest with each successivepayment:




Figure 3.1: Interest and principal over time

• Let’s create an amortization schedule for a $50,000 30 year mortgage financed @ 5.25%. inparticular, we want to compare the interest and principal payments at the end of years 1, 12,and 29...

QUESTION: By the way, what is the monthly payment for this mortgage? 3.20

Okay, now on to the amortization schedule


F V l f A i P h h hl i l i l



• Future Value of an Annuity. Perhaps you have a monthly savings plan, or retirement planthat has fixed payments (contributions to the plan) and you receive a lump sum at the end.(Also has fixed interest rate). This is nothing more than an annuity and you can calculate thefuture value different ways.

1. Compute FV of each cash flow then add

2. Compute P V An then multiply by (1 + i)n

QUESTION: Which do you think is easier?3.21

• Now for the formula:

F V An = P V An × (1 + i)n

= CF

i

1 − 1

(1 + i)n

× (1 + i)n

= CF

i ((1 + i)n − 1) (3.13)

Note: This is similar to what we did with Ex 2.

QUESTION: What is the FVA for a perpetuity?3.22

Example 3.8. Suppose you are saving for a retirement and purchase an annuity (which I cannotrecommend). You are going to retire in 15 years, will save $1,000 per month, and see that the goingrate for 15 year annuities is 4%. How much will you have in 15 years?


R i d Vi i /V l i f d t k t it O S t b 24 2008 W



• Rewind: Viewing/Valuing preferred stock as a perpetuity. On September 24, 2008 WarrenBuffet’s company purchased $5B of perpetual preferred shares of Goldman Sachs that pay a10% dividend.

QUESTION: What is the annual cash flow? Was this a good idea?3.23

3.7 Growing annuities and perpetuities

• Think back to the XYZ example at the beginning of the chapter

• Company X=Starbucks, Company Y=Low Point Coffee, Z=how much should Starbucks payfor Low Point Coffee

Example 3.9. Suppose Low Point’s after-tax cash flows are 100,000 per year, there is a 50-yearlease already in place so we assume the coffee shop will be in business for 50 years, and cash flowswill grow each year at the estimated inflation rate of 3%.

QUESTION: How much should Starbucks pay for Low Point when using a discountrate of 15%?3.24

We begin by modifying the PVA formula to include growing payments:

P V An = CF 1i − g

×

1 −

1 + g

1 + i

n (3.14)

where C F is the cash flow at the end of the first period. By the way, i must be larger than g (i > g).

3.7. GROWING ANNUITIES AND PERPETUITIES 59

QUESTION: Why?3 25



QUESTION: Why?3.25

Now, on to the estimated coffee shop value...

• Several notes:

1. The discount rate, in this case 15%, is reflective of the riskiness associated with futurecash flows.

2. The growth rate, in this case 3%, is constant.

3. Unfortunately, there is not a button to enter the growth rate on the HP12C. However,you can search for “HP 12C growing annuity” on the Internet and find steps to do so.

• The last example (Ex 9) was a growing annuity, now we look at growing perpetuities:

P V A∞ = CF 1i − g

(3.15)

where C F is the cash flow at the end of the first period.

Example 3.10. Suppose the Low Point Coffee Shop to be acquired by Starbucks is anticipated

to be in business forever (you can obtain an indefinite lease just like the United States did withGuantanamo Bay).

QUESTION: Now what should Starbucks pay for an infinitely-lived Low Point CoffeeShop?3.26


3 8 Five ways to describe interest rates



3.8 Five ways to describe interest rates

1. Quoted Interest Rate (QIR): The simple annual interest rate obtained by multiplying thenumber of compounding periods by the per-period rate. E.g., 1% per month represents a QI R

of 12%. This rate does not include fees such as closing costs nor does it include compoundingeffects.

2. Annual Percentage Rate (AP R): In Parrino and Kidwell (2010) this is the same as QI R. Inthe real world this will include fees. AP R is typically associated with loans.

3. Nominal AP R: Not mentioned in Parrino and Kidwell (2010) but is the same as QI R.

4. Effective Annual Interest Rate or Effective AP R (EAR): In Parrino and Kidwell (2010) this

is the annualized rate that includes compounding effects but not fees:

EAR =

1 +

QI R

m

m

− 1 (3.16)

In the real world, EAR includes fees and compounding effects.

5. Annual Percentage Yield (AP Y ): Not mentioned in Parrino and Kidwell (2010). The annual-ized interest rate that does take into account the effects of compounding.

AP Y =

1 + i

m

m

− 1 (3.17)

where i = QI R or nominal AP R. AP Y is typically associated with deposit instruments (CDs,deposit accounts, etc.).

3.9. THREE BONUS EXAMPLES 61

• Two paths to the same summit



• Two paths to the same summit

Path 1: Compute E AR, then use annual F V formula (3.3)

Path 2: Forget about E AR and use modified F V formula (3.4)

3.9 Three bonus examples

Bonus 1: Your business is in need of $100,000 loan to expand operations and have received quotesfrom three different lenders as follows:

Lender Interest rate (QIR) Compounding

A 10.40% monthlyB 10.90% annuallyC 10.50% quarterly

QUESTION: Which lender do you choose and why?3.27

Bonus 2: Compute the future value of a $100 investment in a five year savings bond that pays 10%interest compounded monthly using two approaches. First, compute EAR then use the simple

FV formula. Then try using the modified FV formula.

Bonus 3: You are purchasing a $100,000 home and have the 20% down payment. You are goingto finance the remaining $80,000 with a 30 year fixed rate home loan. You take a look atBankrate.com and see quotes from several lenders:


30 yr fixed mtg, 0 Points - Sorted by APR



30 yr fixed mtg, 0 Points Sorted by APR

Lender APR Rate Costs and fees Comments

4.438%

Fri Sep 17

4.375%at 0.000 pts

30 day ratelock

Fees in APR:$595Est payment:$399

TENNESSEE ISOUR HOME

STATE Contact Us

4.444%Fri Sep 17

4.375%at 0.000 pts30 day ratelock

Fees in APR:$647Est payment:$399

Getting you thehome loan that'sright for you is our business.

Contact Us

4.464%Fri Sep 17

4.250%at 0.000 pts30 day ratelock

Fees in APR:$1,995Est payment:$394

Apply & Lock Rate24/7! View OnlineGFE Contact Us

Figure 3.2: Sample QIR and APR

QUESTION: Calculate the fees associated with each option. Which lender do youchoose and why?3.28

To get you started, I will calculate the fees associated with EverBank.

1. Compute the monthly payment of a $80,000 loan using the APR. This payment is the amount

3.9. THREE BONUS EXAMPLES 63

of the check you will send to the lender.



of the check you will send to the lender.

P V = −80, 000

N = 30 × 12

I = 4.444/12F V = 0

P MT ⇒ 402.69

2. Given that monthly payment and QI R compute the present value of the loan.

N = 30 × 12

I = 4.375/12

F V = 0

P M T = 402.69

P V ⇒ −80, 653.43

Therefore you are being charged $653.43 in fees with this loan (close to the $647 estimate quotedon Bankrate.com). Thus, an $80,000 loan at the AP R of 4.444% is the same as an $80,653.43 loanat the quoted interest rate of 4.375%. After you sign the closing papers you will have an $80,653.43

loan if you do not pay the $653.43 fees at closing. Now your turn to repeat the calculations for theother lenders.

In Step #1 the fees are included (embedded) in the APR. In Step #2 the fees are explicitlyincluded in the loan amount. In both cases fees are accounted for just once. It would be incorrectto use the higher APR and the higher loan amount simultaneously.




Chapter 4

Bond valuation

Overview

• Review bond price and yield calculations (including callable and non-callable bonds)

• Interest rate and reinvestment risk

• Changes in bond prices

• Default risk and bond contract provisions

• Bond ratings (including a brief discussion of junk bonds and bankruptcy)

• Bond markets

65

66 CHAPTER 4. BOND VALUATION

Before I begin,



QUESTION: Who issues bonds and why?4.1

4.1 Bond prices and yields

4.1.1 Non-callable bonds

• Value of any financial asset = present value of all future cash flows discounted at rate appro-priate for asset

P =n

t=1

P M T (1 + Rd)t

+ F V (1 + Rd)n

(4.1)

where Rd is the market yield (a.k.a., discount rate, yield to maturity or YTM) and P MT isthe coupon payment.

• The summation can be replaced with the formula for the present value of an annuity:

P = P MT

Rd

1 − 1

(1 + Rd)n

+

F V

(1 + Rd)n (4.2)

• Coupon rate-discount rate relationship:

4.1. BOND PRICES AND YIELDS 67

Table 4.1: Discount rate interpretations



Table 4.1: Discount rate interpretationsRate Meaning

Rd < Rcoupon bond will sell at a premium

Rd = Rcoupon bond will sell at par value

Rd > Rcoupon bond will sell at a discount

• If payments are semi-annual, substitute 2n for n, P M T /2 for P MT , and Rd/2 for Rd.

Example 4.1. Consider a bond with the following characteristics:

– AAA rated corporate bond

– 10% annual coupon rate

– 3 years until maturity

– semi-annual coupon payments

– face value of $1,000

– current price of $1,052.42

QUESTION: Why is the current price greater than $1,000?4.2

QUESTION: What is the yield to maturity?4.3


QUESTION: What would the bond’s price be if the yield to maturity were% 4 4



12%?4.4

• Current yield

– The ratio of a bond’s annual coupon divided by current market price:

CY = annual coupon

current market price =

10% × $1, 000

$1, 052.42 = 9.5% (4.3)

– Better than quoting just the coupon rate because you will have to incur a cost to receive

the coupon.

– Does not include PV of future redemption at par value.

4.1.2 Callable bonds

• Corporate bonds may be callable, typically after some deferred call period

QUESTION: Why might a corporation call in a bond?4.5

QUESTION: What does this tell you about the yield on callable bond vs. anotherwise identical non-callable bond?4.6

4.2. SINKING FUND PROVISIONS 69

• The yield to call measure can be extracted from:



P =

f c

t=1

P MT

(1 + Y T C )t +

CP

(1 + Y T C )f c (4.4)

where

P = current price of bond

f c = number of periods until first call date

Y T C = yield to call

P MT = coupon payment

CP = call price to be paid by issuer

4.2 Sinking fund provisions

• A sinking fund is money set aside to ensure repayment of face value at maturity.

• The sinking fund can also be used to repurchase a portion of the existing bonds periodicallyat a specified price. The repurchase price is typically lower than that of a callable bond.

• In contrast to callable bonds where the entire issue can be repurchased, there is a limit to theamount that can be repurchased under sinking fund provisions.

• Required funds level can be obtained a few ways


1. Cash



2. Call in a small percentage of bonds (specific bonds chosen randomly) at a specific price

3. Purchase bonds on the open market

• When bonds with sinking fund provisions are called in, the amount of required funds will dropproportionally.

QUESTION: Why?4.7

• In short, a sinking fund provision is both good and bad for the investor.

– Good: The presence of a sinking fund lowers default risk.– Bad: The realized yield will decline as repurchases are made.

4.3 Interest and reinvestment rate risk

• Interest rate risk

– Definition: Risk of bond price decrease due to an interest rate increase.– A bond price increase due to an interest rate decrease is not considered risk. This subtle

point has significance later in our discussion.

• Reinvestment risk

4.3. INTEREST AND REINVESTMENT RATE RISK 71

– Definition: The risk that future reinvestment rates will be less than the YTM at the timeb d h d



bond was purchased.

– YTM calculations assume coupon payments (interest payments) are reinvested at theYTM rate and gain interest again. Since interest rates are not constant one can not

reasonably expect all future reinvestment of coupon payments to be at the YTM.

Table 4.2 emphasizes the impact of the assumed reinvestment rate risk:

Table 4.2: Reinvestment rate risk illustrationIncome for a 10% annual coupon 20 year bond purchased at face value and held until maturity.

Coupon income Reinvestment rate Reinvestment income Total income

2000 8% 2576.20 5576.202000 10% 3727.50 6727.502000 12% 5205 8205

Note the large percentage of total dollar return attributable to reinvestment.

QUESTION: Anyone familiar with duration matching?4.8

• A couple yield measures that incorporate time-varying market rates:

Realized compound yield One of the assumptions in the YTM calculation was reinvest-ment of coupon payments at the YTM rate. An after-the-fact measure, called realized com-


pound yield can be calculated to assess the actual yield realized:



RCY =

total ending wealth

purchase price of bond

1/n

− 1.0 (4.5)

Horizon (or total) return An ex-ante estimate of total return based on explicit reinvest-ment rate assumptions.

4.4 The Malkiel theorems of bond price changes

• Ultimately, bonds will be worth their face value as the maturity date approaches

• Before the maturity date however, interest rates and bond prices do change.

• Burton Malkiel (1962) derived five bond price and yield theorems.

• Here I present three. Table 4.3 shall be used to illustrate the following theorems and corollaries.

4.4.1 Theorem 1: Bond price - interest rate relationshipTheorem Bond prices move inversely to interest rates. This is evident by equation (4.1). Inequation form:

∂P

∂r < 0 (4.6)

4.4. THE MALKIEL THEOREMS OF BOND PRICE CHANGES 73

Table 4.3: Bond price sensitivity to market yields and maturityB d f $ f l % b d



Bond prices for a $1,000 face value 10% coupon bond.Market yield

TTM 8% 10% 12%

5 years 1,081 1,000 92615 years 1,173 1,000 86230 years 1,226 1,000 838

where r is the market yield (or Y T M ).

Proof Simply take the partial derivative with respect to r of (4.1):

∂P

∂r =

nt=1

−ctt(1 + r)t−1

((1 + r)t)2 +

−F V n(1 + r)n−1

((1 + r)n)2

= −

nt=1

ctt(1 + r)−t−1 + F V n(1 + r)−n−1

< 0 (4.7)

4.4.2 Percentage change - interest rate relationship

A corollary1 to the previous theorem.

1a proposition that follows from one already proven


Corollary A decrease in rates will raise bond prices more on a percentage basis than a correspond-ing increase in rates will lower prices



ing increase in rates will lower prices.

Proof Simplify the bond price equation to be P = 1/X where X embodies the interest rate. The

percent change in bond price for an increase in interest rates is:

P 1P 0

=1

X +z1

X

= X

X + z (4.8)

Similarly the percent change in bond price for a corresponding decrease in rate is:

P 1P 0

=1

X −z1

X

= X

X −

z (4.9)

Clearly the percent change for a decrease is larger than the percent change for an increase:

X

X − z >

X

X + z (4.10)

4.4.3 Theorem 2: Bond price - maturity relationship

Theorem As interest rates change, the prices of longer term bonds will change more than the

prices of shorter term bonds, ceteris paribus . Let ∆P n and ∆P m represent the the change in prices for bonds with maturities n and m, respectively. Let n > m. In equation form:

∂ ∆P n∂r

> ∂ ∆P m

∂r (4.11)


Proof Clearly the longer the maturity, the more terms that are added in (4.1).



Example 4.2. Consider two bonds:

Table 4.4: Maturity-interest rate change sensitivityBond M Bond N

Coupon 10% 10%Maturity 15 yr 30 yrPrice @ Y T M = 12% 862 838Price @ Y T M = 10% 1000 1000

Price @ Y T M = 8% 1173 1226

As shown, in either case (increase from 10 to 12 or decrease from 10 to 8), the change in bondprice is larger for the longer maturity bond M. Also see the graph on page 140 of Brigham and Daves(2010).

4.4.4 Percentage change - maturity relationship

A corollary to the previous theorem.


Corollary As T T M increases, the percentage price change that occurs increases at a diminishingrate. Let %∆P represent the percentage price change that occurs from a change in interest rate.



% p p g p g gRestating Theorem 2 in equation form:

∂ (%∆P )∂ T T M > 0 (4.12)

This Corollary states:

∂ 2(%∆P )

∂ T T M 2 < 0 (4.13)

Proof Maybe another time...

4.4.5 Theorem 3: Bond - coupon price relationship

Theorem Bond price volatility , measured in terms of percentage-price fluctuations, is inverselyrelated to coupon rate (not the Y T M ). Let %∆P represent the bond price percentage change as aresult of a change in interest rates. In equation form:

∂ 2(%∆P )∂c∂r

< 0 (4.14)

In other words, the change in price due to a change in interest rates of larger coupon bonds is lessthan that of smaller coupon bonds.


Proof by example Given two bonds, X and Y , identical in all aspects except the coupon rate.The prices of each bonds at different Y T M s are shown below:



p

Table 4.5: Coupon - interest rate sensitivityBond X Bond Y

Coupon 10% (100) 15% (150)Maturity 15 yr 15 yrPrice @ Y T M = 10% 1000 1384Price @ Y T M = 15% 705 1000%∆P 29.5% 27.7%

As shown, the percentage change in bond price decreases as the coupon rate increases , the inverserelationship we were looking for.

4.4.6 Malkiel theorem implications

1. If interest rates are anticipated to decline investors should purchase low-coupon, long-maturitybonds.

2. If interest rates are anticipated to rise investors should purchase short-maturity, high-couponbonds.


Table 4.6: Malkiel Theorem Implicationsr increase r decrease



r increase r decrease∂P ∂r < 0 (The 1) bond price decreases bond price increases

∂ (%∆P )∂ T T M

> 0 (The 2) want short maturity to minimize

exposure to price decrease

want long maturity to maximize

exposure to price increase ∂ (%∆P )

∂c < 0 (The 3) want high coupons to minimize

exposure to bond price decrease

want low coupons to maximize

exposure to price increase

4.5 Default risk and bond contract provisions

Bond indentures Legal document describing bondholder’s protection

• Administered by trustee

• Approved by SEC

• Recall default-risk: risk that a company will default and be unable to repay its obligations.

QUESTION: How can indentures reduce default risk?4.9

Mortgage bonds Bond secured by pledged assets.

QUESTION: How does this impact the ordinary unwinding of assets in abankruptcy?4.10

4.6. BOND RATINGS 79

Debentures Unsecured bond; claims secured by un-pledged property



Subordinated debentures Claims subordinate to all other debt

Development bonds A means to subsidize private industry by issuing tax-exempt bonds on theirbehalf in the name of “development.”

QUESTION: Why is it a subsidy?4.11

Municipal bond insurance Insurance against municipal default.

QUESTION: What impacts the default risk reduction associated with municipalbond insurance?4.12

4.6 Bond ratings

• Ratings are supposed to reflect default-risk.

• High-rated (AAA, AA) bonds are called investment grade.

• Low rated (BB and lower) bonds are called junk or high yield bonds.


4.6.1 Rating criteria

• Criteria include financial ratios legal standing time to maturity and many other items See



• Criteria include financial ratios, legal standing, time to maturity, and many other items. Seepage 135, 136 of Brigham and Daves (2007) or page 136 of Brigham and Daves (2010).

• Ratings have some amount of subjectivity. There is no precise formula with the 15 criteria asinput and bond rating as an output).

QUESTION: Could this lack of a precise formula have anything to do with the 2008financial crisis?4.13

4.6.2 Bond rating importance

• Many institutions are restricted to investment grade securities.

• Rating impacts required yield which in turn impacts cost of capital.

• Covenants may impose rating-sensitive interest rates.

4.6.3 High-yield (junk) bonds

• Definition: high-yield, high-risk bond

• Michael Milken (ab)used historical studies suggesting benefits (high yield) outweighed the costs(high risk of default).

4.6. BOND RATINGS 81

• A brief history:



– 1970s: The beginning: junk bonds were used to finance Public Service of New Hampshire(Seabrook nuclear plant), CNN, and Turner Broadcasting.

– 1980s: Phenomenal growth of junk bonds (CBS, Union Carbide, USX) observed.

– 1989: Milken sentenced to prison.

– Now:

QUESTION: Do MBSs look like junk bonds?4.14

4.6.4 Bankruptcy and reorganization• Firms go bankrupt when they become insolvent. That is, when they can not meet interest andprinciple payments.

• Or... they get bailed out by the U.S. government!

• Chapter 7 bankruptcy is a forced liquidation.

• Chapter 11 bankruptcy is a reorganization.

• Federal bankruptcy judge chooses Chapter 11 if V after re-org > V liquidate.

• In reorganization


– Debt is restructured via lower interest rates, maturity lengthening, etc.

– Debt may be converted to equity.



y q y

– Dilution of common stockholder position occurs.

• There is an order of claims on liquidated firms’ assets.

QUESTION: Guess who comes first?4.15

4.7 Bond markets

Most bond trading occurs over-the-counter between financial institutions, not in organized exchangesdue to the large size of the bonds.

4.8 Term structure of interest rates

• Factors that impact interest rates include, but are not limited to, the following:

1. Marketability risk: The ability to sell with low transaction costs. We call the impact oninterest rates the marketability risk premium :

MRP = ilow mkt − ihigh mkt > 0 (4.15)

4.8. TERM STRUCTURE OF INTEREST RATES 83

QUESTION: Which is more marketable, U.S. Treasury Bonds or bonds of little-known corporations? How does this impact their respective interest

rates?4 16



rates?4.16

2. Call risk: Callable bonds impose risk on the purchaser.

QUESTION: What risk?4.17

Therefore there is a call interest premium (CIP):

CI P = icallable − inot callable > 0 (4.16)

3. Default risk: In a default the issuer of the bond is unable to meet their interest (coupon)obligations and possibly repayment of principal. The default risk premium is the differ-

ence in interest rate of an otherwise identical risk-free bond (e.g., time to maturity andmarketability):

DRP = irisky − irisk free > 0 (4.17)

• With regard to default risk, bonds are rated [albeit imperfectly] by ratings agencies Moody’s

and Standard & Poor’s . The default risk premium increases with riskiness.

– Ratings: http://www.bondsonline.com/asp/research/bondratings.asp

– Rates: http://finance.yahoo.com/bonds/composite_bond_rates

• Term structure of interest rates: the relationship between time to maturity and yield to ma-turity, ceteris paribus .


– Relationship depicted in the yield curve (see Yahoo finance link above for an example).

– Three factors affect the shape of the curve:



1. The real rate of interest.

QUESTION: What is the real rate of interest?4.18

2. Inflation expectations impact the yield curve slope positively if inflation is expectedto increase or negatively if inflation is expected to decrease.

3. Interest rate risk increases with maturity thus longer term bondholders must becompensated for bearing that risk. This puts an upward sloping bias on the yieldcurve.

– So, in general, the yield curve is upward sloping.

– Downward sloping yield curves tend to precede recessions.QUESTION: Any idea why?4.19

4.9 Real vs. nominal rates

• Real rate of interest: The [typically unobservable] rate of interest that does not includeinflation

• Nominal rate of interest: The observable rate of interest that does include inflation. Some-times this is referred to as the “quoted” interest rate.

• Two factors that determine real interest rates: supply and demand!

4.9. REAL VS. NOMINAL RATES 85

1. The demand for money. When rates are high, businesses less likely to borrow money and invest



1. The demand for money. When rates are high, businesses less likely to borrow money and investin projects. Also, consumers less likely to borrow money and consume.

QUESTION: Why? Also, why would a business be more inclined to borrow whenrates are low?4.20

2. The supply of money. When rates are low, might as well consume. When rates are high, buyCDs.

• Equilibrium: When supply equals demand.

• Fluctuations in equilibrium real rate occur when economic conditions change.

– A technology shock could shift demand curve to the right.

QUESTION: Why?4.21

– A reduction in the corporate tax rate will cause the demand curve to shift.

QUESTION: Which way?4.22

– An increase in the personal tax rate will shift the supply curve to the left.

– Read the text for more examples.

• Impact of inflation


– You want to buy a surfboard next year (time t = 1) that costs $1,040 today (time t = 0)

– Today (time t = 0) you lend $1,000 to me @ 4% interest for one year so that you willh $1 040 t ti t 1



have $1,040 at time t = 1.

– Unfortunately, at time t = 1 the price of the surfboard went up 10% and is now $1,144.

– This increase in price from $1,040 to $1,144 is what we call inflation and thus a loss inpurchasing power.

• So what rate should you have charged me? It is hard to say. At time t = 0 you did not knowwhat inflation was going to be. However, you would have an expectation of what inflationwould be.

• Let ∆P e represent the annualized expected inflation rate (in our case, ∆P e = 10%).

• To incorporate expected inflation into the nominal (quoted) interest rate, use the FisherEquation:

1 + i = (1 + r) × (1 + ∆P e) (4.18)

• Intuitively, the real rate (1 + r) is “grossed up” by expected inflation (1 + ∆P e)

• Back to the surfboard example (get your pens out)...

• If r or ∆P e are small, the Fisher Equation (4.18) can be approximated as:

i ≈ r + ∆P e (4.19)

4.10. MARKET INTEREST RATE COMPONENTS 87

• An example of a change in expected inflation (get your pens out)...

• Cyclical [random] nature of interest rates



• Cyclical [random] nature of interest rates.

– Recession: declining real output and increasing unemployment.– [Nominal] interest rates and inflation move together.

QUESTION: Is this a surprise given the Fisher Equation?4.23

– Rates rise in expansionary periods and fall in contractionary periods.

• Impact on financial manager’s decisions: know what stage in the cycle you are in to assesswhether or not capital is “expensive” or “inexpensive.”

QUESTION: Is now a good time to get a fixed rate loan or should a business waituntil next year?4.24

4.10 Market interest rate componentsquoted interest rate = r = r∗ + IP + DRP + LP + MRP (4.20)

Nominal rate r: Stated or quoted interest rate


Real risk-free rate r∗: (on a short term (≤ 1 year) risk less security (government securities) if there were no inflation



Inflation premium IP : average expected inflation over the life of the security. Note rT-bill =rRF = r∗ + IP . The rate on TIPS are “pretty good” estimates of the real risk-free rate.

QUESTION: Why?4.25

Default risk premium DRP : premium that increases with the probability of default by issuer.

QUESTION: What is the DRP for a U.S. T-Bond?4.26

Liquidity premium LP : premium that increases with the difficulty in converting the security

to cash. Care must be taken when distinguishing between marketability and liquidity. Highliquidity means can go from sale to cash quickly. High marketability means one can go fromsale to cash with minimal transaction costs. A home has both low liquidity (takes a long timeto go from sale to cash) and low marketability (lots of fees involved in selling a home).

QUESTION: Can anyone think of a high liquidity low marketability asset? Howabout a low liquidity high marketability?4.27

Maturity risk premium MRP : premium that increases with maturity. This is due to (1) highersensitivity to interest rate changes of long-term bonds vs. short-term bonds, i.e., interestrate risk; (2) the fact that the issuer is holding your par or face value longer. In contrast,short-term bonds are exposed to reinvestment rate risk.

4.11. BOND PRICE AND DURATION EXAMPLE 89

QUESTION: What is reinvestment rate risk and how are short-term bondsexposed to it?4.28



4.11 Bond price and duration example

The problem Consider a bond with a 7% annual coupon rate, current market yield of 10%annually , $1,000 par value, three years until maturity, and makes semi-annual payments.

1. What is the bond price?

2. What is the duration?

The formulas

P =n

t=1

ct

(1 + r)t +

F V

(1 + r)n (4.21)

where P is bond price today, r is the appropriate semi-annual discount rate or market yield , n isthe number of semi-annual periods, and F V is the bond face (par) value.

D =n

t=1 P V [CF t] × t

P =

1

P

nt=1

CF t × t

(1 + r)t

(4.22)

where D is the duration, P is the bond price, and C F t is the cash flow at time t.


Solution

P i



Price

• The number of semi-annual periods is 3 × 2 = 6.

• The semi-annual coupon rate is 7.0%/2 = 3.5%.

• The semi-annual market yield is 10.0%/2 = 5.0%.

Therefore

P =

6t=1

35(1 + 0.05)t + 1000

(1 + 0.05)6

Expanding this equation gives you:

P =

35

1.051 +

35

1.052 +

35

1.053 +

35

1.054 +

35

1.055 +

35

1.056

+

1000

1.056

After several button presses on your calculator (or just a few if you program (4.21) into your calcu-lator) you arrive at:

P ≈ 923.86

4.11. BOND PRICE AND DURATION EXAMPLE 91

Duration According to (4.22), you will need to have computed P correctly above. Pluggingvalues into (4.22):

D 1

6

CF t × t



D =923.86

t=1

t

1.05t

You must be careful when considering the cash flows, CF t. The cash flows are the semi-annualcoupon payments (periods 1 up to and including 6). In semi-annual period 6, you also receive theface (par) value. Therefore, expanding the summation:

D = 1

923.86

35 × 1

1.051 +

35 × 2

1.052 +

35 × 3

1.053 +

35 × 4

1.054 +

35 × 5

1.055 +

(35 + 1000) × 6

1.056

After several button presses on your calculator you arrive at:

D ≈ 5.5 semi-annual periods or 2.75 years


4.A Financial calculators: behind the scenes

In this section I will show what formulas are behind your financial calculator’s finance-specific but-Th l l ( b dh ld b d ) d



tons. This section also relates perspectives (e.g., bondholder vs. bond issuer) and appropriate signs(positive or negative) of inputs into the financial calculator.

The mother of finance equation

Let me begin with the "Mother of Finance" (MF) equation that illustrates the present value V 0 of any financial asset is the discounted (by the discount rate i) future cash flows C F t:

V 0 = CF 1

(1 + i)1

+ CF 2

(1 + i)2

+· · ·

+ CF n

(1 + i)n

Now move V 0 to the right hand side:

0 = −V 0 + CF 1(1 + i)1

+ CF 2(1 + i)2

+ · · · + CF n(1 + i)n

(4.23)

Let C F 0 = −V 0 and we have the net present value (NPV) equation:

N P V ≡ 0 = CF 0 + CF 1(1 + i)1

+ CF 2(1 + i)2

+ · · · + CF n(1 + i)n

(4.24)

where i is also referred to as the internal rate of return IRR. Eq. (4.24) is the formula behind yourfinancial calculator’s cash flow C F i, NPV, and IRR buttons.

4.A. FINANCIAL CALCULATORS: BEHIND THE SCENES 93

The “Fab five” buttons

We can apply Eq. (4.24) to an example with constant periodic cash flows P M T and a cash flow



pp y q ( ) p pof F V in the final period, i.e., a bond. Lets rework Eq. (4.24) to represent a bond by letting

CF 0 = P V , C F 1 = C F 2 = · · · CF n−1 = P MT , and C F n = P MT + F V :

0 = P V + P MT

i

1 − 1

(1 + i)n

+

F V

(1 + i)n (4.25)

Eq. (4.25) reveals why P V is treated as a negative cash flow by your financial calculator: P V is thesame as −V 0 in Eq. (4.23)! Eq. (4.25) is indeed the equation behind your financial calculator’s “Fabfive” buttons: n, i, PMT, PV, and FV.

A matter of perspective

Users of financial calculators must be mindful of the sign of numbers entered in the PMT, PV, andFV buttons. The correct sign is a matter of perspective. Table 4.7 summaries the perspective insigns. In general, the sign is positive if it is a cash inflow and negative if it is a cash outflow .


Table 4.7: Perspectives and signs

Type Perspective P V P MT F V



Bond Purchaser (holder) (−) (+) (+)

Bond Seller (issuer) (+) (−) (−)Periodic savings Individual (saver) 0 (−) (+)Periodic savings Bank 0 (+) (−)Simple interest loan Individual (+) (−) 0Simple interest loan Bank (−) (+) 0

4.B The elusive n

Fortunately financial calculators, when given correct inputs with the correct signs (see Table 4.7),can easily solve for the number of periods n. However, there is some debate on the “correct” n to

report. Should n be rounded up? Rounded down? Allowed to be expressed as a decimal?I don’t take a position on that debate. Here I provide derivations of algebraic solutions to Eq.

(4.25) so you may compute a precise n. At that point you may decide on your own to round up,down, or leave as a decimal. The formulas are:

4.B. THE ELUSIVE N 95

n = − ln

1 + iP V

P M T

Simple interest loan F V = 0 (4 26)



n =ln[1 + i]

Simple interest loan, F V = 0 (4.26)

n = ln 1 − iF V P M T

ln[1 + i] Saving for the future, P V = 0 (4.27)

n = ln

1 − iF V

P MT

1 + iP V P M T

÷ ln[1 + i] Bonds (4.28)

Note: you must enter P V , P MT , and F V with the signs appropriate for the perspective you aretaking (see Table 4.7).

Simple interest loan

In a simple interest loan F V = 0. As such we can rewrite Eq. (4.25):

0 = P V + P M T

i1 − 1

(1 + i)n

+ 0

Applying a little algebra we can arrive at n:


0 = iP V

P MT +

1 − 1

(1 )



0P MT

+

(1 + i)n

1(1 + i)n = 1 + iP V P MT

(1 + i)−n = 1 + iP V

P MT

ln

(1 + i)−n

= ln

1 +

iP V

P M T

−n ln[1 + i] = ln 1 +

iP V

P M T Finally we arrive at:

n = − ln

1 + iP V

P M T

ln[1 + i]

(4.29)

Note: it is imperative to follow the sign conventions of Table 4.7 when computing n.

Example 4.3. How many years will it take to pay off a 10% $8,700 loan with $1,000 annual pay-


ments? Taking the perspective of the lender , P V = −8, 700 and P MT = 1, 000.

n = − ln

1 + iP V

P M T



n ln[1 + i]

= − ln 1 + 0.10

×−8700

1000 ln[1 + 0.1]

= − ln[0.13]

ln[1.1]

= 21.4061

Note: the HP12C reports n = 22 when using the “Fab five.”

Saving for the future

Making periodic deposits of P MT at interest rate i will lead to some future balance F V after nperiods. In this case we begin with P V = 0 and rewrite Eq. (4.25):

0 = 0 + P M T

i

1 − 1

(1 + i)n

+

F V

(1 + i)n

Applying a little algebra we can arrive at n:


0 = 1 − 1

(1 + i)n +

iF V

P MT

1

(1 + i)n



(1 + i)n P MT (1 + i)n

0 = (1 + i)n − 1 + iF V P M T

(1 + i)n = 1 − iF V

P MT

ln [(1 + i)n] = ln

1 − iF V

P M T

n ln[1 + i] = ln

1 − iF V

P M T Finally we arrive at:

n = ln

1 − iF V P M T

ln[1 + i]

(4.30)

Example 4.4. How many years will it take to save $30,000 by saving $1,000 per year and earning10% annual? Taking the perspective of the saver , P MT = −1, 000, F V = 30, 000, i = 0.10, andP V = 0.


n = ln

1 − iF V P M T

ln[1 + i]



=

ln 1

−0.10×30,000

−1,000 ln[1 + 0.1]

= ln[4]

ln[1.1]

= 14.5451


Bonds

In the case of bonds we have both a P V and an F V so the derivation is a bit more complicated.Beginning with Eq. (4.25):

0 = P V + P MT

i

1 − 1

(1 + i)n

+

F V

(1 + i)n

0 = iP V P MT

+ 1 − 1(1 + i)n + iF V

P M T 1

(1 + i)n

0 = (1 + i)n

1 +

iP V

P M T

− 1 +

iF V

P MT


Moving things around a bit more:



(1 + i)

n1 +

iP V

P M T = 1 − iF V

P M T

(1 + i)n = 1 − iF V

P M T

1 + iP V P M T

n ln[1 + i] = ln

1 − iF V

P M T

1 + iP V P MT

And finally we arrive at:

n = ln

1 − iF V

P MT

1 + iP V P M T

÷ ln[1 + i] (4.31)

Example 4.5. Consider a $1,000 par value bond that sells for $847.88. The annual coupon is $80and the yield to maturity is 10%. How many more coupon payments will you receive? Taking theperspective of the bondholder, F V = 1, 000, P V = −847.88, P M T = 80, and i = 0.10.

4.C. THE MORE ELUSIVE I 101

1 − iF V



n = ln1 P M T

1 + iP V

P M T ÷ln[1 + i]

= ln

1 − 0.10×1,000

80

1 + 0.1×(−847.88)80

÷ ln[1 + 0.1]

= ln[4.1771] ÷ ln[1.1]

= 14.9997


4.C The more elusive i

Unfortunately solving for the interest i is more complicated. Technically speaking, there are noclosed form (exact) solutions for i. I have found a couple approximations.


i ≈

1 − P MT

P V

1/q

− 1

q

− 1 where q = ln [1 + 1/n]

ln[2] Simple interest loan, F V = 0



P V

ln[2]

(4.32)

i ≈ P MT + FV /n

F V /2 Saving for the future (4.33)

i ≈ P MT + F V +P V n

F V −P V 2

Bonds (4.34)

Note: you must enter P V , P MT , and F V with the signs appropriate for the perspective you are

taking (see Table 4.7).

Simple interest loan

The approximation was obtained from David Cantrell’s “Finding interest rate without approxima-tion or root finding.” The “without approximation” referred to here is without numerical iterative

approximation.

Example 4.6. Consider an $8,700 loan with 5 annual payments of $2,295.04. What is the interestrate? Taking the perspective of the borrower, P V = 8, 700, F V = 0, n = 5, and P MT =

4.C. THE MORE ELUSIVE I 103

−2, 295.04.

q = ln [1 + 1/5]

ln[2] = 0.2630

1/ 0 2630



i ≈ 1 − −2, 295.04

8, 700 1/0.2630

− 10.2630

− 1

i ≈ 0.0998 or 9.98%

Note: the HP12C reports i = 10 when using the “Fab five.”

Saving for the future

Note: citation needed. I can’t remember where I found the bond interest rate approximation Eq.(4.34). However, setting P V = 0 allows one to arrive at the “saving for the future” formula Eq.(4.33).

Example 4.7. What interest rate do I need to earn to have $610.51 in five years if I save $100 peryear? Taking the saver’s perspective, F V = 650.51, P MT = −100, n = 5, and P V = 0.

i ≈ −100 + 650.515

650.512

≈ 0.0925 or 9.25%

Note: the HP12C reports i = 10 when using the “Fab five.”. Thus, a better approximation would benice. Let me know if you find one!


Bonds

Note: citation needed.

Example 4.8. Consider a $1,000 par value bond that sells for $847.88. The annual coupon is $80



p , p pand there are 15 years until maturity. What is the yield to maturity of this bond? Taking theperspective of the bondholder, F V = 1, 000, P V = −847.88, P M T = 80, and n = 15.

i ≈ P MT + F V +P V n

F V −P V 2

≈ 80 + 1,000+(−847.88)15

1,000−(−847.88)2

≈ 0.0976 or 9.76%

Note: the HP12C reports i = 10.000 when using the “Fab five.” This illustrates how Eq. (4.34) is just an approximation.



Chapter 5

Stock valuation

OverviewMuch like the previous chapter this chapter discounts future cash flows to obtain stock values. Wealso take a look at stock market equilibrium.

5.1 Legal issues

5.1.1 Control of the firm• Stockholders elect directors and directors elect officers.

• In a small firm the largest shareholder is typically CEO/Board chair.

105

106 CHAPTER 5. STOCK VALUATION

• In a large firm officer/director holdings typically insufficient for voting control.

• Votes occur in person or by proxy at annual meetings.



QUESTION: What is a proxy vote?5.1

5.1.2 Preemptive right

• Preemptive right is the current common stockholders’ right to purchase additional shares.

• Preemptive rights prevent management from seizing control and transferring wealth from stock-

holders.

• An example...

Preemptive right vs. employee stock ownership plans The preemptive right allows existingshareholders to purchased newly issued shares of stock. With employee stock ownership plans no newshares are issued. The company itself purchases shares on the open market, sells them to employees

at a discount, and accounts for the loss as some form of business expense. So, the key distinction ispreemptive rights deals with newly issued shares whereas employee stock purchases are with existingshares.

For an executive pre-emptive right workaround see the Appendix 5.A.

5.2. COMMON STOCK MARKETS 107

5.1.3 Classifications

• Classifications vary in voting and dividend rights.

• Dividend payments can be tied to performance including performance of a particular division



(i.e., tracking stock).

QUESTION: Which stock is more valuable, one with voting rights or one without?5.2

5.2 Common stock markets

• Closely-held: owned by a few people (small companies).

• Publicly-held: what you and I own.

• Institutional investors own more than 60% of publicly held stock and account for ≈ 75% of transactions.

• IPO: initial sale of privately owned company to the public.

• SEO: seasoned equity offering. Issuance of new shares of already-public firm (primary market).

• Outstanding shares - what we can trade on NYSE/Nasdaq (secondary market).

• Do not bother with IPOs unless you get in “on the ground floor” (i.e., able to purchase at theoffering price). If you do not you will underperform the market in the long run.


QUESTION: What do we mean by “underperform the market?” 5.3



5.3 The dividend discount model (DDM)

• Current price is present value of expected future cash flows.

QUESTION: If a stock is a non-dividend paying stock, what is the expected futurecash flow?5.4

5.3. THE DIVIDEND DISCOUNT MODEL (DDM) 109




5.3.1 Definitions

Table 5.1: DDM definitionsTerm Definition

D Expected dividend at time t



Dt Expected dividend at time t

P 0 Actual market price today P t Expected value at end of time t P 0 Intrinsic value. May vary from investor to investor. However, P 0 = P 0 inequilibrium.

QUESTION: Why?5.5

D1/P 0 Expected dividend yield (DY)

P 1−P 0P 0 Expected capital gains yield (CGY)g Expected dividend growth rate.

QUESTION: If g is constant, what are the earnings and stock pricegrowth rates?5.6

Rs Required rate of return based on the riskiness of the stock and returns availableon other investments (e.g., obtained from CAPM, the “fundamental” return) Rs Expected rate of return. the sum of DY and CGY, or, the arithmetic average,or, some other estimate. (the “market” return as determined by the “marginal”or “average” investor)

Rs Realized or actual return (geometric average)

5.4. THE CONSTANT GROWTH DDM 111

QUESTION: What are the relationships between Rs, Rs, and Rs?5.7

5.3.2 Expected dividends and stock values

The dividend discount model is one method to compute the intrinsic or fundamental value of a stock:



The dividend discount model is one method to compute the intrinsic or fundamental value of a stock:

P 0 =∞

t=1

Dt

(1 + Rs)t (5.1)

QUESTION: Why start at t = 15.8

QUESTION: Does this change if you plan to sell the stock in a couple years? 5.9

5.4 The constant growth DDMThe constant growth model is also known as the Gordon Growth Model .

P 0 = D0(1 + g)1

(1 + Rs)1 + D0(1 + g)2

(1 + Rs)2 + · · · + D0(1 + g)∞

(1 + Rs)∞ (5.2)

= D0

∞

t=1

(1 + g)t

(1 + Rs)t (5.3)

= D0(1 + g)

Rs − g =

D1

Rs − g Rs > g (5.4)

QUESTION: What happens if Rs < g?5.10


5.4.1 Constant growth stock illustration

Acme corp just paid a $1.15 dividend. It has a required rate of return of 13.4% and dividends areexpected to growth at 8%.

QUESTION: What is the current value of the stock?5.11



QUESTION: What is the current value of the stock?

5.4.2 Dividends and earnings growth

• Dividends are the portion of earnings that are not retained.

QUESTION: Can a firm increase its value by simply increasing its dividends?5.12

5.4.3 Do stock prices reflect long term or short term events?Assume D0 = 1.15, Rs = 13.4%, and g = 8%. The following table illustrates the percentage of firmvalue, as measured by the dividend discount model, by number of annual dividends received.

Observations regarding table 5.2:

• You do not need to wait forever to receive all of the dividend payments included in the stockscurrent value.

• Managers gripe about the market’s unmerited attention to quarterly results. Are they justified?

5.4. THE CONSTANT GROWTH DDM 113

Table 5.2: Value vs. years of dividendsYears % of value5 22%25 70%50 90%



50 90%100 99.4%

– PV of first 5 dividend payments is $5, or 22% of today’s value → near term earn-ings/dividends should not have a huge impact on price since value is obtained from longterm.

– But wait! Reduced earnings because of things like R&D increases are generally good

since it may lead to higher g. However reduced earnings due to slow sales is bad due tolower g .

– Also, managers’ bonuses tend to be tied to quarterly performance, a result of the attentiongiven to quarterly earnings.

5.4.4 When to use the constant growth model

• Mature companies with a history of stable growth, for example, Johnson and Johnson (JNJ).

• General expectation for these firms: 5 to 8% growth, about the same rate as nominal GDP.


5.5 From DDM to expected return

rs = D1

P 0+ g (5.5)

Example 5 1 Let’s look at EQR P = 58 51 D = 2 27 g = 8 82% What is the expected return



Example 5.1. Let s look at EQR. P 0 = 58.51, D0 = 2.27, g = 8.82%. What is the expected returnrs?

Example 5.2. For fun, what is the required return based on CAPM? Presume β = 1.34, Rf =2.00%, and E [Rm] = 6.24%.

QUESTION: What would be the stock price at the beginning of year 1?5.13

• Note: P 1 = P 0(1.08)

• The capital gains yield from t = 0 to t = 1:

CGY = 24.84 − 23

23 = 8% (5.6)

• Dividend yield from t = 0 to t = 1:

DY = D1 P 0= 1.24

23 = 5.4% (5.7)

• Conditions that must hold for constant growth stocks

5.6. MULTIPLE GROWTH RATE DDM 115

1. Dividends expected to grow at constant g forever

2. Stock price growing at the same rate

3. Expected DY is constant

4. Expected CGY= g and is constant



5. rs = DY + CGY

• Note “expected” means “statistically expected,” i.e., the best prediction (guess) for any futureyear is 8%.

5.6 Multiple growth rate DDM

• The “dot-com” boom period could be viewed as supernormal. Afterwards things returned to“normal.”

• If you anticipate a period of super- or sub-normal growth, use the non-constant growth model.

• See an example in Appendix 5.B at the end of this chapter.

5.7 Discounted FCF approach

1. Compute the market value of operating assets:

V op = F CF 0(1 + g)

WACC − g (5.8)


2. Compute the value of the entire firm:

V total = V op + V non-op (5.9)

where V non-op is the value of non-operating assets such as short- and long-term investments.



3. Subtract the value of debt and preferred stock to obtain the value of common stock.

V cs = V total − V debt − V preferred stock (5.10)

4. Divide by the number of common shares outstanding to obtain the price per share of commonstock P .

P = V cs

ncs(5.11)

Example 5.3. Let’s apply the discounted FCF approach to Johnson and Johnson (JNJ)...

5.8 Valuation by market multiple

Price-to-earnings ratio

• Another way to estimate the value of stock.• Less precise than dividend discount method.

• To find the value of a share of common stock:

5.8. VALUATION BY MARKET MULTIPLE 117

1. Compute the average P/E ratio for similar public companies.

P E = 1

n

ni=1

P iE i

(5.12)



2. Multiply by forecasted EPS E of the company under consideration to obtain the priceper share of common stock P .

P = E × P E (5.13)

Example 5.4. Let’s apply the P/E market multiple approach to Johnson and Johnson (JNJ)...

Entity multiple

• Another approach to estimating the firm value estimation is the entity multiple approach.

• The entity multiple, V total/EBITDA, is analogous to P/E but uses the ratio of whole-firmvalue V total to EBITDA rather than price-to-earnings.

• To find the value of a share of common stock:

1. Compute the average entity multiple for similar public companies.

V E = 1

n

ni=1

V total,i

EBITDAi(5.14)


where V total,i is obtained for each firm (except the firm under consideration) using thesteps in Section 5.7. Also, V E is analogous to the average price-to-earnings ratio P E .

2. Multiply by EBITDA of the company under consideration.

V total = EBITDA × V E (5.15)



3. Subtract the value of debt and preferred stock from total value.

V cs = V total − V debt − V preferred stock (5.16)

4. Divide by the number of common shares outstanding to obtain the price per share of common stock P .

P = V cs

ncs(5.17)

Example 5.5. Let’s apply the V total/EBITDA entity multiple approach to Johnson and Johnson(JNJ)...

5.9 Preferred stock

A hybrid between fixed-income and equity securities.

• pays fixed dividend known in advance

• like bonds preferred stock has par value and fixed dividends that must be paid before commonstock

5.A. PREEMPTIVE RIGHT WORKAROUND 119

• unlike bonds, company is not legally required to pay dividends and will not be in default if itfails to pay

• cumulative dividends if dividends can not be paid, unpaid dividends must be paid in thefuture before common stock but after debt obligations



• non-cumulative dividends - in the event of omitted dividends, preferred stock holders maybe allowed to vote for board of director members (you didn’t pay my dividends, I’ll vote youout of there)

• convertible preferred stock provides the preferred stockholder the option to convert preferredshares into common shares.

QUESTION: Can you think of a couple reasons a preferred stockholder would

convert to common shares?5.14

• preferred stockholders have a claim on liquidation value after debt holders but before stock-holders (and has an associated par value)

QUESTION: If dividend payments are fixed and last forever, what is the value of preferred stock?5.15

5.A Preemptive right workaround

Does the issuance of new stock dilute shareholder value? It depends...


Begin with the following:

P 0 = $100

n = 1, 000

MKTCAP = $100 1, 000 = $100, 000



×where P 0 is the current market value, n is the number of shares outstanding, and MKT CAP is thetotal market capitalization.

Scenario 1 The firm issues 1,000 new shares of stock at a price lower than the current marketprice (P ∗0 = 50):

MKTCAP ∗ = $100, 000 + $50 × 1, 000 = $150, 000

P ∗0 = $150, 000 ÷ 2, 000 = $75

Since the new price per share P ∗0 = $75 is less than the original price per share P 0 = $100 thisissuance of stock has diluted the value of outstanding shares.

Scenario 2 The firm issues 1,000 new shares of stock at the current market price (P 0 = $100):

MKTCAP = $100, 000 + $100

×1, 000 = $200, 000

P 0 = $2000, 000 ÷ 2, 000 = $100

Since the new price per share P 0 = $100 is equal to the original price per share P 0 = $100 thisissuance of stock does not dilute the value of outstanding shares.

5.A. PREEMPTIVE RIGHT WORKAROUND 121

We talked about the preemptive right typically held by existing shareholders in Section 5.1.2.Thus, Scenario 1 is unlikely. However, companies can and do issue warrants to executives. Warrantsare like stock options except a new share is issued by the corporation when exercised. Similar to acall option a warrant is exercised only if the exercise price is below the current market price. In thatcase we are back at Scenario 1 where the value of existing shares is diluted.



So, in general, issuing stock does not dilute shareholder value. This is because new shares aretypically issued at the current market price. However, with warrants executives can issue new sharesto themselves at below market prices. It is in this shady and questionable practice that shareholdervalue is transferred from the many existing stockholders to the few executives.


5.B Multi-growth rate DDM

In the Multi-growth rate DDM model dividends grow at a super- (or sub-) normal rate gs for n years.After that dividends grow at a constant rate gc forever. Lets begin with the "Mother of Finance"



equation:

P 0 = D1

(1 + Rs)1 + D2

(1 + Rs)2 + · · · + Dn

(1 + Rs)n + Dn+1

(1 + Rs)n+1 + Dn+2

(1 + Rs)n+2 + · · · (5.18)

Multiple growth rate formula I use P 0 to emphasize this is an intrinsic value calculation, notthe actual market value .

P 0 =

D1

(1 + Rs)1 +

D2

(1 + Rs)2 + · · · +

Dn

(1 + Rs)n +

P n

(1 + Rs)n (5.19)

= D1

(1 + Rs)1 + D2

(1 + Rs)2 + · · · + Dn + P n(1 + Rs)n (5.20)

5.B. MULTI-GROWTH RATE DDM 123

where

gs = short term super- or sub-normal dividend growth rate

gc = long-term constant dividend growth rate



Dn = dividend at the end of the abnormal growth periodRs = required rate of return

P n = Dn+1

Rs − gc= the value of all remaining dividends in year n

Dn+1 = Dn (1 + gc)

Expressed in compact form:

P 0 =

nt=1

D0(1 + gs)t

(1 + Rs)t

+

Dn(1 + gc)

Rs − gc× 1

(1 + Rs)n (5.21)

Example 5.6. D0 = $1.00, gs = 12%, n =5 years, gc = 6%, Rs = 10%1 . What is P 0?

1From the 9th edition of Investments by Charles P. Jones


Plugging into (5.21):

P 0 =

5t=1

1(1 + 0.12)t

(1 + 0.10)t

+

1(1 + 0.12)5(1 + 0.06)

0.10 − 0.06 × 1

(1 + 0.10)5

1(1.12)1 1(1.12)2 1(1.12)5



= 1.101 + 1.102 + · · · + 1.105 + 28.9983

= 5.2794 + 28.9983

= 34.28

For another example, see Brigham and Daves (2010) page 170.

Ch t 6



Chapter 6

Financial options

Overview

Before delving into real options we must first understand how options are priced. Since the value of real options are based on financial option theory we shall start there.

6.1 Financial optionsFinancial options are options to buy or sell an underlying asset at a pre-specified price on or beforea pre-specified date.

125

126 CHAPTER 6. FINANCIAL OPTIONS

6.1.1 Option types and markets

• Call vs. put: buy vs. sell

• American vs. European: any time vs. at expiration date only

C ti l LEAPS 6 th 6 th t 2 5



• Conventional vs. LEAPS: ≈ 6 months vs. 6 months to 2.5 years

• Covered vs. naked: own underlying asset vs. do not

• In-the-money vs. out-of-the-money: could exercise at a gain vs. would not exercise

• Important features: option price, strike price, expiration date, volatility of underlying asset

• Underlying asset can be individual stock, index, futures contract, etc.

• No voting rights until after exercise

• A couple of examples...

Table 6.1: The long and short of call and putCall Put

Buyer (long position) option to buy option to sellSeller (short position) obligation to sell obligation to buy

6.1. FINANCIAL OPTIONS 127

6.1.2 Factors that affect the value of a call option

• S − K , difference between stock and exercise price

• Expiration date

V l tilit



• Volatility

6.1.3 Intrinsic value vs. option price

• Intrinsic value for call option = max[P 0 − X, 0], aka, exercise value

• Market value = intrinsic value + time value

• Time value diminishes as you approach expiration date• Options magnify returns and losses (but with a lower limit)

• An example...

Note the option payoff is asymmetric. The maximum loss for the long position is what you paidfor the option irrespective of how far the stock price drops.

QUESTION: What about the maximum loss for the short position, i.e., writer of acall?6.1

Three important factors associated with option values:


1. Time until expiration: more time to see a large gain. “ c increases with t”

2. Volatility: With greater volatility (risk) comes greater chance of a big gain. Combine this withthe limited downside and you have “ c increases with σ .”

3. Risk free rate: Exercising requires cash. If interest rates are high, it will require less cash now

to exercise in the future



to exercise in the future.


Lower cost makes the option more valuable. Therefore “ c increases with rf ”

6.2 Binomial option pricing model6.2.1 Replicating portfolio approach

6.2.1.1 Given information

• Current stock price = P 0 = 40

• Price in the “up” state = P u = 50

• Price in the “down” state = P d = 32

• Call option strike price = K = 35

6.2. BINOMIAL OPTION PRICING MODEL 129

• Risk free rate = rf = 8%

• Time to expiration = 1 year = 365 days



40

50

32

Figure 6.1: Stock price “tree”


c 0

15



c_0

0unknown

Figure 6.2: Call option value

6.2.1.2 Replicating portfolio and option value

A portfolio is constructed using the underlying stock and risk free borrowing such that the portfoliovalue is the same as the option value in all states (initial, up, and down). The replicating portfoliois formed by purchasing N shares of stock and borrowing B dollars at rf .

We attribute positive values to the long position (purchase of stock) and negative values to theshort position (borrowing at rf ). The value of the portfolio in each of the three states is computed


as follows:

V 0 = 40N − B = c0 (6.1)

V u = 50N

−1 +

0.08

365

365

B = 15 (6.2)

365



365V d = 32N −

1 +

0.08

365

365

B = 0 (6.3)

Note

1 + 0.08365

365 ≈ 1.0833 and we now have three equations with three unknowns (N , B , c0).Graphically:

40N-B

50N-1.0833B

32N-1.0833B

Figure 6.3: Option replicating portfolio


Rearranging equation (6.3):

32N − 1.0833B = 0

32N = 1.0833B (6.4)

Substituting (6 4) into (6 2):



Substituting (6.4) into (6.2):

50N − 32N = 15

18N = 15

N = 0.8333 (6.5)

Substituting (6.5) into (6.4):

32(0.08333) = 1.08333BB = 24.62 (6.6)

Substituting (6.5) and (6.6) into (6.1):

V 0 = 40(0.8333) − 24.62 = 8.71

V 0 = c0 = 8.71

Therefore the “true” or fundamental value of the call option is $8.71.

QUESTION: What are the time and intrinsic values of this option?6.3


6.2.1.3 What if the market price is c0 = 9.71?

We know that the “true” value is lower (8.71). Therefore, we can construct an arbitrage position:i.e., a portfolio that (1) requires no investment, (2) has no risk, and (3) has positive returns. To doso:

• Sell option for 9.71 (short position)



Sell option for 9.71 (short position)

• Buy replicating portfolio for 8.71 (long position). Note this portfolio replicates the value of the call option.

• Invest remaining 9.71 − 8.71 = 1 in rf (long position)

Cash flows in the “up” state:

• The option you sold at time 0 will be exercised and you will lose $15 →-15.

• The replicating portfolio you purchased at time 0 will be worth $15 → +15.

• You also invested $1 at time 0 in the risk free asset and now it is worth 1(1.0833) = 1.0833→ +1.0833

• Net cash flow (up) =

−15 + 15 + 1.0833 = 1.0833

Cash flows in the “down” state:

• The option will not be exercised → 0


• Replicating portfolio = option value = 0

• $1 investment now worth 1.0833

• Net cash flow (down) = 0 + 0 + 1.0833 = 1.0833

Therefore, when the option’s market price is greater than the “true” option prince one can arbitrage:



, p p g p p g

• No initial investment: Proceeds from option sale (short position) used to purchase both thereplicating portfolio (long position) and risk free asset (long position).

• No risk: Whether we are in the “up” or “down” state the payoff is the same, 1.0833.

• Positive returns: 1.0833 > 0 and you used $0 to get it!

This scenario can not occur (not for long at least):

• Selling of option drives the market price of the option down from 9.71 to “true” 8.71.

• Purchasing of portfolio drives the market price of the stock up, which reduces the intrinsicvalue (K − P ), which in turn drives the market price of the option down from 9.71 towards“true” 8.71.

6.2.1.4 What if the market price is c0 = 7.71?

We know the “true’ value is higher (8.71). We can construct an arbitrage portfolio as follows:


• Short sell the replicating portfolio. In effect, you are short selling N shares of stock and lending(investing) B dollars at the risk free rate. → +8.71

• Buy (long position) 1 option at 7.71. → -7.71

• Invest 8.71

−7.71 = 1 at the risk free rate. Note, this is in addition to the B dollars invested

at the risk free rate.



Cash flows in the “up” state:

• Exercise the option purchased at t = 0 and receive $15 → +15.

• Close the short position on the replicating portfolio. In effect, you spend 50N = 50(0.83333) =41.67 to purchase stock and return to owner but receive 1.0833B = 1.0833(24.62) = 26.67

from investing B dollars at the risk free rate. Therefore −41.67 + 26.67 = -15.• Receive 1.0833 from the $1 investment.

• Net cash flow (up) = +15 - 15 + 1.0833 = 1.0833.

Cash flows in the “down” state:

• Do not exercise the option → 0.

• Close the short position. Spend 32N = 32(0.8333) = 26.67 to purchase stock and return toowner but receive 1.0833B = 1.0833(24.62) = 26.67 from investing B dollars at the risk freerate → 0.


• Receive 1.0833 from the $1 investment → 1.0833.

• Net cash flow (down) = 0 + 0 + 1.0833 = 1.0833.

As before we have an arbitrage scenario:

• No initial investment: proceeds from the short sale of the replicating portfolio used to purchaseoption and invest $1 at the risk free rate.



gp $

• No risk: Whether we are in the “up” or “down” state the payoff is the same, 1.0833.

• Positive returns: 1.0833 > 0 and you used $0 to get it!

This can not occur for long:

• Purchasing of option drives the market price of the option up from 7.71 to “true” 8.71.• Shorting of portfolio drives the market price of the stock down which increases the intrinsic

value of the call option, which in turn drives the market price of the option up from 7.71 to“true” 8.71.

6.2.2 Riskless hedge approach

A portfolio that will earn the risk free rate regardless of what the stock does. Consider the binomialapproach for Acme corp. Let S 0 = 40. Consider option with value c (unknown at the moment),strike price K = 35, time until expiration t = 1 year, and risk free rate rf = 8%. We are going toconstruct a risk-less hedge buy purchasing N shares of the stock and selling 1 call option.

6.3. THE BLACK-SCHOLES OPTION PRICING MODEL 137

QUESTION: What happens if call price were higher?6.4

QUESTION: What happens if call price were lower?6.5

• Clearly, it is difficult to know (guess) up and down states one year from now, but it is lessdifficult 6 months, 3 months, 1 month from now

• This leads to the binomial lattice (or tree)



• This leads to the binomial lattice (or tree).

• Simply repeat exercise of before on each “branch”

• A simple calculation that can be handled by recursive computer algorithm

QUESTION: Where do the new P u and P d values come from?6.6

• As the number of levels approaches ∞ the binomial option value converges to the Black-Scholesoption value

6.3 The Black-Scholes option pricing model

6.3.1 Assumptions

1. No dividends.

2. No transaction costs or taxes.


3. Constant rf .

4. Can borrow at rf .

5. Short selling allowed.

6. European option.



QUESTION: What does this mean?6.7

7. Random stock price movement with continuous trading.

• Derivation of B-S OPM based on riskless hedge.

• Formulas for the value of a call option

c = P (N [d1]) − Xe−rf t (N [d2]) (6.7)

d1 =ln[P/X ] +

rf +

σ2

2

t

σ√

t(6.8)

d2 = d1 − σ√ t (6.9)

with

6.3. THE BLACK-SCHOLES OPTION PRICING MODEL 139

Variable Descriptionc current call option valueP current price of underlying stockN [·] probabilitye 2.7183rf continuously compounded risk free rateln natural logarithm

2



σ2 variance

• Think of the left hand term P (N [d1]) as the expected present value of the stock price givenP t > X (option will be exercised).

• Think of the right hand term Xe−rf t (N [d2]) as the present value of the exercise price giventhe option will be exercised.

• Derivation is difficult, use of model is not.

• Traders use this formula and actual prices are about the same as predicted by the formula.

6.3.2 OPM illustration

Let P 0 = 20, X = 20, t = 3 months (0.25 year), rf = 6.4%, and σ2 = 0.16.


1. Compute d1 and d2

d1 =ln[P/X ] +

rf +

σ2

2

t

σ√

t

= ln[20/20] + 0.064 + 0.16

2 0.250 4

√ 0 25



0.4

√0.25

= 0.180

d2 = d1 − 0.4√

0.25

= −0.020

2. Use fancy calculator, table, or NORMSDIST in excel to obtain:

N [d1] = N [0.180] = 0.5714

N [d2] = N [−0.020] = 0.4920

3. Compute value of option

c = 20(0.5714) − 20e−0.064(0.25)(0.4920) = 1.74

6.4. PUT OPTIONS 141

6.3.3 OPM factors and option value

If factor ___ increases... Then call option value...P increasesX decreasest increases

rf increasesσ2 increases



σ increases

6.4 Put options

The value of put options can be obtained from the put-call parity relationship. Construct twoportfolios

Portfolio A Portfolio Baction buy put, buy stock buy call, invest PV of X cost p + P 0 c + Xe−rt

payoff at expiration P OA P OB

• For portfolio A, if P t ≤ X , you will exercise your put option and sell high at X . If P t > X you will not exercise the put option for if you did you would be selling low (but you still have

P t).

• For portfolio B, P t ≤ X , you will not buy high at X , therefore you will be left with X . If P t > X , you will buy low at X and have an asset worth P t.


• Note both payoffs are the same. Therefore

P OA = P OB =

X P t ≤ X

P t P t > X

• Therefore both portfolios must have the same cost. We arrive at the put-call parity relation:



p + P 0 = c + Xe−rf t (6.10)

p = c + Xe−rf t − P 0 (6.11)

6.5 Corporate finance applications

6.5.1 Real options

• How much is the option to develop cell phone software one year from now?

– Up state: Market looks good, invest 30M in development (X ), PV of profits=100M (i.e.,exercised the real option).

– Down state: Market looks bad, do not invest 30M, PV of profits=0. (do not exercise).

• May be valued using techniques similar to those discussed earlier.

6.5. CORPORATE FINANCE APPLICATIONS 143

6.5.2 Risk management

• Plant currently under construction, will issue 400M in bonds 6 months from now to pay for it

• If rates remain the same (or fall) the plant will be profitable.

• If rates rise the plant will be unprofitable.

• Purchase put option on T-bond index



• Purchase put option on T bond index.

• If rates go up, company must issue high interest rate bonds (bad) but offset this with gainsfrom put option (good).

• If rates go down, company issue low interest rate bonds (good) but eats the cost of the putoption (bad).

6.5.3 Capital structure decisions

• Let’s say a firm has debt with principal payment of 60M due in one year.

• If the value of the firm is 61M at expiration, then make the principal payment (exercise optionto “buy” firm for 60M, net 1M).

• If the value of the firm is 59M at expiration, do not make principal payment, allow bankruptcyto happen, and the value to shareholders is zero.

• How much is the option to buy the asset (the firm) worth?


QUESTION: Where is the debt vs equity decision?6.8

6.5.4 Compensation plans

• FASB2004 requires options to be reported as an expense. What is the value of those options?

• B-S or binomial OPM can be used to value those option grants



Chapter 7



pRisk and return

Overview

• Why look at investment returns? Concepts related to returns of securities also apply toinvestments in projects.

QUESTION: What concepts might those be?7.1

• Section 1: Return and risk from a stand-alone perspective.

• Section 2: Return and risk from a portfolio perspective.

• Section 3: Efficient portfolios and portfolio selection.

• Section 4: Asset pricing models.

145

146 CHAPTER 7. RISK AND RETURN

7.1 Stand alone return and risk

7.1.1 Basic return measures

Total return Typically applied to an individual security, measures the “total return” which includesthe yield component and capital gain component.

T R = (P 1 − P 0) + CF

P(7.1)



P 0( )

Note that total return may be positive or negative.

Relative return It is often to convenient to express return as a relative measure, hence the namerelative return:

RR = P 1 + CF

P 0

(7.2)

Can anyone relate RR to TR? .

An example...Additional explanations can be found in Brigham and Daves (2010) pages 29 to 30.

7.1.2 Risk

• Risk is the dispersion of returns (could be measured by standard deviation, range, downsiderisk, P r[r < 0], coefficient of variation, etc).

• Stand-alone risk is the risk faced if holding only one asset.

7.1. STAND ALONE RETURN AND RISK 147

7.1.2.1 Probability distribution

• Definition: Outcomes and probabilities of these outcomes.

• An example:

Demand Probability RTechCo RFoodCo

strong 0.3 100% 40%



normal 0.4 15% 15%weak 0.3 -70% -10%

QUESTION: Which stock is more risky and why?7.2

QUESTION: What should probabilities add up to?7.3

Now the calculations...

7.1.2.2 Expected rate of return

• Given a discrete probability distribution:

R = E [R] =n

i=1

P ri × Ri (7.3)


QUESTION: What are RTechCo and RFoodCo?7.4

• When given historical data you can compute:

– Arithmetic mean:

R = E [Ri] = 1

n

ni=1

Ri (7.4)



– Geometric mean:

G =

ni=1

RRi

1/n

− 1 (7.5)

– Arithmetic mean is typically used to estimate future returns (statistically, it is an unbiased

estimator) and Geometric mean is used to measure the realized compound rate of return.– A quick example...

7.1.2.3 Quantifying stand-alone risk: standard deviation

• Given a discrete probability distribution:

variance = σ2 =

ni=1Ri − R2

P ri (7.6)

standard deviation =√

variance = σ (7.7)

7.1. STAND ALONE RETURN AND RISK 149

Note: (7.7) applies to both discrete and continuous distributions. For an example see Brighamand Daves (2010) page 32 and 35.

• When given historical data there are are three types of continuous distribution variance esti-mates. These estimates are based on whether or not you have observed the entire population(N ) or just a sample of the population (n):

1. Input: population, output: population variance.



σ2 = 1

N

N i=1

Ri − R2

(7.8)

2. Input: sample, output: sample variance.

s2n = σ

2

= 1

n

ni=1Ri − R2

(7.9)

3. Input: sample, output: unbiased estimate of population variance.

s2 = 1

n − 1

ni=1

Ri − R2

(7.10)

We will primarily use (7.10) and call it σ2. For an example see Brigham and Daves (2010)pages 37 and 38.

QUESTION: Has anyone heard of six-sigma quality?7.5


7.1.2.4 Coefficient of variation

Another measure combines risk and return into a single number. This is called the coefficient of variation (CV). CV measures risk per unit of expected return.

CV = σ

R7 2 Portfolio return and risk



7.2 Portfolio return and risk

Consider a portfolio with n securities. Let the percentage of a portfolio invested in security i berepresented by the portfolio weight wi. Note 0 ≤ wi ≤ 1.


Thereforen

i=1

wi = 1

7.2.1 Portfolio return

The expected return on a portfolio p can be calculated as:

R p = E [R p] =n

i=1

wiE [Ri] (7.11)

7.2. PORTFOLIO RETURN AND RISK 151

where wi is the weight of security i and E [Ri] is the expected return of security i obtained from Eq.(7.4) or Eq. (7.3).

An example...

7.2.2 What portfolio risk is not

Portfolio risk can not be calculated by simply taking a weighted average of individual risks:



σ2 p =

ni=1

wiσ2i (7.12)

But this is a good thing. In reality, the portfolio’s risk will be less.

7.2.3 Analyzing portfolio risk

• If all securities have the same risk σ2i = σ2, and these risks are independent of each other, then

the standard deviation of the portfolio is given by:

σ p = σ

n1/2

(7.13)

• In reality, everything is related to some extent, so such a simple formula can not be used.


7.2.4 Diversification

• Diversification is critical to managing risk.

• The simplest diversification is called random or naive diversification. This is accomplished by

randomly picking securities from what is available.



7.2.5 Modern portfolio theory

• The inequality in equation (7.12) is due to relationships between the movement of stocks

• Modern portfolio theory (MPT) is essentially the derivation of a portfolio risk measure thataccounts for

1. weighted individual security risks, and

2. weighted co-movements between securities returns.




Figure 7.1: Portfolio risk vs. number of securities


7.2.6 Measuring co-movements in security returns

7.2.6.1 Correlation coefficient

• The relative relationship between co-movements of returns of returns is measured by the cor-relation coefficient ρ:

ρ = +1.0 perfect positive correlation

0 no correlation

−1 0 perfect negative correlation



1.0 perfect negative correlation

• Nothing is perfect.

QUESTION: Intel / Dell positive or negative? American Airlines and Exxon?7.7

7.2.6.2 Covariance

• The absolute measure of co-movement is called covariance σAB.

• To compute covariance using a discrete probability distribution:

σab =n

i=1

Rai − Ra

Rbi − Rb

P ri (7.14)

• To compute covariance using historical data:

cov[a, b] = σab = 1

n − 1

ni=1

Rai − Ra

Rbi − Rb

(7.15)


• Covariance and correlation are related in the following manner:

ρij = σij

σiσ j(7.16)



7.2.7 Calculating portfolio risk

7.2.7.1 Two-security case

For the two-security case portfolio risk σ p is calculated as:

σ2 p = w2

1σ21 + w2

2σ22 + 2w1w2ρ12σ1σ2 (7.17)

An example...


7.2.7.2 The n-security case

In general,

σ2 p =

n

i=1

w2i σ2

i +n

i=1

n

j=1

i= j

wiw jσij (7.18)

=n n

wiwjσij (7 19)



=i=1

j=1

wiw jσij (7.19)

=n

i=1

n j=1

wiw jρijσiσ j (7.20)

Therefore three variables determine portfolio risk:

1. Individual variances, σ 2i

2. Covariances, σij

3. Weights, wi

Note: as the number of securities increases, the importance of each security’s variance decreases.

QUESTION: Why?7.8

7.3. EFFICIENT PORTFOLIOS AND PORTFOLIO SELECTION 157

7.2.8 Markowitz portfolio model

The set of portfolios generated by the Markowitz portfolio model, i.e., feasible portfolios obtainedby varying wi and w j in:

E [R p] =

n

i=1

wiE [Ri] (7.21)

2n n



σ2 p =

i=1

j=1

wiw jσij (7.22)

7.3 Efficient portfolios and portfolio selection

Now that we know how to construct all feasible portfolios, which is best?

7.3.1 Building a portfolio using Markowitz principles

The Markowitz technique for optimal portfolio selection has two steps.

1. Identify optimal risk-return combinations from available risky assets.

2. Choose optimal portfolio from efficient frontier based on investor’s risk preferences.The Markowitz portfolio selection model (how investors should act to diversify) is based on threeassumptions:


A1 Only a single investment period is considered.

A2 There are no transaction costs.

A3 Preferences are based only on expected return and risk

7.3.2 Individual utilityEfficient frontier The set of portfolios generated by the Markowitz portfolio model. These port-

f l h h h h f l l f k



folios have the highest return for a given level of risk.

Indifference curves Curves describing investor preferences for risk and return

Risk averse If given a choice, you will not take a fair gamble (gamble that has equal probabilitiesof gain or loss).

7.3.3 Generating the efficient frontier

Given the following inputs,

• estimates of expected return for each security (n estimates) r i ,

• estimates of risk for each security (n more estimates) σi, and

• correlation of securities (some more estimates) ρij,

a computer program varies portfolio weights until the return is maximized for a given level of risk.

7.3. EFFICIENT PORTFOLIOS AND PORTFOLIO SELECTION 159

7.3.4 Summary of the Markowitz model

1. The model is a two-parameter model (expected return and risk).

2. Portfolios on a given indifference curve are equally “good.”

3. The model does not incorporate risk-free assets.

4. Model input estimation varies.

5 Model is cumbersome As n increases the number of required estimates increases according



5. Model is cumbersome. As n increases, the number of required estimates increases accordingto:

number of estimates = n(n + 3)

2 (7.23)

Elaborating on (7.23), lets look at the number of estimates required for a 3 security case. The

covariance matrix is: σ11 σ12 σ13

σ21 σ22 σ23

σ31 σ32 σ33

However, we know σii = σ2

i and σij = σ ji. Therefore:

σ21 σ12 σ13

σ12 σ22 σ23

σ13 σ23 σ2

3

Finally, the number of estimates required for the Markowitz model includes 3 variances, 3 covariances,and 3 expected returns for a total of 9 estimates.


7.3.5 Alternative method of obtaining the efficient frontier: Excel solver

7.4 Asset pricing models

7.4.1 Capital market theory

CMT is a set of predictions concerning equilibrium expected returns. It is based on some simplifyingassumptions.

1 All i t b l d t R



1. All investors can borrow or lend money at RF .

2. Investors have homogeneous expectations based on expected return, variance of returns, andcorrelations.

3. All investors have the same one-period time horizon.

4. There are no transaction costs.

5. There are no taxes.

6. There is no inflation.

7. No single investor can affect the price of a stock.

8. Capital markets are in equilibrium.

QUESTION: What did we say equilibrium was?7.9

7.4. ASSET PRICING MODELS 161

It is important to note that although these assumptions may seem unrealistic, a true measure of amodel’s worth is its explanatory power.

“All models are wrong, some are useful.“

Introduction of the risk free asset

QUESTION: What is a risk free asset?7.10



7.4.2 The capital market line

Capital Market line: The trade off between expected return and risk for efficient portfolios.Instead of RF, A, and B, the CML is the straight line when applied to the Markowitz efficient

portfolio. Now for a picture...

Market portfolio: The portfolio of all risky assetsUnder CMT, all investors will hold some combination of the risk free asset and the market

portfolio.

QUESTION: Why?7.11

Separation theorem: The decision of which portfolio of risky assets to hold is separate from thedecision of how to allocate investable funds between the risk-free asset and the risky asset.


7.4.3 The security market line

The CML represents the risk/return trade off for combinations of risk free asset and efficient portfolio.The SML represents the risk/return trade off for individual securities or inefficient portfolios.

Beta: A measure of a security’s risk relative to the market.

CAPM: Capital asset pricing model. Relates the required rate of return for a security given itsl l f i k d b b



level of risk as measured by beta. Note the required rate of return is the risk free rate plus a risk premium. The CAPM equation

is simply the equation of the SML:

E [Ri] = Rf + β i(E [Rm]

−Rf ) (7.24)

More information on the inputs to the CAPM model are found in Section 11.4.1. Now for anexample...

7.4.4 Estimating SML (CAPM)

Market Model Linear relationship between the return on each stock to the return on the market.

The SML (collection of β /E [Ri] relationships, is often estimated using standard OLS regression:

Rit = αi + β iRmt + it (7.25)

7.5. TESTS OF THE CAPM 163

In this model, the total return measurement is used. Because all models are wrong and some areuseful, observations will be observed above and below the fitted line. You can estimate beta via theregression above or the following equation:

β i = σim

σ2m

= ρim

σi

σm

(7.26)

7.5 Tests of the CAPM



The conclusions are of CAPM are sensible:

1. Return and risk are positively related - greater risk should carry greater return.

2. The relevant risk for a security is a measure of its market (systematic) risk.

An obvious question is: how well does the model match reality? Extensive research has been doneby academics and by practitioners. There is some consensus on conclusions:

1. The SML appears to be linear.

2. The intercept term is generally higher than RF.

3. The slope of CAPM is generally less steep than posited by the theory.

4. No persuasive case has been made that non systematic risk commands a risk premium. Thatis the ratio of risk/return is not better for a highly risky company and therefore investors arerewarded only for assuming systematic risk.


7.6 Stock market equilibrium

• Consider stock with β = 2, Rf = 8%, and Rm = E [Rm] = 12%.

QUESTION: What is the required return of the stock?7.12

• You expect constant growth of 5%, the last dividend was $2.8571, and the current price is $30.

QUESTION: Should you buy, sell, or hold the stock?7.13



• Thus, in equilibrium, Rs = Rs and P 0 = P 0, with Rs and P 0 set by the “marginal” investor.

7.6.1 Changes in equilibrium prices

• Of course stock prices change day-to-day, minute-to-minute... why?

• Consider the following changes:

Variable Old NewRf 8% 7%E [Rm] 12% 10%β 2 1

g 5% 6%D0 2.8571 2.8571P 0 27.27 ?

7.6. STOCK MARKET EQUILIBRIUM 165

QUESTION: What is the new price?7.14

• Stock prices adjust to changing conditions and expectations

7.6.2 Efficient Markets Hypothesis (EMH)

• Market always in equilibrium: Rs = Rs and P 0 = P 0.

• One can not consistently “beat the market.”



7.6.3 Levels of market efficiency

Weak form All past price and volume information are fully reflected in current prices. You can

not find a “pattern.”Semi-strong form Weak plus public information (earnings reports, management changes, etc.)

Strong form Semi-strong plus private information

7.6.4 Implications

• Can’t “beat the market”: tests support weak and semi-strong EMH but corporate officers cando better than market.

• A quote from Brigham and Daves (2007)


“some investors may be able to analyze and react more quickly...these investors may havea temporary advantage.”

• This does not include any of us gathering data from Yahoo finance, crunching numbers withexcel, and then making a trade.

• If market is strong form efficient management decisions based on under- or over-valuation donot make sense.



QUESTION: Why?7.15

7.6.5 Actual stock prices and returns

Generally expected and realized prices (returns) differ

Investing in international stocks

• May improve diversification.

QUESTION: What is missing in the chapter to support this claim?7.16

• Don’t forget about exchange rate fluctuations. Swiss stocks gained only 4.78% in 2004 in theirlocal currency but 14.18% in USD!

7.6. STOCK MARKET EQUILIBRIUM 167

Stock market reporting

• You can obtain detailed real time info from Bloomberg for a pretty steep fee of course.

• Still not fast enough to beat those with expensive computers moved next door to NYSE orNasdaq servers.



Part II



Corporate valuation

169



Chapter 8

Managerial accounting



g g

Overview

Topic covered in this chapter...

• There are three basic financial statements.

QUESTION: What are they?8.1

• Relevant information on those statements

• How income is inflated and debt is hidden

• “Modifying” financial statements for use by managers and investors: Net income, EPS, EBITDA,NOPAT, FCF, MVA, EVA

171

172 CHAPTER 8. MANAGERIAL ACCOUNTING

• Taxes from company and investor perspectives

8.1 Financial reports

• Include quantitative (what happened) and verbal (why it happened) information

• Provides a picture of operations, the financial position, and outlook

8.2 Balance sheet (BS)



8.2 Balance sheet (BS)

• The balance sheet is a snapshot of current financial position (often includes historical infor-mation).

• The balance: Assets = Liabilities + shareholder’s equity

QUESTION: What order are assets listed in?8.2

QUESTION: What order are liabilities and shareholder equity listed in?8.3

• Where a lot of operating capital measures are derived from.

• Assets are typically reported at [depreciated] book value.

• Assets were purchased via liabilities (debt, accounts payable and accruals, or deferred taxes)and equity (money initially invested by owners and retained earnings).

8.2. BALANCE SHEET (BS) 173

• Remember the beer equation A = L + E

Let’s look at Table 8.1 line-by-line.

4. Current assets

• Inventory accounting as LIFO or FIFO impacts the balance sheet and the income statement.

• Current assets are assets that can be converted to cash within one year



• Current assets are assets that can be converted to cash within one year.

QUESTION: What are some examples of current assets?8.4

5-8. Long-term assets and liabilities• While short-term liabilities are typically used to finance current assets, long-term assets tend

to be funded by long-term liabilities and equity.

QUESTION: Can anyone think of personal finance analogues?8.5

• Long-term assets can be tangible or intangible.

– 7. Tangible: Net PP&E, vehicles, subsidiaries

– 8. Intangible: patents, copyrights, licensing agreements, customer lists, goodwill, etc.


Table 8.1: Balance sheetI. Assets

1. Cash2. Inventories3. Other Current Assets

4. Total Current Assets: #1 + #2 + #3

5. Property, Plant, and Equipment6. Less: Accumulated Depreciation



6. Less: Accumulated Depreciation7. Net PP&E: #5 - #68. Goodwill and Other Assets9. Total Assets: #4 + #7 + #8

II. Liabilities

10. Accounts Payable and Accruals11. Notes Payable12. Accrued Taxes13. Total Current Liabilities: #10 + #11 + #1214. Long-Term Debt

15. Total Liabilities: #13 + #14

III. Equity16. Preferred Stock

17. Common Stock18. Additional Paid In Capital


QUESTION: What is “Net” PP&E?8.6

QUESTION: What is Goodwill?8.7

• As Ross Perot said, “stuff breaks,” their value declines over time. “Net PP&E” is the initialcost less accumulated depreciation.

• There are choices on how much to depreciate each year: straight-line, double declining balance,sum-of-years digits, accelerated schedules, etc.

• Long term liabilities include debt with maturities > greater than one year, pension obligations,and



and...

QUESTION: What else?8.8

13. Current liabilities

• Current liabilities are liabilities due within one year.

QUESTION: What are some examples of current liabilities?8.9

16. Equity: preferred stock

• Preferred Stockholders receive a fixed dividend payment

• The Board of Directors can stop dividend payments. However, when times are good again,typically the missed preferred dividends must be paid before any common stockholders canpay dividends.


17. Equity: common stock

• Common stock holders have voting rights, pre-emptive rights, dividend rights, and residualvalue rights.

• To explain the distinctions between common stock, additional paid-in capital, and total paid-incapital consider a firm started with $100,000 (the total paid in capital). The firm raised the

$100,000 by issuing 1,000 shares with a par value of $1, but a market value of $100. Given the$1 par value, the common stock account item on the balance sheet is $1 x 1,000 = $1,000 andthe additional paid-in capital is 100,000-1,000=$99,000

• Interpretation: The par value is arbitrary and meaningless What really matters is total paid in



• Interpretation: The par value is arbitrary and meaningless. What really matters is total paid-incapital.

20. Equity: retained earnings

• Earnings that are not distributed to common stockholders as dividends are retained earnings.

• Earnings = Cash.


21. Equity: treasury stock

• Companies that repurchase their own stock account for those holdings as Treasury Stock.

• The prudence of repurchasing stock is debatable. One theory is market timing by firm man-agement.


Market and book values

QUESTION: What is the difference between market value and book value?8.11

• One advantage of market value is the current representation of true financial position.

• A disadvantage is the difficulty in “Marking to market” for illiquid assets and liabilities.

Assets



• The book value (reported value) of current assets tends to be close to the market value.

• The book value of longer-term assets (such as equipment depreciated on an accelerated scheduleor land purchased some time ago that has had substantial appreciation) can vary significantly

from the market value.

Liabilities

• The book value of long term liabilities such as long-term bonds will differ from the marketvalue as interest rates and default risk varies.

Equity

• The book value of equity provides little information on the value of the firm.


• However, if all assets and liabilities were “marked-to-market,” the resulting equity value wouldbe a more informative measure, albeit incorrect, measure of market value.

• This points to the very important concept of synergy.

QUESTION: Does anyone want to take a guess at how synergy applies to a larger

true market value of common stock than the estimated market value from a“marked-to-market” ALE equation?8.12

8 3 I (IS)



8.3 Income statement (IS)

• Performance during the period (cash and non-cash items included)

• EBITDA: Earnings before interest, taxes, depreciation and amortization

QUESTION: What is the distinction between depreciation and amortization?8.13

• Net income = net income available to common stockholders = revenues - expenses - taxes -preferred dividends = “the bottom line”

• The income statement is a statement of profitability over a period of time (one quarter or oneyear).

8.3. INCOME STATEMENT (IS) 179

Table 8.2: Income statement1. Net Sales (Revenues) REV 2. Cost of Goods Sold CGS 3. Selling, General, and Administrative SGA4. Earnings Before Interest, Taxes, Depreciation,

and AmortizationEBITDA

5. Depreciation and Amortization DA6. Earnings Before Interest and Taxes EBIT 7. Interest Expense I 8. Earnings Before Taxes EB T



9. Taxes T 10. Net Income N I 11. Common Stock Dividends CS D12. Additions to Retained Earnings ARE

• The high-level equation for the income statement is:

N I = R − E

(net income equals revenues less expenses).

• Let’s look at Table 8.2 line-by-line.


1. Revenues: Revenues are obtained from the sale of goods (e.g., cars) or services (e.g., consultingor air travel.

QUESTION: Do you remember what was said about revenue recognition and thematching principle?8.14

2. Cost of Goods Sold: Includes the variable costs of labor, supplies, utilities, etc.3. Selling, General, and Administrative: Includes costs not directly related to the production of

goods and services such as marketing, advertising, office building (net factory) lease, bonuschecks, etc.



checks, etc.

4. EBITDA: Represents earnings from operations

EBITDA = RE V

−CGS

−SGA

5. Depreciation and Amortization:

(a) Both of these are non-cash expenses.

(b) Firms tend to use accelerated depreciation schedules when reporting to the IRS andstraight-line when reporting to the SEC and shareholders.

QUESTION: Why?8.15

(c) Depreciation is associated with tangible assets while Amortization is associated withintangible assets.

8.3. INCOME STATEMENT (IS) 181

QUESTION: Does it make sense that an intangible asset (such as patents)is depreciable?8.16

6. EBIT = EBITDA − DA

7. Interest Expense. Just as your mortgage has both interest and principle (hopefully), theinterest is tax deductible.

QUESTION: Where is the principal repayment accounted for?8.17

8. EBT = EBIT − I



9. Taxes: Firm must pay Uncle Sam based on EBT.

QUESTION: Why not based on EBIT?8.18

10. N I = EBT − T

11. Common Stock Dividends: If any common stock dividends are paid during the income state-ment period they are reported here.

12. Additions to Retained Earnings: All income that is not distributed to stockholders is anaddition to retained earnings.

ARE = N I − CS D

QUESTION: What if NI < 0?8.19


8.3.1 Statement of retained earnings (SoRE)

• Retained earnings: portion of earnings that has been saved (could be cash, short-term financialinstruments, long-term financial instruments, equipment purchases, etc.)

• The statement

retained earningst = retained earningst−1 + net incomet − dividendst

8.3.2 Net cash flow



• Net income (a.k.a., accounting profit) includes non-cash items, net cash flow does not:

net cash flow (NCF) = net income

−noncash rev. + noncash charges

≈ net income + depreciation and amortization

QUESTION: Why add non cash charges and subtract non cash revenues? 8.20

QUESTION: Why the “≈” sign?8.21

• Non cash revenues: changes in deferred revenues

• Non cash expenses: depreciation, amortization, goodwill

8.4. STATEMENT OF CASH FLOWS (SOCF) 183

8.4 Statement of cash flows (SoCF)

• casht = casht−1 + net incomet because...

– preferred dividends

– non cash adjustments

– changes in working capital: increase in inventories → decrease cash, decrease in accountspayable → reduction of cash

– purchase/sale of fixed assets



– issue stock → raises cash; buyback stock or repay debt → reduces cash

• All of the above are reflected in SoCF

QUESTION: What are the three categories in the SoCF?8.22

Three hints:

1. Category one includes net income and non cash adjustments; changes in current assets andliabilities (accounts payable, receivables, inventories, accruals)

2. Category two includes the purchase/sale of fixed assets.

3. Category three includes the sale/issue of short/long term debt, sale/issue of stock.


• Net cash flow from operating activities is perhaps the most important item in all of the financialstatements.

1. Net income can be manipulated and presented as positive all the way to bankruptcy.

2. It is more difficult to lie about cash.

3. If net cash flow is negative your operations (core business) is not generating cash.

4. With negative cash flows comes borrowing and/or liquidation of short term investmentsso watch the trend.



• Let’s walk through the statement of cash flows, Table 8.3, line-by-line.

Operating activities

• Line 1. Net income. This is directly from the income statement and includes numerous non-cash expense deductions (e.g., depreciation and amortization) and non-cash income additions(e.g., increase in accounts receivable)

• Line 2. Depreciation and Amortization. This is a non-cash deduction from EBITDA that isreversed by adding it back.

• Line 3. Increase in Accounts Payable. Some of the items in CGS are materials used forproduction but purchased on credit. Thus, the deduction from revenues in the amount of ∆AP was a noncash expense that is reversed by adding ∆AP to NI.


Table 8.3: Statement of cash flowsI. Operating activities

1. Net Income

Additions (Noncash Expenses)

2. Depreciation and Amortization3. Increase in Accounts Payable4. Decrease in Other Current Assets5. Increase in Accrued Income Taxes



Subtractions (Noncash Income)

6. Increase in Accounts Receivable

7. Increase in Inventories8. Net Cash From Operating Activities

II. Investing activities

9. Property, Plant, and Equipment and Other Assets10. Increase in Goodwill and Other Assets11. Net Cash From Investing Activities

III. Financing activities

12. Increase in Notes Payable13. Increase in Long-Term Debt14. Common Stock Dividend Payments


• Line 4. Decrease in other Current Assets. “Other” current assets are current assets other thanaccounts receivable inventories, cash, marketable securities, bank loans, and notes payable.Suppose office supplies were purchases last year but not yet used (you got 10,000 reams of paper at a huge discount). This year, the year of reporting, the company uses $3,000 of paper.This triggers, or impacts the balance sheet via a reduction in other current assets of $3,000and impacts the income statement as a noncash expense included in SG&A. Since this noncash

expense was deducted from revenues via SG&A, it is reversed by adding the decrease in othercurrent assets to NI. As an example:

MPK 23 =@N5



M

MJKK 23 .0/.&2A &''/1'C 9'/ MPK

-1(/0 6900/31 &''/1' 0/A96/A <; MPK

• Line 5. Increase in Accrued Income Taxes. NI includes taxes owed (T) on earnings beforetaxes (EBT) for that period. However, the check to the IRS will not be mailed until nextperiod. In addition to appearing on the Income Statement, the amount of taxes owed (T) isalso added to the Balance Sheet liability “Accrued Income Taxes.” Therefore an increase inaccrued taxes represents a noncash expense that was deducted from revenues that is reversed

by adding the increase in Accrued Income Taxes to NI.

• Line 6. Increase in Accounts Receivable.


QUESTION: Why is this a “non-cash income”?8.23

• Line 7. Increase in Inventories. An increase in inventory is not explicitly accounted for in theIncome Statement yet may be necessary as part of routine operations. For example, an increasein inventory may be the result of preparation for sales in the next period. The additionalinventory may have been purchased with cash in which case the deduction of ∆Inventory from

NI is obvious. The additional inventory could have been purchased on credit in which theincrease in inventory would be offset by the increase in Accounts Payable.

• Line 8. Net cash from Operating Activities.



Investing activities

• Line 9. PP&E and Other Assets. This includes the purchase (use of cash - negative number)or sale (source of cash - positive number) of long-term tangible assets.

QUESTION: What if PP&E were purchased via long-term debt?8.24

• Line 10. Increase in Goodwill and Other Assets. Indicates the purchase (use of cash, negativenumber) or sale (source of cash, positive number) of intangible assets.

• Line 11. Net Cash Used in Investing Activities. The sum of #9 and #10.


Financing activities

• Line 12. Increase in notes payable.

QUESTION: Does an increase in notes payable reflect cash received or cashspent by the company?8.25

• Line 13. Increase in Long-Term Debt. Some deal as notes payable.

• Line 14. Common Stock Dividend. Dividend payments are cash expense.

• Line 15. Purchase of Treasury Stock. Cash is required to purchase treasury stock.

• Line 16 Net Cash Flow from Financing Activities The sum of #12 to #15



• Line 16. Net Cash Flow from Financing Activities. The sum of #12 to #15.

Cash reconciliation

• Line 17. Net increase in cash and marketable securities. The sum of #8, #11, and #16.• Line 18. Beginning cash and securities. Self explanatory.

• Line 19. End of period cash and securities. The sum of #7 and #18.

8.5 Modifying accounting data

• Thus far data presented for creditor, tax collector, SEC, and accounting consultant perspective.• Now we modify the data for use by managers and investors.

8.5. MODIFYING ACCOUNTING DATA 189

8.5.1 Operating assets and total net operating capital (TNOC)

• Firms and divisions differ in financial structure, tax situation, and mix of operating and non-operating assets.

• To make apples-to-apples comparisons, you want to look at what a manager generates (oper-ating income, EBIT) with what he/she has (operating assets).

• First modification: Total assets

– Non operating assets: cash and short-term investments in excess of that required fornormal operations land held for future use etc



normal operations, land held for future use, etc.

– Operating assets: necessary to operate business

∗ long-term operating assets: plant and equipment

∗ current operating assets (a.k.a., operating working capital): inventory, cash, accountsreceivable

• Where are we going with this? Money from investors (stockholders, bondholders, banks whogave loans) is used to acquire capital. “too much” capital → lower ROI for investors.

• Note: not all capital is paid for by investors.

QUESTION: Where does the rest come from?8.26


• Capital acquired with investor-supplied funds

NOWC = OC A − OCL (8.1)

where NOWC is Net Operating Working Capital, OCA is Operating Current Assets, andOCL is Operating Current Liabilities

• General rule of thumb: if item is a discretionary choice it is not an operating current asset nora operating current liability.

QUESTION: Can anyone think of some examples?8.27



• Thus, in general:

OCA = cash + accounts rcv. + inventories (8.2)

OCL = accounts pay. + accruals (8.3)

• Now, add operating long-term assets (OLTA) (typically net PP&E) and you have Total Net

Operating Capital (TNOC, aka, operating capital, net operating assets, capital)

TNOC = NOWC + OLT A (8.4)

• An example...

• Things to look for

8.5. MODIFYING ACCOUNTING DATA 191

1. Trend of capital relative to revenue (from income statement)

2. Are we increasing capital but not increasing revenue?

3. How are capital increases financed (investor money or suppliers/employees)?

8.5.2 Net operating profits after taxes (NOPAT)

• If two companies differ only in amount of debt the company with more debt would have higherinterest expenses and therefore lower...

QUESTION: ...What?8.28



• This is where NOPAT comes in:

NOPAT = EBIT (1 − τ ) (8.5)

where τ is the tax rate

• Things to look for

1. The trend in NOPAT relative to EPS. Increase in NOPAT with decrease in EPS →decrease in EPS not due to decrease in operating profit.

2. NOPAT/NOWC: How good is the company at managing operating cash, suppliers, andaccruals: more profits with less investor-supplied capital?


8.6 Free cash flow (FCF)

• Free cash flow is the cash flow available after necessary fixed asset and working capital invest-ment to sustain ongoing operations. The investment to sustain ongoing operations could beviewed as the investment required to maintain the current sales growth rate.

QUESTION: What is another way to interpret FCF?8.29

8.6.1 Calculating FCF

1 C t th t i t t i ti it l



1. Compute the net investment in operating capital.

∆TNOC t = TN OC t − TNOC t−1 (8.6)

2. Compute FCF

F CF = NOP AT − ∆TNOC (8.7)

An example...

QUESTION: Interest expense is used to lower taxable income and tax expense. Doesthat mean that net income will increase with interest expense due to the lower tax

expense?8.30

8.6. FREE CASH FLOW (FCF) 193

8.6.2 Uses of FCF

• Essentially two: (1) invest in capital (tangible and intangible) for growth or (2) return toinvestors (debt repayment, pay dividends, pay interest, repurchase stock).

• Some evidence exists that associates high levels of FCF with lower firm value. This could bedue to wasteful spending with all that extra money (overpaying for acquisition).

8.6.3 FCF and corporate value

• Again, FCF is cash available to distribute to stakeholders.

• This takes into consideration necessary investment (e g ongoing operations or investment to



• This takes into consideration necessary investment (e.g., ongoing operations or investment tomaintain g).

• Value = discounted value of future FCF discounted at WACC.

• We will see how to forecast FCFs in future chapters and connect this with a model to arriveat firm value.

8.6.4 Evaluating FCF, NOPAT, and operating capital

• What to look for

1. If F C F < 0, investors had to provide additional money via cash, debt issuance, or equityissuance to maintain operations.


2. If F C F > 0 and growing: need to make some decisions on what to do with the money.

• Is F C F < 0 necessarily bad?

– If NOPAT < 0 it could be bad.

– If NOPAT > 0 could be a high growth company that requires additional investment toachieve the desired growth level.

QUESTION: How can a firm have positive FCF yet negative NOPAT?8.31

• Okay, additional money from investors is used for growth, but is this growth profitable enough ?

• Insert the Return on Invested Capital (ROIC):



• Insert the Return on Invested Capital (ROIC):

ROIC = NOP AT

TNOC

(8.8)

• We will see in Section 8.7.2 if ROIC > W ACC then the growth is profitable

• An example...

8.7 MVA and EVA

• Thus far we have not mentioned stock price.

• Managers should be maximizing shareholder value.

8.7. MVA AND EVA 195

• MVA and EVA can be used to assess managerial and firm performance.

8.7.1 Market Value Added (MVA)

• Let MVS = market value of stock.

M V A = M V S − equity= (common shares outstanding)P − total common equity (8.9)

where P is the current stock price.



• Note: MVA is based on the time frame of company inception to the present.

• To assess current management we turn to EVA.

8.7.2 Economic Value Added (EVA)

• EVA is the difference between after-tax profits and after-tax cost of all capital.

• The cost of debt capital is fairly straightforward: the interest rate agreed to

• The cost of equity represents the opportunity cost: the rate the investor could have earnedelsewhere.


• EVA computation:

EV A = NOP AT − TNOC (WACC )

= TNOC (ROIC − WACC ) (8.10)

QUESTION: Where did the second equation come from?8.32

• Thus, if ROIC < WACC , further investment of free cash flows reduces the value of the firm.

• EVA is used for structuring compensation packages and can be applied at the division level aswell as the firm-level.



• MVA incorporates the stock price and is based on expectations about the future.

• Managers are typically evaluated and compensated based on what they have done (EVA)rather than what they are expected to do (MVA).

8.8 Federal tax considerations

• In valuing an asset, we are concerned about usable income.

• This means income after taxes (e.g., NOPAT and FCF).

• In the U.S. there are corporate taxes and personal income taxes.

8.8. FEDERAL TAX CONSIDERATIONS 197

8.8.1 Corporate income taxes

• Fairly easy to calculate. If you get fancy, you could setup a single formula in Excel.

• An example...

8.8.1.1 Interest and dividend income

• Corporations may own stock (including its own) and receive dividends.

• Corporations may own interest-bearing financial instruments.

• Interest is taxed at regular corporate tax rate.



g p

• Dividends are not. A significant portion is excluded prior to applying corporate tax rate:

Ownership % ExclusionOW N < 20% 70%20% ≤ OWN < 80% 80%OW N ≥ 80% 100%

• The different tax rates impact the manager’s decision to invest FCF in bond investments, stock

investments, or internal projects.• Example: GE has $100,000 in FCF. Assume GE has two choices


1. Bonds that pay 8% coupons annually ($8,000 per year)

2. Preferred stock that pays 7% dividends ($7,000 per year)

QUESTION: Which should they purchase?8.33

8.8.1.2 Interest and dividend payments

• Finance operations with debt → pay interest (which can be deducted from income)

• Finance operations with equity → pay dividends (not deductible)



• Again, this impacts a manager’s decision: how should I finance the firm or project?

• Consider the pre-tax income required to pay $1 in dividends.

pre-tax income to pay $1 dividend = 1

1 − τ (8.11)

• An example...

8.8.1.3 Corporate capital gainsCorporate capital gains are taxed at same rate as operating income.


8.8.1.4 Corporate loss carry back and carry forward

• Carry back: an operating loss in 2008 can be applied to 2007 or 2006 to recover taxes paid inthose years (2 year limit).

• Carry forward: an operating loss in 2008 can be used to reduce taxable income in 2008 → 2028(20 year limit).

• Another means to minimize tax payments (read: another loophole).

8.8.1.5 Improper accumulation to avoid dividend payments

QUESTION Wh ld i id di id d ?8 34



QUESTION: Why would a corporation want to avoid dividend payments?8.34

• Retained earnings (i.e., unpaid dividends) in excess of $250,000 must be proven to be necessary to meet the reasonable needs of the business.

8.8.1.6 Consolidated corporate tax returns

• If parent company owns more than 80% it can consolidate and uses losses from one companyto offset income of another

• Allows losses associated with risky new ventures to offset income from core business (read:another loophole).


8.8.1.7 Overseas income

• Foreign earnings reinvested overseas are not subject to U.S. taxes.

• When foreign earnings are returned to the U.S., a credit is applied for foreign taxes paid priorto computing U.S. tax due.

• The result: fewer dollars taxed at the higher U.S. rate (read: another loophole).

8.8.2 Taxation of small businesses: S-corps

• Thus far we have talked about “normal” corporations, aka, C-corps



• S-corp may elect taxation as proprietorship/partnership or C-corp

• Advantageous for companies that pay ≈ 100% of income as dividends.

QUESTION: Why?8.35

• S-corp also allows for limited liability.

8.8.3 Personal taxes• Ordinary income includes wages, profits from partnership/proprietorship, investment income.


• With a progressive tax system the more you make the larger percentage1. Sometimes referredto as a marginal tax rate that increases with income.

• Most municipal bond interest income is not subject to federal taxes.

• Capital assets (real estate, stocks, bonds):

– Long-term (held more than 1 year) gains tax: lower rate, 15%– Short-term (held less than 1 year) gains tax: higher rate, ordinary income

• As of 2003 dividends were taxed at capital gains rate.



1don’t forget there are many deductions, i.e., loopholes, to get around this




Chapter 9

Financial statement analysis

O



Overview

Topic covered in this chapter...• Why analyze financial statements?

1. To enable fair performance comparisons.

2. To evaluate and identify trends in financial position. This is useful for managementdecision making.

• Different ratios, who uses them, and what for• Actions that impact ratios

203

204 CHAPTER 9. FINANCIAL STATEMENT ANALYSIS

• Using “ratio analysis” and the DuPont system to maximize firm value

• Ratio sensitivity to seasonality, debt/equity position, sales stimulation efforts, etc.

• Establishing norms or target ratio values

9.1 Why ratio analysis?Firm A Firm B

total debt 5,248,760 52,647,980interest charges 600,000 3,000,000

9 1



QUESTION: Which firm is “stronger?” 9.1

9.2 Liquidity ratios

Liquidity ratios provide insight on a firm’s ability to pay for short term (≤ 1 year) liabilities.

9.2.1 Current ratio

current ratio = current assets

current liabilities

(9.1)

• Current assets include cash, marketable securities, accounts receivable, and inventories.

9.3. ASSET MANAGEMENT RATIOS 205

• Current liabilities include accounts payable, short-term notes payable, current maturities of long term debt, accrued expenses (taxes, wages, etc.).

QUESTION: Do you want the number to be “high” or “low?” 9.2

• Although in general you would work towards the industry average there are a couple reasonswhy you would not.

QUESTION: Why?9.3

9.2.2 Quick or acid test ratio



quick ratio = current assets − inventories

current liabilities (9.2)

• Maybe those inventories are not so liquid...

• As either liquidity ratio approaches unity the company may be unable to meet current liabili-ties.

9.3 Asset management ratios

• How efficient is firm at managing assets?


• If asset levels (inventories) are too low the firm may miss sales opportunities. Have you everbeen to the store, wanting to buy something, it wasn’t there, so you bought something else?

• If asset levels are too high the firm may be wasting free cash flow (firm value). Also, reducedfree cash flow translates into lower firm value.

9.3.1 Day sales outstanding (DSO)

DSO = receivables

average daily sales (9.3)

where average daily sales is sales ÷ 365.

• Days sales outstanding is also known as average collection period (ACP) and days’ sales in



y g g p ( ) yreceivables (DSR).

• DSO represents the average time from sale to receiving cash for that sale.

QUESTION: What do we need to be mindful of the revenue recognition methodwhen considering this definition of DSO?9.4

• Compare with stated credit policies (sales terms) .

QUESTION: By the way, where does one find a company’s sales terms? 9.5

– If DSO > sales terms → customers are not paying on time

9.3. ASSET MANAGEMENT RATIOS 207

– If DSO ≤ sales terms → they are1

• Watch the trend!

9.3.2 Inventory turnover ratio (ITR)

IT R =

sales

inventories (9.4)

• Represents the number of times per year (or quarter) inventory turns (restocked)

• If number is significantly below industry average the firm may have obsolete products (largedenominator) or poor sales force (small numerator).



• Dell...

QUESTION: High or low ITR?9.6

• If ITR is low, then current ratio is questionable.

QUESTION: Why?9.7

• Important: Sales are reported at market prices but inventory at cost. If you were to be precise,

substitute cost of goods sold for sales.1maybe you could charge a little more?


Days sales in inventory

DSI = inventories

average daily sales

• How long does inventory sit around?

9.3.3 Fixed assets turnover ratio (FATR)

FATR = sales

net fixed assets (9.5)

• Net fixed assets = gross fixed assets - cumulative depreciation

• Compare with industry averages



p y g

QUESTION: When comparing companies within an industry, does it matter when

they purchased their production equipment?9.8

9.3.4 Total asset turnover ratio (TATR)

TATR = sales

total assets (9.6)

• Can be interpreted as a combination of ITR and FATR.

QUESTION: Why?9.9

9.4. DEBT MANAGEMENT RATIOS 209

9.4 Debt management ratios

• As we saw in earlier chapters, the use of debt, now called financial leverage , can magnify gainsand losses.

• In the presence of financial leverage equity holders still have control. However, creditors aremindful of risks involved in supplying credit. More equity → less risk → lower interest rates.

QUESTION: Does this sound familiar to any common real world debt/equityarrangement?9.10

• Let’s look at some ratios used by creditors to assess risk...

D b i



9.4.1 Debt ratio

debt ratio = total liabilities

total assets (9.7)

• If > 50% then the majority of financing from borrowed funds.

• If high it may be more difficult (read: costly) to obtain additional funds.

9.4.2 Times interest earned (TIE)

T IE = EBIT interest charges

(9.8)


• Similar to a liquidity ratio (ability to pay current liabilities) with a focus on interest charges

• A measure of ability to pay interest charges from operating income

• If “low” (e.g., below industry average) it may be more difficult (read:costly) to obtain additionalfunds.

9.4.3 EBITDA coverage ratio (ECR)

EC R = EBITDA + lease payments

interest + principal payments + lease payments (9.9)

• A measure of ability to service debt



• A measure of ability to service debt

• Two problems with TIE

1. Must repay principal too! Also, some firms lease equipment.

2. EBIT does not represent available cash since the non cash charge of depreciation wasremoved.

QUESTION: Why have lease payments in the numerator?9.11

QUESTION: Long-term lenders focus on TIE, short term lenders on ECR. Why?9.12

9.5. PROFITABILITY RATIOS 211

9.5 Profitability ratios

9.5.1 Profit margin on sales (PM)

P M = net income available to common stockholders

sales (9.10)

• Low PM could be due to

1. High costs related to inefficient operations

2. Higher debt → higher interest expense → smaller numerator

QUESTION: Is higher debt necessarily bad?9.13



9.5.2 Basic earning power (BEP)

BE P = EBIT

total assets (9.11)

The ability to convert assets into earnings, without considering interest or taxes.

9.5.3 EBITDA Margin

EBITDA margin = EBITDAsales


• EBITDA margin does not include impact of capital structure and taxes.

• EBITDA margin is a more direct measure of operating profitability.

9.5.4 Return on total assets (ROA)

ROA = net income available to common stockholders

total assets (9.12)

If low, check BEP:

• BEP low → company not converting assets into earnings

• BEP high → may have high interest (more debt)



• BEP high → may have high interest (more debt)

9.5.5 Return on equity (ROE)

ROE = net income available to common stockholders

common equity (9.13)

• The “bottom line” ratio

• When comparing to industry averages, look at both ROA and ROE. For instance if ROAi <ROA but ROE i ≈ ROE then the firm is using debt. More on this later.

9.6. MARKET VALUE RATIOS 213

9.6 Market value ratios

9.6.1 P/E ratio

• Price per share divided by earnings per share, same as before

• High P/E ratios may represent high growth prospects.

QUESTION: Why?9.14

• Low P/E may represent riskier firm.

QUESTION: Why?9 15



QUESTION: Why?9.15

9.6.2 Price/cash flow ratio

• Cash flow = net income + depreciation and amortization

• Could also use price/sales, price/EBITDA, and so on

• “What works on Wall Street” calls the Price/Sales ratio the “king” of value ratios.

QUESTION: Any idea why?9.16


9.6.3 Market/book ratio (M/B) or book/market (B/M) ratio

• Book value per share (B) = common equity / shares outstanding

• Let P = M = market value per share

• Therefore the Market-to-Book ratio is M/B... simple huh?

• Represents how much (M) investors are willing to pay for $1 in accounting (book, B) value• Typically M/B > 1.

QUESTION: Why?9.17

• High M/B (low B/M) → lower risk



• Low M/B (high B/M)

→ ‘distressed’ company

• Related to Fama-French 3-factor model factor: HML:

HM L = Rhigh B/M − Rlow B/M

9.7 Trend, common size, and percent change analysis

9.7.1 Trend analysisPlot ratios vs. time for company and industry average and interpret results. For example:

9.7. TREND, COMMON SIZE, AND PERCENT CHANGE ANALYSIS 215

Table 9.1: ROE interpretations

ROE i ROE (industry average) Interpretationdecreasing steady or increasing fix something!steady steady average performanceincreasing increasing average performanceincreasing steady or declining pay bonuses or mgt. is cheating

9.7.2 Common size analysis

• Divide all income statement items by sales

• Divide all balance sheet items by total assets



• Facilitates comparison of line-items across firms with varying size

• Bonus: also, when doing trend analysis, dividing by sales or assets removes the effect of inflationand can make the variables stationary (i.e., usable for regression analysis). More on this whenyou go get your Ph.D.!

• Now for a couple examples of common size analysis...

9.7.3 Percent change analysis• Simply compute the percent change from previous year, quarter, or year-ago quarter


• An example...

9.7.4 Summary

Ratios, trend, common size, percent change, and DuPont equation (next section) analysis can beused to pinpoint areas of improvement and “make the case,” whatever that case may be.

QUESTION: Why use multiple ways to say the same thing?9.18

9.8 The DuPont equation

ROA = P M × TATR (9.14)



( )

=

net income

sales × sales

total assets

• Example

– PM = 3.8%, i.e., made 3.8 cents for every dollar in sales

– TATR, i.e., turned assets into sales 1.5 times during year

– Return on assets (for the year) = 3.8 x 1.5 = 5.7%

• If financed exclusively with equity → liabilities=0 → assets=equity → ROA=ROE

9.8. THE DUPONT EQUATION 217

• If you do use debt, common equity < total assets.

QUESTION: Why?9.19

• Therefore ROE ≥ ROA. Lets go back...

ROA =

net income

total assets (9.15)

ROE = net income


If using debt common equity < total assets therefore ROE > ROA



• Can connect ROA to ROE with the equity multiplier

EM = total assets


thereforeROE = ROA × EM (9.18)

• Now, the extended DuPont equation

ROE = P M × TATR × EM (9.19)


• Why go through all of these algebraic gyrations? To isolate areas that impact ROE and for“what-if” analyses. In equation (9.19) we see:

– Operating efficiency (PM)

– Asset management efficiency (TATR)

– Financial leverage (EM)

9.9 Benchmarking

• Benchmarking: comparing with leading companies in the same industry



• Can benchmark with other industries also. For example, if a portion of your business sellsproducts online, compare that to amazon.com.

• Can obtain benchmarks from D&B, RMA, Reuters, etc. Or, develop yourself:

1. Obtain data on all firms from Compustat

2. Sort on industry and ROE

3. Take the top 10% in each “bin” as your benchmark

9.10. CLOSING COMMENTS ON RATIO ANALYSIS 219

9.10 Closing comments on ratio analysis

9.10.1 Uses

• Managers - diagnose and correct operational, investing, and financing inefficiencies

• Creditors - assess risk and charge accordingly

• Investors - efficiency, risk, and growth analysis

9.10.2 Limitations

1. Conglomerates - what is the “industry average” if you do business in 5 different industries?

QUESTION: What can you do?9.20



y

2. Don’t use industry average alone: do not strive to be simply average, shoot for above average.

3. Watch out for inflation - is upward trend simply due to inflation?

QUESTION: What can you do?9.21

4. Seasonality - be mindful of sowing vs. reaping season when comparing quarterly results

5. Window dressing - take 2-year loan

→ cash now but long term liability

→ release results

(leverage ratio lower and current ratio higher) → after results release, payoff debt (leverageratio high again)


6. Cheating with leased assets - not a debt, not on balance sheet, therefore distorts turnover anddebt ratio measures

7. What is “good?” - Example, does high current ratio indicate strong liquidity or excessive cash?

8. Interpretation of good and bad ratios - which are more important?

9. Accuracy/legitimacy of financial statements

9.11 Qualitative analysis

Don’t stop with ratio, trend, common size, % change analysis, and benchmarking. Consider somequalitative factors as well.



9.11.1 Porter’s five forces1. Buyer power (customers)

2. Supplier power

3. Threat of substitutes

4. Barriers to entry

5. Competition

9.11. QUALITATIVE ANALYSIS 221

9.11.2 The AAII list

1. Are revenues spread across customers?

2. Are revenues spread across products?

3. Are multiple suppliers available?

4. Any overseas business? Political (where did our jobs go) and business issue that impactsbottom line (shipping stuff back and forth, exchange rate, etc.).

5. Competition

6. Future prospects

7. Legal environment? Do you fix operations or hire lobbyists? Think about how the cell phone



companies fought vigorously against number portability.




Chapter 10

Financial statement forecasting

Overview



• We will investigate the major components of strategic plan and role of pro-forma (projected)financial statements.

QUESTION: What is the difference between strategy and tactics?10.1

• Forecasts using the percent of sales method given nothing more than previous financial state-ments

• Use of industry average ratios

• Impacts of forecast errors

223

224 CHAPTER 10. FINANCIAL STATEMENT FORECASTING

• Economies of scale, lumpy assets, excess capacity

• Estimating required funds with the financial statement method and AFN formula method

• Sustainable growth rate: What it is and how to determine it.

10.1 Financial planning

A little philosophy:

“Failing to plan is planning to fail.”“A person who does not know where they are going may end up anywhere”



10.1.1 Strategic plans

Corporate purpose solely technological excellence → bad; solely profits → bad. Do both.

QUESTION: Can you think of any examples?10.2

Corporate scope products and customers; the market tends to value focused firms more thandiversified.

QUESTION: Why?10.3

10.1. FINANCIAL PLANNING 225

Corporate objectives quantitative (e.g., ROE, market share, earnings growth, etc.) and qualita-tive (e.g., successful roll-out of corporate branding)

In sum, purpose (technological excellence and shareholder value maximization) → scope (e.g., softdrinks only, but globally) → objectives (market share, ROE) → strategy (no-frills airline vs. high-end)

10.1.2 Operating plans• Aka, the tactical plan

• Detailed plans on how to meet corporate objectives

• Typically a 5 year plan



10.1.3 Financial planFive steps:

1. Construct pro-forma financial statements: reveals profit impacts of operating plan

2. Compute funding requirements

3. Break down internal (profit) and external (loans, bonds, equity issuance) funding sources

4. Connect management compensation with successful completion of operating plan (absolutelyno golden parachutes!!!)


5. Monitor and adjust

Although there are 5 steps , there are 3 components :

1. Sales forecast

2. Pro-forma financial statements

3. External financing plan

10.2 Sales forecast

• “Past is prologue”

• When estimating (forecasting) growth , the arithmetic average can be too high. An example...



• Computing compound growth rate is problematic as well. The estimate is sensitive to beginningand end points.

sales0(1 + g)n = salesn (10.1)

• Regression analysis is a better approach. Assuming constant growth you need to take naturallog of sales. Behind the scenes of LOGEST function of excel:

salest = (1 + g)tsales0

ln [salest] = t ln[1 + g] + ln [sales0]

= a0 + a1t (10.2)

10.3. PERCENT OF SALES FORECASTING METHOD 227

with a0 = ln [sales0] and a1 = ln[1 + g]. LOGEST estimates a0 and a1 and reports exp[a1] =exp[ln[1 + g]] = 1 + g

• An example...

• In practice, you will complicate this a bit by including economic indicators (e.g., GDP), interestrates, analysts estimates, estimates for E [RM ], etc. Inclusion of these factors may improveexplanatory power (i.e., R2 of regression).

• The regression/LOGEST method provides a good baseline for growth rate estimation.

• Accuracy is important: g higher than reality → excess inventory, loans, interest, etc.; g lowerthan reality → not enough inventory, lose market share, etc.

10 3 Percent of sales forecasting method



10.3 Percent of sales forecasting method

• Begin with sales forecast

• Look at historical average and industry average ratios

• Forecast

10.3.1 Analyze historical ratios

• Take historical financial statements and divide by given year’s sales


• This approach assumes everything is proportional to sales in the past and in the future. Notnecessarily true for all financial statements items.

• For example, in the short run consider sales and PP&E.

– Manufacturing firm: higher sales may come without building more plants (just run theexisting ones longer).

– Retail firm: higher sales may come only from more stores (more PP&E) as opposed toincreasing daytime hours.



• In the long run,sales will be related to PP&E.

10.3.2 Forecast the income statement

• Keep in mind all statements are interconnected.

• IS: depreciation → BS: Net PP&E; IS: additions to retained earnings → BS: retained earnings


Table 10.1: Forecasted income statement# Description Forecast1. Revenues REV t+1 = RE V t(1 + g)2. Cost of goods sold CGS t+1 = γ cgs × REV t+1

3. Dep. exp. DE t+1 = γ de × P P E t+1

4. EBIT EBIT t+1 = RE V t+1 − CGS t+1 − DE t+1

5. Int. exp. IE t+1 = I E std,t+1 + IE ltd,t+1

IE std,t+1 = rstd,t+1 (ST Dt − ST I t)IE ltd,t+1 = rltd,t+1 × LT Dt

6. Earn. b4 tax EBT t+1 = EBIT t+1 − IE t+1

7. NI b4 pref. div. NIBPDt+1 = (1 − τ )EBT t+1

8. Pref. div. exp. P DE t+1 = νP S t9. NI avail. to cs N I t+1 = NIBPDt+1 − P DE t+1

10. No. shareout ncs,t+1 = ncs,t

D h DP S DP S ( )



11. Div. per share DP S t+1 = DP S t(1 + gd)12. Com. div. exp. CDE t+1 = ncs,t+1 × DP S t+1

13. Add. ret. earn. ARE t+1 = N I t+1 − CDE t+1

14. Earn per share EP S t+1 = N I t+1/ncs,t+1

10.3.2.1 Comments on forecasted income statement

1. Sales (revenues) forecast: see Section 10.2


2. Cost of goods sold: use most current period’s data to establish CGS multiplier1 γ cgs =CGS t/REV t

3. Depreciation expense: use most recent period’s data to establish DE multiplier γ de = DE t/PPE t

4. Earnings before interest and taxes: revenues less costs and depreciation expense

5. Interest expense: calculated as interest charges less interest income

• With multiple debt obligations and investments with different maturities, interest rates,fixed, variable comes difficulty in estimating interest expense. Therefore we use twosimplifying assumptions.

(a) How much debt?

– Do not use beginning of year number.




– Do not use end of year number.QUESTION: Why not?10.5

– The simplification: use beginning of year debt and add 0.5% to the interest rate:

ST Dt+1 = ST Dt (10.3)

LT Dt+1 = LT Dt (10.4)

1You could also average the multipliers of the previous 5 years to estimate the multiplier for next year or use some other elaborateestimate.


Net effect: an approximation that avoids circularity and accounts for possibleincreases in the amount of debt2.

(b) What interest rate(s)?

– Specify just two: short-term and long-term

– Short-term rate: rates typically “float” so best estimate is “usually” the previousrate. Therefore:

rstd,t+1 = rstd,t + 0.5% (10.5)

– Long-term rate: Companies have several LT debt obligations with different rates.Some LT debt may be paid off and new LT debt issued. Therefore, take averageof existing LT debt rates and new rates:

rltd,t+1 = 1

n + 1

ni=1

rltd,i + rltd,t

+ 0.5% (10.6)



with rltd,i = rate of debt obligation i and rltd,t = the current market rate for adebt with maturity equal to ?

QUESTION: Why n + 1?10.6

.

QUESTION: Why add 0.5%?10.7

6. Earnings before taxes: EBIT less interest expense

2Note: year t data represents the end of year t and therefore the beginning of year t + 1.


7. Net income before preferred dividends: EBT less taxes.

QUESTION: Can anyone tell me where the equation came from?10.8

8. Preferred dividend expense: ν represents the stated preferred dividend rate and P S t representsthe level of preferred stock

9. Net income available to common stockholders: NIBPD less PDE

10. Number of shares outstanding: adjust for any issuances or repurchases

11. Dividends per share: adjust for any increase or decrease in dividends

12. Common stock dividend expense: number of shares times DPS

13 Additions to retained earnings: NI less CDE



13. Additions to retained earnings: NI less CDE

14. Earnings per share: easy calculation

10.3.3 Forecast the balance sheet

• Sales growth → assets must grow → must obtain funds → how much and where from?

• Use percent of sales technique: γ = t/salest.

• Assumptions for preliminary forecasts


1. Short-term investments will not change.

QUESTION: Why?10.9

2. Mature company therefore ncs,t+1 = ncs,t

3. Constant dividend growth rate

4. Most companies do not use preferred stock ∴ P S t+1 = P S t



5. No new long term bonds ∴ LT Dt+1 = LT Dt

6. Allow for short term loans via notes payable (a.k.a., commercial paper).

QUESTION: Sound familiar?10.10


Table 10.2: Forecasted balance sheet# Item ForecastAssets

Current assets1. Cash CASH t+1 = γ cash × REV t+1

2. Short term investments ST I ∗t+1 = ST I t3. Accounts receivable ARt+1 = γ ar × REV t+1

4. Inventories IN V t+1 = γ inv × REV t+15. Total current assets T CAt+1 = CASH t+1 + ST I t+1 + ARt+1 + IN V t+1

Long-term assets6. Net PP&E P P E t+1 = γ ppe × REV t+1

7. Long-term investments LT I t+1 = γ lti × REV t+1

8. Total long-term assets T LAt+1 = P P E t+1 + LT I t+1

9. Total Assets T At+1 = T CAt+1 + T LAt+1

Liabilities



Liabilities

Current liabilities10. Accounts payable AP t+1 = γ ap × REV t+1

11. Accruals ACC t+1 = γ acc × REV t+1

12. Notes payable N P ∗t+1 = N P t13. Total current liabilities T CLt+1 = AP t+1 + ACC t+1 + N P t+1

Long-term liabilities14. Long-term bonds LT Bt+1 = LT Bt

15. Total long-term liabilities T LLt+1 = LT Bt+116. Total Liabilities T Lt+1 = T CLt+1 + T LLt+1

Shareholder’s equity17. Preferred stock P S t+1 = P S t18. Common stock CS t+1 = C S t19. Retained earnings RE t+1 = RE t + ARE t+1


10.3.3.1 Comments on the forecasted sheet and AFN

Aside from the standard percentage of sales and accounting calculations, a few of the forecasteditems require a little attention.

• 2. Short-term investments: consistent with the earlier assumption, forecasted ST I is the same

as previous year’s S T I . This may be adjusted after the preliminary forecast.

• 12. Notes payable: short-term loans are possible. This may be adjusted after the preliminaryforecast.

• 22. Total liabilities and stockholder’s equity: an approximation since forecasted assets doesnot necessarily equal forecasted liabilities and stockholder’s equity.

10 11



QUESTION: Why not?

10.11

• 25. Additional funds needed: if positive, need to obtain external funds; if negative, need toplace extra money somewhere

AF N t+1 > 0 → N P t+1 = N P t + AF N t+1

AF N t+1 < 0 → ST I t+1 = ST I t + |AF N t+1|

• This is an preliminary forecast that will be revised after comparison with operation goals (nextsection)


• γ ’s can be historical average, most recent ratio, or other estimate

• An example...

10.3.4 Analysis of the forecast

• Compare ratios to industry average

• Determine ways to improve ratios

• Re-forecast under different improvement scenarios and sales growth estimates

QUESTION: Why use different sales forecasts?10.12



10.3.4.1 Observations

1. AR too high.

• γ ar is 20% higher than industry average

• DSO = AR/avg. daily sales is high as well

• Negatively impacts ROA, ROE, ROIC (which are also significantly lower than industryaverage)


QUESTION: What corrective actions can be done?10.13

2. Inventories too high

• γ inv is almost twice the industry average! IT R is almost half. Note: IT R = 1/γ inv

• Negatively impacts ROA, ROE, ROIC, and TATR (which is also significantly lower)

QUESTION: What corrective actions can be done?10.14

3. Debt too high

• Current ratio significantly lower than industry average

• Extra debt → extra interest expense → lower profit margin (3.8% vs. industry average



5.0%)

QUESTION: Why did management decide to layoff workers and close certainoperations?10.15

10.3.4.2 Revised forecast

• Terminating people increased NOP AT

• AR policy adjustment reduced AR


• Profit margin increase → increased ARE t+1

• Inventory controls → lower DSO, reduced inventories

• Now have a negative AFN.


• ROA, ROE, and ROIC also increase

• γ inv, γ ar, and DSO still above industry average

10.3.4.3 Concluding remarks

• In practice you will analyze different scenarios.

When looking at impact of changes on stock price, this is called value-based management.



• When looking at impact of changes on stock price, this is called value based management.

• Forecasting is an iterative process: a lot of what-if analyses

• When facing potential layoffs also consider company-wide pay cuts.

10.4 The AFN formula

• Although the preliminary forecast assumed constant ratios revisions may cause year t+1 ratiosto be different than year t.

10.4. THE AFN FORMULA 239

• However, if we assume the ratios are constant (i.e., γ ’s do not change from one year to thenext) we can estimate the forecasted AFN using the AFN formula.

• Also, the AFN formula breaks down funding of internal vs. external sources.

AF N t+1 = (A∗/REV t) ∆REV − (L∗/REV t) ∆REV − (P M ) (REV t+1) (RR) (10.7)

where RE V t+1 = (1 + g) REV t and ∆REV = RE V t+1 − REV t

Table 10.3: AFN formula inputsItem DescriptionA∗ Required assets. When operating at full capacity, required assets equal total

assets (A∗ = A) otherwise A∗ < AA∗/REV t Capital intensity ratio: level of assets used to support sales

L∗ liabilities that increase spontaneously with sales. Typically the sum of accounts



payable and accruals.QUESTION: Why not notes payable?10.17

L∗/REV t Liabilities that increase spontaneously as a percentage of salesP M Profit margin: net income available to common stockholders divided by

revenuesRR Retention ratio: portion of earnings that are retained (e.g., not paid out as

dividends)

∆REV Change in revenues, REV t − REV t−1


• Consider this a “back of an envelope” estimate

• The financial statement method is more accurate.

• The required asset increase represented by (A∗/REV t) ∆REV will be paid using funds from:

1. spontaneous liability increase (L∗/REV t) ∆REV , and/or

2. retained earnings (P M ) (REV t+1) (RR), and

3. external resources AF N .

• An example...

AFN and growth

• The maximum growth rate using internal funds is the internal growth rate:



IGR = ROA × RR1 − ROA × RR

(10.8)

QUESTION: What are some examples of internal funds?10.18

• The maximum growth rate without additional equity financing, thus with additional debtfinancing, while maintaining the same debt to equity ratio is the sustainable growth rate:

SGR = ROE

×RR

1 − ROE × RR (10.9)

10.5. FORECASTING WITH VARIABLE BALANCE SHEET RATIOS 241

QUESTION: What are some examples of external funds?10.19

• Note, we are using ROAt, ROE t, and RRt, not t + 1 values.

• Equations (10.8) and (10.9) are based on end of period t data (Angell, 2011).

10.5 Forecasting with variable balance sheet ratios

10.5.1 Constant ratios

Thus far we have discussed constant ratios.

10.5.2 Economies of scale

The ratio of inventory to sales decreases with sales. Conversely, we tend to observe more sales for



each additional unit of inventory. Also, the relationship can be nonlinear.

10.5.3 Lumpy assets

• When capacity can not be increased smoothly

• For example, to build more cars another factory must be constructed since building 1/100thof a factory is infeasible.

• There are options available prior to making those huge investments:


1. Add more shifts to existing plants

2. Share someone else’s plant

3. Take turns building plants

10.5.4 Excess capacity (capacity under-utilization) adjustments

Suppose capacity utilization was 96% while sales were $3B. To estimate sales assuming full capacity:

full capacity salest = actual salest

capacity utilizationt

= 3B

0.96 = 3.125B

QUESTION: Where did this formula come from?10.20

• A new target fixed assets/revenues ratio can be computed. Doing so assumes the plant(s) willbe running at full capacity next period:



γ ∗F A = F Aactual,t

REV full,t= 1.0

3.125 = 32%

In English the ratio of actual time t fixed assets that could produce 3.125B in revenues if operating at full capacity.

• Now incorporate revenue target to determine F A∗t+1, the amount of fixed assets needed to

accommodate sales forecast of REV t+1.

F A∗t+1 = γ ∗F A × REV t+1 = 0.32(3.3) = 1.056B

10.5. FORECASTING WITH VARIABLE BALANCE SHEET RATIOS 243

• Note the preliminary forecast had this number at 1.1B, Thus at full capacity fewer fixed assetsmust be purchased (precisely, 1.1B - 1.056B = 44M fewer).

• Therefore AFN is reduced

AF N ∗ = AF N − 44M = 118M − 44M = 74M

• There are at least two ways to deal with excess capacity. In other words, at least two ways to

deal with capacity under utilization.

1. Just use the financial statement method.

2. Ignore capacity utilization and use AFN assuming full capacity to compute F At+1. Nextincorporate capacity utilization and compute F A∗

t+1, Then use this revised AFN formula:

AF N ∗t+1 = AF N t+1 − (F At+1 − F A∗t+1) (10.10)



Chapter 11

Cost of capital

Overview

Cost of capital is important when deciding whether or not to take on a project, to acquire a

d h f l



• company, and the structure of compensation plans.

• We will examine the components of a company’s cost of capital.

• WACC and why it is necessary for capital budgeting.

• “Weights” used in WACC.

• Three methods for determining the cost of common equity (CAPM, DCF, BYPRP) .

• Flotation costs and WACC.

245

246 CHAPTER 11. COST OF CAPITAL

• Time variability of WACC.

• Different WACCs for different divisions and projects.

11.1 The weighted average cost of capital (WACC)

Capital components common stock, preferred stock, and...

QUESTION: ...What else?11.1

Component cost required rate of return for each component

WACC weighted average of component costs

Target capital structure the target weights, e.g., a 30/10/60 debt/preferred/common target.

WACC R (1 ) R R (11 1)



WACC = wdRd(1 − τ ) + w psR ps + wsRs (11.1)

• WACC is the cost of a marginal or new dollar of capital.

• The weights should be based on target capital structure. But what exactly is the target capitalstructure? Many academic articles have been written on what the target structure is, is therea target structure, does it vary over time, why does it vary over time, etc. For now we canpresume the current book value of debt, book value of preferred stock, and market value of common stock can be used to approximate the target weights.

11.2. COST OF DEBT RD(1 − τ ) 247

QUESTION: If you plan on issuing only debt in the planning period, can you get awaywith WACC = Rd?11.2

11.2 Cost of debt Rd(1 − τ )

• Marginal debt: new issues of debt

• Embedded debt: historical or pre-existing debt

• Since we are computing WACC to assess costs in the upcoming or planning period, we considerthe cost of marginal debt to be the relevant cost.

• Interest payments on debt are tax deductible. Therefore the after-tax cost of debt is Rd(1−τ ).

• Flotation costs (i.e., costs associated with issuing new debt) are typically small thus we ignorethem for now.



11.3 Cost of preferred stock R ps

• Preferred dividends are not tax deductible.

• Although firms legally do not have to pay preferred dividends they typically do.

QUESTION: Why?11.3


• Flotation costs are significant for preferred stock, therefore these costs are incorporated intothe component cost:

R ps = D ps

P ∗n=

D ps

P n − F ps(11.2)

with D ps is the level of preferred dividends, P ∗n is the amount received after flotation (under-writing) costs F ps are deducted from the issue price P n.

• An example...

11.4 Cost of common equity Rs

• Common equity can be raised by

1. issuing new stock (cash enters company), or

2 t i i i ( h i i )



2. retaining earnings (cash remains in company).

• In either case, the investment in common equity must earn the required return Rs.

• Mature firms typically do not issue new stock for a few reasons.

1. High flotation costs.

2. Negative signal.

QUESTION: What negative signal is sent with issuing new shares?11.4

11.4. COST OF COMMON EQUITY RS 249

3. More common stock → higher supply → lower price.

• Rs is also the opportunity cost , the return investors could obtain elsewhere with their cash.

• There are at least three methods to estimate Rs. Choose the method with the more reliabledata. However, you may consider taking the average of all three estimates.

11.4.1 CAPM approach“Simple” four step process:

1. Estimate RF

2. Estimate M RP = E [RM ] − RF

3. Estimate β

4 C l l t R R β (E[R ] R )



4. Calculate Rs = RF + β i(E [RM ] − RF )

11.4.1.1 Estimating the risk free rate

• Nothing is truly “risk free” since interest rates and therefore prices and returns fluctuate.

• We use the long-term Treasury Bond (T-Bond) rate for RF for 3 reasons.

1. Most stockholders are long-term investors.


QUESTION: Why might this be true?11.5

2. T-bill rates are more volatile than T-bond rates and Rs.

3. CAPM estimate is for holding period → estimate for cost of equity is for long-term project(long-term holding period) → use T-bond

• The 10 year T-bond is generally used. You may also use a bond that has a similar maturityas the project under consideration.

11.4.1.2 Estimating the market risk premium (MRP)

Historical MRP

• Could use the historical number (average) from Ibbotson Associates or calculate it yourself.

• But which do you use, geometric or arithmetic average?

• Risk premiums vary over time therefore either average will be wrong



• Risk premiums vary over time therefore either average will be wrong.

Forward-looking MRP

• This crystal ball will be wrong also.

• Use market dividend yield to estimate E [RM ].

QUESTION: What is the dividend yield?11.6


• We have seen this before:

E [RM ] = RM = D1

P 0+ g =

D0

P 0(1 + g)

+ g

QUESTION: Where do we obtain g?11.7

• Dividend yields and growth rates can be obtained from Reuters.com, finance.yahoo.com, or

other financial websites.• An example...

QUESTION: Can you name two problems with using dividend growth rates?11.8

• Could also use published analysts’ forecasts to estimate g .

QUESTION: What are two problems with analysts’ forecasts?11.9



• Some evidence from academics put the forward-looking MRP in the 1% to 2.55% range

So what is the right MRP to use?

• Brigham and Daves (2010) opinion: use a value between 3.5% and 6.5%.

• If prices are relatively high → strong demand → less risk averse → use value closer to 3.5%

• If prices are relatively low → low demand → more risk averse → use value closer to 6.5%


11.4.1.3 Estimating beta

• Recall the market model:

Ri,t = α + β iRM,t (11.3)

• A few problems:

1. What holding period and time frame? Four to five years of monthly returns or one to

two years of weekly data are typically used.

2. Which index? S&P500, Willshire, DJIA, World market, etc.

3. Estimated, adjusted, or fundamental beta?

4. Wide confidence interval for beta estimates

5. An example...

11 4 1 4 B i i it ll t th



11.4.1.4 Bringing it all together

Rs = RF + β (E [RM ] − RF ) (11.4)

11.4.2 Discount cash flow (DCF) approach

Rs =

D1

P 0 + g (11.5)


• In the CAPM approach, we applied this formula to market returns to obtain E [RM ] and thenRs via the CAPM equation.

• Here we go direct using the firm’s dividend yield and expected growth rate to obtain Rs.

11.4.2.1 The inputs

Historical growth rates If growth rates are relatively stable you may use historical averages

Retention growth model If historical ROE and retention ratios averages are relatively stable,use:

g = ROE × RR

Analysts’ forecasts Can use the median, mean, and range of analyst forecasts to obtain expectedg.

11.4.2.2 Illustration



11.4.2.2 Illustration

An example...

11.4.2.3 Evaluating methods for growth rate estimation

• Dividend yield is estimated fairly precisely.

QUESTION: Why?11.10


• The problem is g .

• Believe it or not analysts forecasts are usually the best for DCF cost of capital estimates.

11.4.3 Bond-yield-plus-risk-premium (BYPRP) approach

• Produces a ball park estimate

• Add 3% to 5% to firm’s rltd

• Therefore:

Rs = rltd + bond risk premium

QUESTION: Where does “bond risk premium” come from?11.11

• BYPRP is the least precise method



• BYPRP is the least precise method.

11.4.4 Estimation approach comparisons

• Use judgement when evaluating varied estimates.

• Most firms use CAPM (74% to 85% of the time), about 16% use DCF, and BYPRP is used

primarily by private companies.

11.5. WACC FACTORS 255

11.5 WACC factors11.5.1 Outside of firm control

Level of interest rates Lower rates translate into lower cost of debt and equity.

Tax rates Tax rates affect that cost of debt and can also affect cost of equity.

Market risk premium The market risk premium (MRP) is a function of perceived risk and de-gree of risk aversion. This affects the cost of equity directly and debt indirectly through asubstitution effect.


11.5.2 Within firm control

C i l li ( ) β β[l ] l k h h ( )



Capital structure policy (1) β = β [leverage] → more leverage → more risk → higher Rs; (2)use more debt → more risk → higher Rs and Rd but potentially lower WACC.

Dividend policy More dividends → less cash available for investment → may have to incur moredebt or issue stock to fund projects → impacts W ACC

Investment policy Invest in same line of business

→ generally no change in risk

→ no change in

WACC . Invest in new line of business → change in risk → change in W ACC


11.6 Divisional and project risk adjustmentsThis section deals with adjustments for different divisional and project risks.

11.6.1 Divisional cost of capital

• Different divisions have different risk levels and therefore divisional W ACC .

• Assuming no debt you could use CAPM and portfolio theory:

1. Obtain divisional betas as described in Section 11.6.2.

2. Divisional betas → divisional required rates of return.

3. Weighted average beta (“portfolio beta”) → overall required rate of return.

• An example: SML for divisions...



p

• The approach applies to firms with debt as well → compute divisional W ACC

11.6.2 Measuring divisional betas

Pure play method Find several comparable single-product companies and average their betas

Accounting beta method Regress ROAi,t = α + βROAM,t

11.7. FLOTATION COST ADJUSTMENTS 257

11.6.3 Individual project cost of capital

1. Sort projects into subjective categories (high, average, and low risk)

2. Use the divisional W ACC as a baseline. E.g., let the division’s W ACC div = 10%:

Project risk WACC criterionabove average 12%average 10%below average 8%

11.7 Flotation cost adjustments



11.7 Flotation cost adjustments

• Privately raised debt → no flotation costs

• Retained earnings → no flotation costs

• Public debt or stock issue → incur flotation costs


11.7.1 DebtItem DescriptionM face or par valueIN T dollars of interest paidN bond maturityR∗

d(1 − τ ) after-tax cost of debt adjusted for flotation costsRd (1 − τ ) after-tax cost of debt in the absence of flotation costs

F flotation percentage

M (1 − F ) =N

t=1

IN T (1 − τ )

(1 + R∗d (1 − τ ))t

+ M

(1 + R∗d (1 − τ ))N

(11.6)

• The (1 − F ) is the flotation cost adjustment resulting in R∗d > Rd.

QUESTION: Why is the after tax cost of debt adjusted for flotation costs (F > 0)greater than the after tax cost of debt when there are no flotation costs



g(F = 0)?11.13

• An example: τ = 0.40, M = 1000, F = .01, N = 30, Rd = 0.10.

QUESTION: What is the after-tax cost of debt adjusted for flotation costs?11.14

• Note: R∗d would be higher if F were higher or N were smaller. An example...

11.7. FLOTATION COST ADJUSTMENTS 259

11.7.2 Newly issued equity• For a constant growth stock

R∗s =

D1

P 0(1 − F ) + g (11.7)

• R∗s represents the return required on funds raised with new issue when flotation costs are

incorporated.

• R∗s > Rs to achieve Rs on funds used to purchase the new stock

• An example: P 0 = 23, F = 0.10, g = 0.08, D1 = 1.24. Compute R∗s and Rs

• If firm earns 14% on new funds → EPS is unchanged → dividends remain the same → priceis unchanged

• If firm earns < 14% on new funds → EPS declines → dividends declines → stock price declines



p

• If using CAPM to determine the cost of equity, you can follow the procedure above to obtainR∗

s − Rs, then add this amount to the CAPM estimate for Rs for a flotation cost-adjusted costof capital

• Or, you could obtain Rs estimates from CAPM, DCF, and BYPRP methods; compute the

average, then add R∗s − Rs


11.8 Cost of capital estimation problems1. Private firms: “the goal” not necessarily maximizing shareholder wealth; data availability;

however, in general, principles apply.

2. Small businesses: typically privately owned.

3. Measurement: recall cost of equity issues (CAPM data, g estimate, “bond risk premium”).

4. Project cost of capital: difficult to measure project risk.

5. Capital structure weights: establishing these weights requires effort.

11.9 Common WACC estimation mistakes

1. Never use coupon rate of existing debt. Use current market yields.



2. When computing M RP , do not mix historical average for E [RM ] with current RF .

3. Do not use book value of equity when estimating capital structure weights. This is historical.You want the target weights based on current market values.

4. Only funds from investors should be considered as capital components. Do not count accounts

payable and accruals.

11.A. EXAMPLE RS ESTIMATION 261

11.A Example Rs estimationThe following calculations are based on www.reuters.com data for Intel corporation (ticker INTC)as of 2009.10.26.

CAPM approach to Rs estimation

Rintc = Rf + β intc (E [Rm] − Rf ) (11.8)

Step 1: Define the risk free rate as the rate on a 10 year treasury bond:

Rf = 3.56%

Step 2: Compute the expected return of the market using data for the S&P500. You could use



data for the broad market etf V T I instead.

E [Rm] = Rm = D1

P 0+ g

= D01 (+g)

P 0+ g


The S&P 500 dividend yield is D0/P 0 = 1.46% and the five year S&P500 dividend growth rate isg = 9.42%.

E [Rm] = 1.46(1.0942) + 9.42

= 11.02

Step 3: Compute the market risk premium:

M RP = E [Rm] − Rf = 11.02 − 3.56 = 7.46

Step 4: Given β intc = 1.18 compute the required return for Intel Rintc using Eq. (11.8):

Rintc = 3.56 + 1.18(7.46) = 12.36

DCF approach to Rs estimation

You could “go direct” to obtain Rs = Rintc:



Rintc = D0 (1 + g)

P 0+ g

The dividend yield for intel is D0/P 0 = 2.78%. The long term growth rate for Intel is g = 10.92%.Therefore the required return for Intel is:

Rintc = 2.78(1.1092) + 10.92 = 14.00

Chapter 12

Value based management

12.1 Overview

• Distinction between operating assets and non-operating assets; net operating working capital

and net working capital• FCF relation to alue of firm’s operations and the corporate aluation model (CVM)



• FCF, relation to value of firm’s operations, and the corporate valuation model (CVM)

• CVM vs. DDM

• Re-visit EVA & MVA and relate to value based management (VBM)

• Value-based management, relationship to CVM, and VBM alternatives

• Relevance of corporate governance

263

264 CHAPTER 12. VALUE BASED MANAGEMENT

• Enron/Worldcom, corporate governance, options, and regulation

12.2 Corporate valuation

• Basic decision process: (1) forecast financial statements for alternatives; (2) choose alternativewhich maximizes present value

• Forecast using techniques of Chapter 10 on page 223. Discount free cash flows using WACCas computed in Chapter 11 on page 245.

QUESTION: What is wrong with the DDM method from Chapter 5 in the context of evaluating alternatives?12.1

• Insert the Corporate Valuation Model that does not depend on dividends.

12 3 The corporate valuation model



12.3 The corporate valuation model

• There are two types of assets:

Operating land, buildings, machines, inventory; also includes intangibles such as customerlists, patents, reputation, know how

Non operating short-term investments, investments in other businesses

12.3. THE CORPORATE VALUATION MODEL 265

• Most companies have a low percentage of non-operating assets (e.g., WalMart has about 1%of total assets in non-operating assets). Here we focus on operating assets.

• Note: Ford, in 2004, had about 8.5% of total assets in non-operating assets.

QUESTION: Do you see something wrong with this?12.2

12.3.1 Estimating the value of operations

Three steps to obtaining the value of operations, V op:

1. Forecast financial statements assuming constant growth at some point in the future

2. Compute FCF for each forecast year



3. Discount FCFs using WACC to obtain the current value of operations

12.3.1.1 Forecast financial statements

Use the techniques of Chapter 10. Lets look at an example...


12.3.1.2 Compute future FCFs1. Compute required working capital1 (RW C ), which is similar to NOWC from Chapter 8, for

each year including the current year:

RW C t = (CASH t + ARt + IN V t) − (AP t + ACC t) (12.1)

An example...

2. Compute required operating capital (ROC ), which is similar to TNOC from Chapter 7, foreach year including the current year:

ROC t = RW C t + F At (12.2)

where F At is net fixed assets at time t. An example...

3. Compute free cash flows for each of the forecast years:

F CF t = NOP AT t − ∆ROC t (12.3)



QUESTION: What is NOP AT ?12.3

An example....

QUESTION: What does the negative FCF mean?12.4

1sometimes referred to as “required net operating working capital”


12.3.1.3 Discount FCFsAn example.... MagnaVision...

P V [F CF 2007] = −18/(1.1084)1 = −16.24

P V [F CF 2008] = −23/(1.1084)2 = −18.72

P V [F CF 2009] = 46.40/(1.1084)3 = 34.07

P V [F CF 2010] = 49/1.10844 = 32.46

Now, use constant growth formula to obtain 2010 value of future FCFs:

V op,2010 = 49(1.05)

0.1084 − 0.05 = 880.99

Note: Free cash flows grow at 5% forever after 2010. This is sometimes referred to as the horizonvalue. Now discount horizon value and add to other PVs:

P V [V op,2010] = 880.99

1 10844 = 583.69



1.10844

V op,2006 = −16.24 − 18.72 + 34.07 + 32.46 + 583.69 = 615.26

12.3.2 Estimating share price using CVM

1. Begin with the present value of all future FCFs, V op


2. Add the value of non-operating assets, V non-op to obtain the total value of the firm:

V tot = V op + V non-op (12.4)

QUESTION: What is V non-op in our example?12.5

V tot calculation...

3. Obtain the value of common equity, V CE

V CE = V tot − V debt − V PS (12.5)

QUESTION: What are V debt and V PS in our example?12.6

V CE calculation...



4. Divide by the number of shares, shrout, to obtain the share price

P = V CE

shares outstanding (12.6)

Our example...


12.3.3 A quick look at Market Value Added (MVA)• We know V CE = 369, and this represents the market value of equity. I.e., the market value of

common stockholder’s claims to future FCFs.

QUESTION: What is the implicit assumption here?12.7

• However, the book value of common equity is BV CE = 245

• Therefore, the market value added is:

MV A = V CE − BV CE

For our example...

12.3.4 Establishing the share price using DDM



Recall the multi-growth discussion of Chapter 5:

V CE =n

t=1

Dt

(1 + Rs)t + Dn (1 + g)

Rs − g

1

(1 + Rs)n (12.7)

Our example (with Rs = 14%)...


12.3.5 CVM or DDM?• If you care about VBM (the next section) → use CVM

• Mature firm already paying dividends → DDM

• Firm in temporary high (or low) growth mode → will have to estimate future dividends anyway→ DDM or CVM

• Never paid dividends, new firm about to IPO, division that is going to be spun off → CVM

12.4 Value-based Management (VBM)

• Four factors that impact firm value as established with the CVM

1. Sales growth, g

2. Operating profitability, OP = N OPAT /Sales



3. Capital requirements, C R = ROC/Sales

4. Cost of capital, W ACC

Note: Required working capital RW C of this chapter is the same as net operating workingcapital NOWC of Chapter 8. Also, required operating capital ROC of this chapter is the

same as total net operating capital TNOC of Chapter 8.

12.4. VALUE-BASED MANAGEMENT (VBM) 271

• To see how these factors impact firm value, consider the CVM of a constant growth firm

V op,t = F CF t+1

WACC − g (12.8)

– Expand the numerator

F CF t+1 = NOP AT t+1 − ∆ROC t+1

= OP (Salest+1)

−(CR(Salest+1)

−CR(Salest))

= OP (Salest)(1 + g) − CR(Salest(1 + g) − Salest)= OP (Salest)(1 + g) − CR(Salest)(g)

– Insert into (12.8)

V op,t = OP (Salest)(1 + g) − CR(Salest)(g)

WACC − g (12.9)

– Examine how each factor impacts V op,t

Sales growth Looking at (12.9) the impact of g is ambiguous.QUESTION: Why is it ambiguous?12.8



However, we know from Chapter 8 that growth is profitable enough if ROIC >WACC :

EV A = ROC (ROIC − WACC ) (12.10)

with ROIC = NOPAT/ROC . In other words, investment adds value when ROIC >WACC . You can also think of EVA as the value added to a company by its opera-

tions in a given time period.


Operating profitability Clearly V op,t increases with OP . Intuitively, higher profitabil-ity is always better (more earnings per unit of sales is always better)

Capital requirements Lower CR → subtract less in the numerator → larger numer-ator → larger V op,t. Intuitively, a low CR means more sales per unit of operatingcapital.

Cost of capital Looking at the denominator, a smaller WACC implies a larger V op.Intuitively, access to cheap capital (low WACC ) increases value while expensivecapital (high W ACC ) decreases value

– These insights apply to all firms although the specific equations apply only to constantgrowth firms.

• VBM is the process or series of decisions that increase value by improving one or more of thefour factors.

QUESTION: Since “improving” g does not necessarily mean increasing or

decreasing g, how does a manager improve value as impacted by the salesgrowth rate?12.9



• A four-step VBM approach

1. Assess where you are: prepare preliminary (Rev 0) financial statement forecasts, computeFCFs, EVA, MVA, OP, and CR.

2. Identify areas to improve value via the four value drivers.


3. Forecast financial statements for multiple scenarios.

QUESTION: Why multiple scenarios?12.10

4. Compute MVA, EVA, OP, CR, for each scenario and choose the value-maximizing sce-nario.

12.4.1 Assess where you are

• Compute OP, CR, ROIC, and EVA.

QUESTION: Do you need financial statement forecasts for these measures?12.11

• Forecast financial statements



• Compute FCFs

• Compute MV

• A summary for our example if they stay the course:


Item Memory Instruments WholeSales 1,000.0 500.0 1,500.0ROC 870.0 200.0 1,070.0NOPAT 78.6 36.0 114.6OP = N OP AT/Sales 7.9% 7.2% 7.6%CR = ROC/Sales 87.0% 40.0% 71.3%ROIC = NOPAT/ROC 9.0% 18.0% 10.7%WACC 10.5% 10.5% 10.5%

g 5% 5% 5%EV A = ROC (ROIC − WACC ) -13.1 15.0 2.1M V A = V op − ROC -160.4 305.5 145.1

12.4.2 Identify areas to improve value

• You should avoid developing a plan to boost sales growth for the memory division.

12 12



QUESTION: Why?12.12

• Reduce C Rmem so that ROIC ∗mem > WACC

• Increase gins since ROIC ins > WACC


12.4.3 Forecast financial statements under multiple scenarios12.4.4 Compute value parameters for each scenario and choose best

A few sample calculations...



Chapter 13

Capital structure

Overview

• The market value of a firm V is the sum of the market value of debt D and the market valueof equity S .

V = D + S (13.1)



QUESTION: Why?13.1

• Does the choice of debt vs. equity financing impact the value of the firm? Is one better thanthe other? These are the questions addressed in this chapter.

• All items in Eq. (13.1) vary over time due to

277

278 CHAPTER 13. CAPITAL STRUCTURE

1. changes in market interest rates,

2. changes in the market risk premium, and

3. changes in the market perception of future cash flows generated by assets.

QUESTION: Can you elaborate on how these three factors impact V, D, and S in Eq.(13.1)?13.2

13.1 Tax free world

• Don’t you wish you lived in such a world?

• Modigliani and Miller (1958) proposed that in the absence of taxes the choice of debt vs. equityis irrelevant.

• Proposition I: The value of the firm is not impacted by leverage.

VL = VU (13.2)



V L V U (13.2)

This implies

WACC L = W ACC U (13.3)

QUESTION: Where did Eq. (13.3) come from?13.3

13.1. TAX FREE WORLD 279

• Proposition II: The cost of equity increases with leverage.

rsL = rsU + (rsU − rdL)

DL

S L

(13.4)

QUESTION: How do we know, by looking at Eq. (13.4), that rsL increases withleverage?13.4

• We could derive Eq. (13.4) from Eq. (13.2), Eq. (13.3) andWACC = wdRd + wsRs, (13.5)

but lets move on if we are in agreement that Propositions I and II lead to Eq. (13.4).

• A numerical example. Suppose UnleveredCo has EBIT of 500,000, no growth (g = 0), andgiven its level of market risk rsU = 14%. Further suppose LeveredCo is identical to Un-leveredCo with the exception of 1,000,000 in debt financing at rdL = 8%. Taking the MM

propositions as gospel, compute and summarize wd, ws, Rd, Rs, WACC , D, S , and V forboth firms.



• Intuitively it makes sense for the cost of equity to increase with leverage since the presence of debt subordinates the claims of equity holders. That is, in the event of bankruptcy more of

the remaining assets must be transferred to debt holders. This leaves less for stockholders.


13.2 A world with taxes• Modigliani and Miller (1963) extend their earlier work and note the distribution of after taxearnings is affected by leverage.


• The MM1963 results suggest firm value increases with debt.

QUESTION: If that is true, how should a firm finance itself?13.6

• Proposition I: The value of the firm increases with debt due to the tax deductibility of debt.

V L = V U + tcDL (13.6)

where tc is the corporate tax rate.

• Proposition II: The cost of equity increases with debt, but at a slower rate than a world without



Proposition II: The cost of equity increases with debt, but at a slower rate than a world withouttaxes.

rsL = rsU + (rsU − rdL) (1 − tc)

DL

S L

(13.7)

QUESTION: Why do I say “at a slower rate”?13.7

13.3. SUMMARY 281

• These propositions imply

WACC L ≤ WACC U

In English, the weighted average cost of capital decreases as debt increases in a world withcorporate taxes. Let’s prove it for fun!

• Let’s try another numerical example. Same as before but add tc = 40%. What are wd, ws, Rd,

Rs, W ACC , D , S , and V for both the levered and unlevered firms?

13.3 Summary

No taxes With taxesUnlevered Levered Unlevered Levered

wd 0 28% 0% 39.33%ws 100% 72% 100% 60.67%R 8% 8% 8% 4 8%



Rd 8% 8% 8% 4.8%Rs 14% 16.33% 14% 16.33%D 0 1,000,000 0 1,000,000S 3,571,429 2,571,429 2,142,857 1,542,857V 3,571,429 3,571,429 2,142,857 2,542,857

WACC 14% 14% 14% 11.80%


• Proposition II has been interpreted as: “... corporate taxes cause the cost of equity to rise lessrapidly with leverage than it would in the absence of taxes.”



Part III

Project selection



283



Chapter 14

Project selection criteria

Overview

• Capital budgeting is the decision process for identifying projects that maximize firm’s value.

• Project ideas come from executives and employees.



14.1 Project classifications

Several types of projects must be evaluated by management. The classifications vary in the level of

analysis required and potential rewards.

285

286 CHAPTER 14. PROJECT SELECTION CRITERIA

Table 14.1: Project classifications, analysis, and rewardsClassification Analysis Potential rewardsMaintenance of business DCF,simple necessary to maintainCost reduction DCF, detailed incremental improvementExpansion of existingproducts/markets

DCF, detailed high

Expansion into new products/markets DCF, detailed highSafety/environmental DCF, moderate necessary

Research and development decision tree/realoptions

high

Long-term contracts DCF medium-high

14.2 Decision rules

A manager is faced with multiple projects to evaluate, rank, and make accept/reject decisions. Thissection describes seven methods used to rank projects for inclusion into the capital budget. Let’s



begin with a couple definitions:

Independent projects Projects whose cash flows are independent of each other.

Mutually exclusive projects Projects whose cash flows are dependent on each other in the sense

that all projects can not be accepted at the same time due to constraints.

14.2. DECISION RULES 287

QUESTION: Any idea what some of those constraints might be?14.1

14.2.1 Payback period

Payback period is the number of years required to recover original investment and is calculated asfollows:

payback = year before full recovery + |unrecovered cost at start of recovery year|

cash flow during year (14.1)

Consider net cash flows for two projects S (Sooner) and L (Later):

Year: 0 1 2 3 4Project SNet cash flow -1,000 500 400 300 100Cumulative NCF -1,000 -500 -100 200 300Project LNet cash flow -1,000 100 300 400 600

Cumulative NCF -1,000 -900 -600 -200 400

QUESTION: Why is it necessary to compute the cumulative NCF?14.2



Clearly, payback for Project S should be between 2 and 3 while payback for Project L should bebetween 3 and 4. The calculation...

QUESTION: If these projects are mutually exclusive, which one would you choose?

14.3


• Unfortunately, the net cash flows do not take the cost of capital into consideration (i.e., they

are not discounted).

• Insert “Discounted payback.”

14.2.2 Discounted payback period

Same calculation as “payback period” but discount the net cash flows first. Then compute the

cumulative discounted net cash flow (NCF) followed by the discounted payback.

Year: 0 1 2 3 4Project SNet cash flow -1,000 500 400 300 100P V [NCF, 10%] -1,000 455 331 225 68Cumulative P V [NCF, 10%] -1,000 -545 -214 11 79Project L

Net cash flow -1,000 100 300 400 600P V [NCF, 10%] -1,000 91 248 301 410Cumulative P V [NCF, 10%] -1,000 -909 -661 -360 50



The calculation...

QUESTION: Why is the discounted payback number larger than the regular payback

calculation?14.4


• Both regular and discounted payback ignore cash flows after the payback period. For example,

what if project L had a positive cash flow of $5,000 in year 5 it would be the clear winner?

• If you are going to discount cash flows, you might as well use...

14.2.3 Net present value (NPV)

To obtain NPV, follow five simple steps:

1. Determine project cost (initial cash outlay).

2. Estimate future net cash flows.

3. Assess risk of project.

QUESTION: Why assess project risk?14.5

4. Compute NPV by discounting cash flows.

5. Make an accept/reject decision.



The capital budgeting decision using NPV is straightforward:

• If projects are independent → accept all positive NPV projects

• If projects are mutually exclusive → choose higher NPV projects


To compute NPV use the following formula:

N P V =n

t=0

N CF t

(1 + W ACC )t (14.2)

with N CF t = expected net cash flow at time t, W ACC = discount rate (the cost of capital), andn = number of periods. NPV for sooner and later... When there are many projects and manycash flows a spreadsheet is typically used.

Interpreting NPV

• N P V = 0 → project earns the required rate of return and cash flows are sufficient to repaythe invested capital.

• N P V > 0 → project earns the required rate of return, cash flows are sufficient to repay theinvested capital, and provides extra cash flows that accrue to the firm’s stockholders.

• N P V < 0

→ project does not earn the required rate of return.

14.2.4 Internal rate of return (IRR)

M h lik fi di i ld t t it ith b d j t i t l t f t b f d b



Much like finding yield to maturity with bonds, project internal rate of return can be found bysolving the NPV equation for I RR:

0 =n

t=0

N CF t

(1 + IRR)t (14.3)


• Unfortunately, solving this equation without a financial calculator is difficult (you would need

to solve a polynomial of order n). Without a financial calculator you can use trial and error,picking different values of I RR until equation (14.3) is satisfied.

• Using a financial calculator (or spreadsheet) the values for sooner and later are: IRRs = 14.5%and I RRL = 11.8%

Interpreting IRR There are a few ways to interpret IRR:

1. IRR is the yield of a project given its cost and future cash flows.

2. IRR is the rate that equates future cash flows to the current cost.

3. IRR is the rate in which a project’s N P V = 0.

Two problems with IRR

1. Just as the Y T M measure assumes future coupon payments are reinvested at Y T M , the I RRmeasure assumes future cash flows are reinvested at IRR. In contrast, the NPV calculationassumes cash flows can be reinvested at the cost of capital. The latter (cash flows can be



reinvested at the cost of capital) is a more realistic assumption.

2. If cash flows are non-normal, IRR will produce multiple results. Specifically, one result foreach change in sign. In this case the IRR accept/reject decision can conflict with the NPV

method.


What to do with the IRR number

• Independent projects: accept all projects with IRR > W ACC (the project earns a return inexcess of the capital used to fund it).

• Mutually exclusive projects: Use NPV method instead.

QUESTION: Why?14.6

14.2.5 NPV profilesNPV profiles are obtained by varying the discount rate (required rate of return) in the NPV equation(14.2). Lets take a look at a spreadsheet example...

QUESTION: Where does the NPV conflict with IRR occur?14.7

• As you can see the NPV rankings are a function of the cost of capital.

QUESTION: So what if the cost of capital is exactly equal to the crossover point (i.e.,both projects have the same NPV)?14.8



14.2.6 Modified IRR

• Examples thus far have been based on normal cash flows (conventional cash flows),. That is,cash flows that have only one change in sign (negative at beginning to reflect outflows, then

positive after payback period)


• Non-normal cash flows are cash flows with more than one change in sign and can produce

multiple IRRs.

• To illustrate, consider project M...

• MIRR has two advantages over IRR

1. It avoids the possibility of obtaining multiple IRRs

2. It uses a better cash flow reinvestment rate assumption: cash flows are reinvested at the

cost of capital k .

MIRR is computed by solving the following equation for MIRR:

nt=0

COF t

(1 + W ACC )t =

nt=0

CIF t (1 + W ACC )n−t

× 1

(1 + MIRR)n (14.4)

where COF = cash out flows, CIF = cash in flows, and k = cost of capital. A few observations

about this equation:

• The left hand side represents the present value of costs.



• The right hand side represents the present value of the terminal value, with the terminal valuerepresented by the future value of cash inflows invested at the cost of capital rate.

QUESTION: How is discounting the terminal value by MIRR not assuming cash flows

are reinvested at MIRR?

14.9


An example (Project M)... So how does MIRR compare with NPV when evaluating mutually

exclusive projects?

• Equal size and same life: NPV and MIRR are equivalent.

• Equal size and different lives: fill in zeroes for shorter-life project then NPV and MIRR areequivalent.

• Different sizes: NPV and MIRR may conflict.

14.2.7 Profitability index

Yet another project project evaluation method is the profitability index:

P I = PV of future cash flows

initial cost =

nt=1

CF t(1+r)

t

CF 0

For project Sooner:P I S =

1, 078.82

1, 000 = 1.079



• Provides a relative measure: for Project Sooner, each $1 invested produces $1.079.

• Independent projects: accept all with P I > 1.

• Mutually exclusive projects: higher P I is better but rankings may conflict with NPV.

14.3. IMPLEMENTATION OF CAPITAL BUDGETING METHODS 295

14.3 Implementation of capital budgeting methods

14.3.1 Comparison of methods

Referring to Table 14.2:Payback We saw how $5,000 cash flow in post analysis period is not accounted for in Section 14.2.2

NPV Consider two projects, Small and Big with cash flows:

Year 0 1Project Smallz -10,000 16,500Project Biggie -100,000 115,500

QUESTION: If WACC = 0.10, what is the NPV for each of the projects?14.12

• However, project Big is more risky since 10X more capital is required. Also, if reality

does not match expectations in the future, project Small has more of a “safety margin.”• To illustrate, consider a 3313 % drop in future cash flows for project Small and a 4.76%

drop in future cash flows for project Big.

QUESTION Wh t i th NPV f b th j t ?14 13



QUESTION: What is the NPV of both projects?14.13

IRR/MIRR Now compute IRR for projects Big and Small: IRRbig = 15.5% and IRRsmall =65.0%. Thus two projects with the same NPV (5,000) can be ranked using IRR, and IRR

gives a better indicator of project risk.


Table 14.2: Capital budgeting method matrixMethod What it measures Drawbackspayback risk and liquidity does not consider cash flows beyond payback

period nor the cost of capitalPV[payback] risk and liquidity does not consider cash flows beyond payback

periodNPV dollar benefit to shareholders unable to rank mutually exclusive projects with

identical NPVs, may conflict with IRR/MIRR

when ranking mutually exclusive projects.QUESTION: When does the conflict

occur?14.10

IRR rate of return earned oninvested capital

assumes cash flows are reinvested at IRR, canhave multiple IRRs, and may conflict with NPV

when ranking mutually exclusive projects

QUESTION: When do multiple IRRsoccur?14.11

MIRR rate of return on invested can conflict with NPV when ranking mutually



MIRR rate of return on investedcapital

can conflict with NPV when ranking mutuallyexclusive projects

PI bang for the buck can conflict with NPV when ranking mutuallyexclusive projects

14.3. IMPLEMENTATION OF CAPITAL BUDGETING METHODS 297

QUESTION: Unlike stocks, how can higher IRR be interpreted as lower risk?14.14

14.3.2 In practice

• Since computing time is cheap, you should compute all of the measures (perhaps avoid IRRunless you are looking for a quick calculation of a normal cash flow project).

• Do not rely solely on the quantitative measures.

• Be skeptical of high NPV projects. Positive NPV projects imply you are earning a returngreater than your cost of capital. This happens only if you have some competitive advantagein an efficient market or you are running a monopoly or oligopoly.

• Keep in mind how long these competitive advantages will last (patentable vs. non-patenable,replaceable vs. non-replaceable).



• Firms in the real-world use the methods discussed in this chapter. The following data is fromBierman’s 1992 study of Fortune 500 industrial companies (B) and the Parrino and Kidwell(2010) textbook (PK).


Table 14.3: Capital budgeting methods used in industryItem 1955 (B) 1981 (PK) 1992 (B) 1999 (PK)DCF methods 4% ? 100% ?payback “most important” 5% 84% 56.7%NPV ? 16.5% 85% 74.9%IRR ? 65.3% 99% 75.7%

• Small firms use these methods less (21% for DCF methods) and it is hypothesized this is dueto (1) more concerned about liquidity, (2) do not know how to use these methods, and (3)belief that small projects will not benefit from DCF analysis.

QUESTION: What do you think?14.15

14.3.3 Post-audit

At this point, managers have two choices:



1. Make the capital budgeting decision and let the projects ride.

2. Make the decision but follow up (herein called the post-audit). Post audit compares actualresults with expected results and explains why differences occurred.

14.4. SPECIAL APPLICATIONS 299

The post-audit comparisons and explanations serve three primary purposes:

1. Improve forecasts: would be nice if they were more accurate!

2. Improve operations: maybe forecasts are accurate but employee and capital productivity couldbe improved to meet those forecasts

3. Improve profitability via termination of projects that are no longer economically viable (i.e.,no longer likely to obtain the required return).

14.4 Special applications

14.4.1 Unequal lives

• There are two approaches: the equivalent annual annuity approach and the replacement chain(common life) approach. We will look at the common life approach here and the equivalentannual annuity approach in Chapter 16.

• A common life approach example (r = 11.5%)...

QUESTION: Which project would you choose and why?14.16



p j y y

• When to use common-life analysis

1. If projects are mutually exclusive and have very different lives


2. High probability that the project will be repeated in the future

• Problems with common-life analysis: inflation and technological improvements will impactfuture cash flows

14.4.2 Economic vs. physical life

Physical life how long project can operate

Economic life how long project should operate to maximize NPV

• Sometimes it is better to terminate a project and receive the salvage value of equipment ratherthan run the equipment until salvage value is zero.

• An example...

QUESTION: What is the economic life of the project? What is the physical life?

14.17

14.5 The optimal project mix



• Definition: the set of projects that maximizes firm value.

• In theory, all projects with positive NPVs should be accepted, but you may be unable to acceptall due to constraints:

14.5. THE OPTIMAL PROJECT MIX 301

1. The marginal cost of capital increases.

2. You may have to ration capital

14.5.1 Increasing marginal cost of capital

• The more capital you require, the more expensive each additional dollar becomes.

• Larger projects may require additional funding → increases WACC → may reduce NPV such

that N P V ∗ < 0 → can not accept project

14.5.2 Capital rationing

1. Reluctance to issue new stock (or debt)

• Lazy approach: choose “artificial” limit to capital expenditures out of concern of increasingWACC.

QUESTION: Why might a manager do this?14.18

• Better approach: estimate NPVs with W ACC ∗ > W ACC with W ACC ∗ = new cost of capital given additional debt or equity issuance. Then make accept/reject decision.



2. Do not have enough non-monetary resources (e.g., people)

• Lazy approach: set “artificial” limit.


• Better approach: Do some more analysis (such as linear programming) to find optimum

combination of projects.

QUESTION: What else?14.19

3. Do not trust project manager’s estimates

• Lazy approach: add a little to WACC or require project managers to use higher W ACC

QUESTION: What is wrong with this?14.20

• Better approach: Use real numbers and post-audit.

14.A Another look at IRR vs. MIRR plus incremental IRR

14.A.1 Standard IRR

Before exploring I RR lets revisit N P V :

N P V =n

t=0

N CF t

(1 + W ACC )t (14.5)



Note that Eq. (14.5) is similar to the bond price equation:

P V =n

t=1

C

(1 + Y T M )t + F V

(1 + Y T M )n (14.6)

14.A. ANOTHER LOOK AT IRR VS. MIRR PLUS INCREMENTAL IRR 303

In the bond price equation, Eq. (14.6), we start at t = 1 in contrast to the NPV Eq. (14.5) where

we start from t = 0. If we set N P V = 0 and rearrange Eq. (14.5) we have an equation nearlyidentical to Eq. (14.6):

N CF 0 =n

t=1

N CF t

(1 + IRR)t (14.7)

Just as you use your financial calculator to solve for Y T M in the bond pricing equation Eq. (14.6),you can solve for the internal rate of return I RR in Eq. (14.7). Well, not exactly. You need to usethe CF buttons instead of P V , P M T , and F V since the period cash flows CF are not identical.At the risk of being redundant, let me rewrite Eq. (14.5) using N P V = 0:

0 =n

t=0

N CF t

(1 + W ACC )t (14.8)

You can see that Eqs. (14.6), (14.7), and (14.8) all require the t = 0 cash flow, either P V or N CF 0,to be entered as negative numbers in your financial calculator. This leads to three interpretations of

IRR:

1. IRR is the yield of a project given its cost and future cash flows.

2. IRR is the rate that equates future cash flows to the current cost.



RR qu u u u

3. IRR is the rate that makes a project’s N P V = 0.

There are two problems with I RR:


1. Just as the Y T M measure assumes future coupon payments are reinvested at Y T M , the I RR

measure assumes future cash flows are invested at I RR.

2. If cash flows are non-normal I RR will provide multiple results, specifically, one for each changeof sign.

14.A.2 Modified IRR

MIRR is calculated in a three step process:

1. Discount cash outflows to time 0 using W ACC .

2. Compute the terminal value (ending value) of all cash inflows using W ACC .

3. Set P V equal to the result of step 1 (negative number!), F V equal to the result of step 2, N to the number of periods, and the resulting interest rate, that equates F V to P V , is MIRR

Example 14.1. W ACC = 10%, C F 0 = −1.6, C F 1 = +10.0, C F 2 = −10.0. What is MIRR?

To compute MIRR we are converting the problem to a zero-coupon bond. For fun, calculate theMIRR and NPV of this project.



14.A.3 Incremental IRR

Consider the following cash flows for project Biggie and Smallz:

14.A. ANOTHER LOOK AT IRR VS. MIRR PLUS INCREMENTAL IRR 305

Project CF 0 CF 1

Biggie -100,000 120,000Smallz -10,000 16,500

Incremental -90000 103,500

In other words, it costs an additional 90,000 to receive an additional 103,500 when choosingproject Biggie over project Smallz. For fun, complete the following table:

Project N PV IRR

BiggieSmallz

Incremental



Chapter 15

Estimating project cash flows

Overview

In this chapter we will look at:

• The role of externalities and sunk costs.

• The impact of depreciation approaches.

• The impact of inflation.



• Estimating project risk.

• Incorporating project risk in decision analysis.

307

308 CHAPTER 15. ESTIMATING PROJECT CASH FLOWS

• Real options and capital budgeting.

15.1 Who estimates cash flows?

• Estimates come from teams, not just one person.

• Marketing, engineering, cost accountants, and sales make up that team.

• Make sure all team members use consistent and realistic assumptions.

15.2 Relevant cash flows: incremental free cash flow

• Use cash flows, not accounting income.



• We are concerned about incremental cash flows provided by a project: the additional FCFgenerated by a project vs. not taking the project.

15.2. RELEVANT CASH FLOWS: INCREMENTAL FREE CASH FLOW 309

15.2.1 Project cash flow vs. accounting income

• Begin with the Chapter 8 construction of the free cash flow measure:

NOWC = OC A − OCL

TNOC = NOWC + OLT A

= (OCA − OCL) + OLT A

∆TNOC t = TN OC t − TNOC t−1

NOPAT = EBIT (1

−τ )

F CF t = NOP AT t − ∆TNOC t

• Next assign specific balance sheet items to OCA, OCL, and OLT A:

RW C = OC A − OCL

= (Cash + AR + Inventory) − (AP + ACC)

ROC = RW C + F A

∆ROC t = RW C t − RW C t−1

NOPAT = EBIT (1 − τ )

F CF t = NOP AT t − ∆ROC t

E ti (13 3) i B i h d D (2010) l t ti i t h fl



• Equation (13-3) in Brigham and Daves (2010) relates accounting income to cash flow as:

F CF = Operating cash flow − Gross fixed asset expenditures − Change in working cap(15.1)


But how does one arrive at Eq. (15.1)? I will show you:

F CF t = NOPAT t − ∆T NOC t

= EBIT t (1 − τ ) − ((OC At − OC Lt + F At) − (OC At−1 − OC Lt−1 + F At−1))

= EBIT t (1 − τ ) − ((F At − F At−1) + (OC At − OC At−1) − (OC Lt − OC Lt−1))

= (EBIT t (1 − τ ) + DEP t) − (∆F At + DEP t + ∆OC At − ∆OC Lt)

= (EBIT t (1 − τ ) + DEP t) − (∆F At + DEP t) − (∆OC At − ∆OC Lt)

= Operating cash flow − Gross fixed asset expenditures − Change in working cap

I add deprecation in operating cash flow but subtract it again in the gross fixed asset expenditures.The net effect of my depreciation inclusions is zero.

QUESTION: In the context of cash flow, why add depreciation to EBIT (1 − τ ) and to∆F A?15.1

Costs of fixed assets

• Although fixed asset costs are not included in accounting income calculations they are includedin capital budgeting calculations.

• Costs include shipping and installation; this total cost is used as the depreciable basis1.



• The salvage value matters when computing operating income the year the fixed asset is sold.

1this is used later on to calculate the amount of depreciation expense we use in (??)


Non-cash charges Even though depreciation is a non cash expense and has an impact on after-tax

cash flows, it is not a cash flow.

Changes in required working capital New project → new inventories, accounts payable, re-ceivables, etc.

Exclusion of interest expenses

• Note we begin with earnings before interest and taxes.• Interest expense is already accounted for in WACC.

• Accounting income (net income) is the income available to stockholders.

• Project income (free cash flow) is the income available to all investors (stakeholders).

15.2.2 Incremental cash flowsThree issues to keep in mind when determining incremental cash flows provided by a project:

1. Sunk costs



• Definition: cash that has already been spent.

• Do not include sunk costs in incremental cash flow calculations.


• E.g., research and development already performed, marketing survey purchased last year,

land purchased last year, etc.

2. Opportunity costs

• Definition: cash flows that could be generated with existing assets that are required bythe new project

• Market value of this asset is the cost that should be treated as a negative cash flow (acost).

• E.g., land that could be sold for $X but is needed to start a new project is considered anopportunity cost of $X associated with the new project

3. Externalities

• Definition: a side effect or consequence of taking on project

• Positive: opening a suburban bank branch could increase traffic (and therefore revenue)at both the suburban and downtown branches. Be sure not to double-count transfersfrom the old (downtown) branch to the new (suburban) branch



from the old (downtown) branch to the new (suburban) branch.

• Negative: if Nautica decides to open a web-store, sales at retail outlets may decline. Therevenue from online operations must exceed the [likely] lost sales at retail outlets.


Timing of cash flows

• Daily cash flow computations would be nice but it is impractical

• Typically assume cash flows occur at the end of the year (or quarter)

An example of incremental cash flow computations: Replacement project

• Decision: to replace, or not to replace, that is the question

• Will cost $100,000 to replace existing equipment but:

1. Output will increase

2. Sales will increase

3. Unit costs will decrease

4. Will have larger tax write off.

QUESTION: Why?15.2

5. Will receive income from sale of old equipment

• The ultimate question: do benefits outweigh the costs?

15 3



QUESTION: What is assumed when suggesting “increased sales?” 15.3

• An example...


15.3 Tax effects

15.3.1 Overview of depreciation

• Companies can and do use different depreciation methods for investors than for tax reporting.

• These methods include straight-line (pre 1954), double-declining balance and sum-of-yearsdigits (1954 to 1981), accelerated cost recovery system (1981 to 1986), MACRS (1986 to1993), others (1993+).

QUESTION: Why different reporting methods?15.4

• For stockholder reporting, subtracting the salvage value lowers the depreciation expense; wedo not do this for tax reporting purposes.

• Tax laws are complicated and change often: contact the IRS or an expert for up-to-dateinformation.

15.3.2 Tax depreciation life

• Before: depreciable life = estimated useful life → fully depreciated at end of useful life

• After: MACRS shortens depreciable life and allows for larger depreciation expenses earlier in



an asset’s life

• Note: Real estate must be depreciated using the straight-line method.

15.3. TAX EFFECTS 315

Half-year convention Asset is put into service in the middle of the first year → recovery period

is extended one year beyond “asset life” of the particular class.Depreciable basis is the cost of equipment plus shipping and installation

Sale of depreciable asset If asset is sold the difference between the sale price (salvage value) anddepreciated or book value is added to operating income.

Depreciation illustration

• Cost of equipment = $150,000• MACRS class life = 5 years

• Delivery and installation = $30,000

• Date placed into service = October 15, year t = 0

Year t Depreciation expense1 0.2(180, 000) = 36, 000

2 0.32(180, 000) = 57, 6003 0.19(180, 000) = 34, 2004 0.12(180, 000) = 21, 6005 0.11(180, 000) = 19, 8006 0.06(180, 000) = 10, 800

t t l 180 000



total = 180, 000

QUESTION: What happens if equipment is sold at the end of year 3 for $90,000? 15.5


15.4 Capital budgeting project example

• Up to now: factors that impact cash flows

• Now: how cash flow analysis impacts the budgeting decision

• Two broad categories for projects:

1. Expansion project: invest to increase sales

2. Replacement project: replace existing asset to increase net cash flows.

QUESTION: What is “net cash flow”?15.6

• What to include in project cash flows

1. Initial investment (more than just FA invest, you must include initial RWC investmentalso)

2. Periodic (annual) cash flows: include depreciation but exclude interest

3. Terminal cash flows adjusted for taxes

Example This example illustrates (1) how cash flow estimates are obtained by the various team



members and (2) the cash flow analysis for making a decision to accept or reject a project.

Marketing (Sales estimates)

15.4. CAPITAL BUDGETING PROJECT EXAMPLE 317

• Price per unit = $3,000

• Annual sales (units) = 20,000• Annual sales (dollars) = $60,000,000

• Growth rate of price (aka, inflation) g price = 2%

• Growth rate of unit sales gunits = 0%

Engineering (Resource requirements)

• Additional manufacturing space (building) needed

• When building will be needed (December 31, 2007)

• Equipment needed

Production (May be part of engineering and/or accounting)

• Per-unit variable cost = $2,100

• Fixed overhead = $8,000,000 per year excluding depreciation

• Growth rate of variable costs gvc = 2%

• Growth rate of fixed costs gf c = 1%

A ti ( )



Accounting (cost accountants)

• Marginal federal plus state tax rate τ = 40%


• WACC = 12%

• Manufacturing space (building) cost = $12,000,000• Equipment cost including and shipping and installation = $8,000,000

• Deprecation schedule of building → MACRS 39-year class

• Depreciation schedule of equipment → MACRS 5-year class life

• Book value of building in year 4 → B V bldg,4 = 10, 908, 000

• Book value of equipment in year 4

→ BV equip,4 = 1, 360, 000

QUESTION: How are year 4 book values obtained?15.7

Management (CEO, board of directors, perhaps others)

• Economic life estimate = 4 years.

QUESTION: How was the projects economic life estimated? How would youverify?15.8

• Same risk as average project therefore use W ACC as the discount rate for project cashflows

• Market value of building in year 4 → M V bldg,4 = 7, 500, 000

• Market value of equipment in year 4 → M V = 2 000 000



• Market value of equipment in year 4 → M V equip,4 = 2, 000, 000

QUESTION: How are year 4 market values obtained?15.9

15.4. CAPITAL BUDGETING PROJECT EXAMPLE 319

15.4.1 Part 1 - Input data

• A summary of all the team inputs

• RWC/Sales = 10%, an estimate of how much working capital needs to be on hand to supportsales (more on this in Part 4)

15.4.2 Part 2 - Depreciation schedule

• Building uses straight line depreciation with year 1 depreciation 12

100%39

≈ 1.3%, year 2 through

39 depreciation 100%39 ≈ 2.6%, and year 40 depreciation 1

2100%

39 ≈ 1.3%

• Equipment depreciation based on MACRS 5 year class life.

15.4.3 Part 3 - Cash flows associated with building and equipment dis-

posal

QUESTION: Why is the market value of the building in 2011 less than the bookvalue?15.10



• The loss on the building sale provides a tax credit of $1,363. In other words, the company willpay $1,363 less in taxes since the loss of $3,408 is deducted from income.


15.4.4 Part 4 - Compute projected cash flows

• The “crystal ball” applies more to the marketing department’s inputs: units sold and salesprice.

QUESTION: Why suggest the other forecasts require less “magic?” 15.11

• The tax savings from interest expenses are ignored in this example. See footnote on page 227.

15.4.5 Part 5 - Key output and making the decision

• N P V > 0 → good

• Payback period=3.22 → good or bad?

• IRR > W ACC and MI RR > WACC → good

• What if project is riskier than average? To be continued...

15.5 Inflation adjustment

• recall rnom ≈ rreal + IP . See page 61 of Brigham and Daves (2007) or page 58 of Brigham andD (2010)



Daves (2010).

• In general, W ACC = W ACC nom

15.5. INFLATION ADJUSTMENT 321

QUESTION: Why?15.12

• Must ensure net clash flows are expressed in the same terms (nominal or real) as W ACC

• Two methods of inflation adjustment

1. Use real NCFs and adjust WACC to reflect W ACC real (therefore you need to adjust, orare implicitly adjusting Rd, Rs, and R ps

2. Leave WACC alone (assuming it is a nominal value) and incorporating inflation into NCFs

• Method #2 is preferred since Method #1 either assumes Rd, Rs, and R ps are affect by inflationin the same way. or requires that they be adjusted separately

• An example of incorporating inflation...



Chapter 16

Equivalent annual costOverview

• Allow me to rename “Equivalent Annual Cost” of Ross et al. (2010) to “Annualized EquivalentCost” (AEC).

• Up to this point capital budgeting (accept/reject) decisions were based on NPV, IRR, MIRR,and other measures.

• Potential problems with the prior approach:



1. Revenue forecasts are a source of significant error in capital budgeting analysis. Who hasthe best crystal ball?

323

324 CHAPTER 16. EQUIVALENT ANNUAL COST

2. It may be difficult to attribute revenues to one particular machine under consideration.

3. When looking at projects with unequal lives NPV can be misleading.

• The annualized equivalent cost (AEC) approach bypasses revenue forecasting and revenueattribution by focusing on costs . The AEC approach also accommodates projects with unequallives.

• AEC is useful for replacement and make vs. buy decisions.

16.1 The AEC procedure and interpretations

16.1.1 General procedure

• Step 1: Compute net present cost (NPC) which includes initial cash outlay, opportunity costs,and future production costs.

• Step 2: Compute AEC as

AEC = N P C

P V A[r, n] (16.1)

where P V A[r, n] is the present value annuity factor with interest rate r and n years. Note:



P V A [r, n] = 1 − (1 + r)−n

r (16.2)

16.2. ACME INC. EXAMPLE 325

QUESTION: Can anyone think of an easy way to obtain P V A[r, n]?16.1

• Step 3: Divide AEC by number of units and compare resulting per-unit costs.

16.1.2 Interpretation

• AEC represents the annual cost of the project in today’s dollars.

• This approach expands on N P C by “spreading out” the initial cash outlay over the life of the

project.

QUESTION: Why would you want to do this?16.2

• Although this formulation presumes level production (same # of units per year) it can bemodified to accommodate unlevel production.

16.2 Acme Inc. example• Acme is considering replacing an existing (old) machine.

• The old machine still works and will last another 10 years.



• The proposed new machine will reduce direct production costs from $26,000 to $20,000 annu-ally.


• The cost of capital is 14% and the marginal tax rate is 34%.

• Assume 10,000 units of production annually, straight-line depreciation, and 10 years of opera-tion.

• Should the new project be accepted? Justify the answer with relative cash flow approach (NPVof incremental cash flows) and absolute cash flow approach (AEC per unit w/ old vs. new).

16.2.1 Scenario 1: Zero book, zero salvage value

QUESTION: What does zero book / zero salvage value tell you?16.3

Relative [incremental] cash flow approach Keep in mind these calculations represent theincremental cash flow from replacing the machine.

QUESTION: Should Acme purchase the new machine?16.4

Absolute (AEC) approach


QUESTION If h id d d b hi hi ld b h d h h



QUESTION: If the widget produced by this machine could be purchased rather thanmanufactured, what is the max Acme should pay?16.6

16.2. ACME INC. EXAMPLE 327

16.2.2 Scenario 2: Nonzero book value, zero salvage value

• Now assume the book value of the old machine is 8,000 and annual deprecation would be 800per year for 10 years if the old machine is retained. Salvage value is still zero.

QUESTION: How will a non-zero book value for the old equipment impact ourcalculations?16.7

Relative [incremental] cash flow approach Keep in mind these calculations represent theincremental cash flow from replacing the machine.


QUESTION: What is the seemingly counter-intuitive implication of the higher bookvalue?16.9



QUESTION If th id t d d b thi hi ld b h d th th





16.2.3 Scenario 3: Nonzero book, nonzero salvage value

• Now machine has a salvage value (t = 0) of 4,000 and book value of 8,000 (also t = 0).

• Assume salvage value after 10 years is zero

• Annual deprecation is 800 per year for 10 years if the old machine is retained.

QUESTION: How will a non-zero salvage value for the old equipment impact ourcalculations?16.12

Relative [incremental] cash flow approach I.e., what if we did replace the equipment.


QUESTION: What is the seemingly counter-intuitive implication of the higher salvage value?16.14



QUESTION: If the widget produced by this machine could be purchased rather than




16.3. SUMMARY 329

16.3 Summary

• AEC provides a means to evaluate replacement projects and make vs. buy decisions.

• AEC avoids problematic revenue forecasting.

• A couple tax accounting concepts reinforced.

1. After tax impact of write-off = τ × writeoff.

2. After-tax impact of cost reduction = after-tax impact of revenue increase = (1−

τ )×cost reduction.

• The more valuable the old equipment (salvage and book value) the more beneficial it is replaceit, provided the replacement has significantly lower annual expenses.

• This lecture prompted me to trade in my 2007 Infiniti G35S for a 2009 Honda Civic (not aPorsche 911)!



Chapter 17

Project risk analysisOverview

In the previous three chapters we looked at criteria for project selection. This chapter expands theanalysis by incorporating project risk. The chapter concludes with an introduction to managing,rather than just analyzing, project risk.

17.1 Project (stand-alone) risk

• Sales and unit numbers are really expected values.



QUESTION: What does this imply?17.1

331

332 CHAPTER 17. PROJECT RISK ANALYSIS

• PDFs + correlations of cash flows → NPV PDF

• A goal: to determine appropriate discount rate for a given project’s cash flows

17.1.1 Sensitivity analysis

• Begin with base case, the case using expected values

• Change values (by some percentage) and tabulate NPV

• The steeper the line, the greater the sensitivity

QUESTION: What is missing in this analysis?17.2

17.1.2 Scenario analysis

• Overcomes two of the shortcomings of sensitivity analysis.

QUESTION: Any idea which two?17.3

• A quick way to see the best and worst case.

• Procedure



1. For each of the key variables, have team members provide best and worst case numbers

17.1. PROJECT (STAND-ALONE) RISK 333

2. Assign probabilities of 25% to the best case, 50% to the base case, and 25% to the worstcase.

QUESTION: What did we just do, in a mathematical (statistics) sense?17.4

3. Calculate three NPVs: N P V best, N P V base, and N P V worst

4. Calculate E [N P V ], σNP V , and C V [N P V ]:

E [N P V ] =n

i=1

P ri

×N P V i (17.1)

σNP V =

ni=1

P ri (N P V i − E [N P V ])2

1

2

(17.2)

CV [N P V ] = σNP V

E [N P V ] (17.3)

QUESTION: Why are the AVERAGE() and STDEV() functions of Excelinappropriate in this case?17.5

5. Calculate C V [N P V ]



• An example...


17.1.3 Monte Carlo simulation

• Technique originates from work on the Manhattan Project (first atomic bomb) and named“Monte Carlo” because it employed the mathematics of gambling (how many people are goingto die, on average?)

• Improves on scenario analysis by

1. Utilizing continuous distributions as opposed to discrete

2. Incorporates correlation among inputs

• Basic process

1. Define random variables for each input (incorporate correlations if available)

2. Generate random value for each input based on info in step #1

3. Compute NPV based on these simulated values

4. Repeat steps #2 and #3 a thousand or so times, recording input variable and NPV valuesfor each “try”

5. Compute E [N P V ], σNP V , and CV [N P V ] = σNP V /E [N P V ] using simulated NPVs fromstep #4

• Input variable definition (key variables):



Sales price Normal distribution with µ = 3.00 and σ = 0.35

17.2. INCORPORATING PROJECT RISK 335

QUESTION: What if you sell to businesses (e.g., oil) and have priceagreements in place?17.6

Variable costs Triangular distribution with lower bound 1.40, most likely value = 2.10, andupper bound of 2.50. Existing labor contracts and supplier relationships have limited thevariability of variable costs.

QUESTION: How is this PDF “limited”?17.7

Unit sales Triangular distribution. Purchase agreements with customers enable lower limitof 15,000; manufacturing capacity sets upper limit of 30,000

Sales growth Normal distribution with µ = 0%, σ = 15%, and correlated with unit sales.

QUESTION: What is the intuition behind sales growth correlation with unitsales?17.8

• An example...

• E [N P V ] > 0, but C V [N P V ] >> 1.0, the average CV of the firm.


17.2 Incorporating project risk

• Risk can be incorporated via the certainty equivalent approach (not discussed here) or the



p y q pp ( )risk-adjusted discount rate approach (what we have been eluding to)


• Essentially, if project risk (CV) is greater than the firm’s average risk (CV), increase WACC.

• Brigham and Daves (2010) suggest there is no good way of specifying exactly how much and itis necessarily judgmental. However, I offer a suggestion: If the CV of the project is x% higher(lower) than the firm’s average CV, then raise (lower) the project’s discount rate (projectWACC) by x%

QUESTION: After you adjust WACC, then what?17.10

17.3 Phased decisions and risk management• Rather than “go all in,” you can “phase in” your investments for some projects.

• Doing so enables the manager to reduce risk rather than just measure it.

• Eligible projects and be evaluated with decision trees.

The basic decision tree• The project: produce industrial robot. See page 475 of Brigham and Daves (2010) .

• What is going on

Node 1 Pay 0.5M (t = 0) for marketing study. The outcome of the study has two branches



– large market exists → continue with prototype (go to Node 2)

17.4. REAL OPTIONS INTRODUCTION 337

– small market exists → drop the project

Node 2 Market exists, now spend 1M (t = 1) to build prototype. Two outcomes are possible– engineers approve of the prototype → continue with production (go to Node 3)

– engineers say it is junk → terminate project

Node 3 Market exists, engineers approve prototype, invest 10M (t = 2) and build factory.Three outcomes are possible:

– High market acceptance → 18,000 income in t = 3 → continue another two years

– Medium market acceptance →

8,000 income in t = 3 →

continue another two years

– Low market acceptance → 2,000 loss in t = 3 → terminate project (go to Node 4)

• For each path, compute joint probabilities and NPV using firm average WACC

• Compute E [N P V ], σNP V , and C V [N P V ] = σN P V /E [N P V ]

• If C V proj > CV , adjust WACC, recompute E [N P V ]

• From the footnote on page 467: Although a single WACC was used, with different phasescomes different WACCS (risk levels).

17.4 Real options introduction

• Before: determine possible outcomes, embark on positive NPV project, no influence on out-



comes


• After: managerial/real/strategic options → opportunities for managers to make decisions thatinfluence outcomes

17.4.1 Growth options

• Consider some time before the Blue-Ray HD-DVD battle was resolved.

• Sony had an option: invest to ramp up production of Blue-Ray DVD players (in the eventdemand during the holiday season will be high) or maintain then-current production levels (in

the event the financial crisis dampens consumer discretionary spending this holiday season)

• If investment is avoided now: can invest elsewhere but competitors may establish market share

• If gains from investing elsewhere exceed losses due to decreased market share, this option isvaluable

• Like financial options the real option value increases with rf

17.4.2 Investment timing option

• Introduce product now or wait until you can assess market size

Si il i th ti



• Similar reasoning as growth option

17.4. REAL OPTIONS INTRODUCTION 339

17.4.3 Abandonment options

• GM is locked into agreements with suppliers to purchase specified quantities at specified prices1

.

• In hindsight (and foresight if their management had any), an option to abandon those agree-ments would be of value.

• Capacity reduction and temporary suspension options can be valuable as well.

17.4.4 Flexibility options

• BMW South Carolina plant: pay extra (the “option premium”) for a plant that can producemore than just Z4s rather than a Z4-only plant

17.4.5 Valuing real options

• Each of the real options just described has a cost (value)

Option Cost (value)Growth pay more to increase capacityInvestment timing investment nowAbandonment option higher price or volume requirementFlexibility option incremental cost of flexible vs. focused plant



1at least until they file bankruptcy




Chapter 18

Real options

Overview

We are now armed with the tools to value options. In this chapter we look at a few applications of financial option valuation to real options.

18.1 Real option valuation

• Project that expands opportunity set → an option → has positive value

• While exact value of real option may be elusive, the estimate obtained can aid in the ac-t/ j t d i i



cept/reject decision

341

342 CHAPTER 18. REAL OPTIONS

• Dealing with real options:

1. Use DCF and ignore option

2. #1 + qualitative assessment of real option value

3. Decision tree analysis to provide quantitative assessment of real option value

4. Apply B-S financial option model to real option scenario

5. Use financial engineering to make up your own model

18.2 Investment timing option

18.2.1 Approach 1: DCF ignoring the option

QUESTION: How was the expected annual cash flow computed?18.1

• Note how risky the project is:

– if the $22 million changes to $21.5 million, the NPV becomes negative

– 25% chance that revenues are only $5 million → NPV = -$38 million

• Thus, although the expected NPV >0, the project is risky and at this point we have not fullyquantified the risk nor done anything to mitigate it



quantified the risk nor done anything to mitigate it.

18.2. INVESTMENT TIMING OPTION 343

18.2.2 Approach 2: DCF and qualitative analysis

• Let c = option price: if c > 1.08M then wait (“purchase the option”), if c < 1.08M do notwait (do not “purchase the option”)

• Is the option to wait valuable? Consider what makes options valuable:

1. High current price: NPV of future cash flows ≈ 51.08.

QUESTION: Where did this number come from?18.2

2. Time to maturity: one year is relatively long3. Risk: project is “quite risky”

In sum, these qualitative factors suggest the option has value.

• Since value > 0, then do the analysis to see if value > 1.08

18.2.3 Approach 3: Decision treePart 1 Forget the option, implement project today.

• E [N P V ] = 1.08, σnpv = 24.02, C V = 22.32

• → high risk! but positive NPV. You could conclude that since E [N P V ] > 0 you [mis-takenly] proceed immediately



takenly] proceed immediately


Part 2 Wait one year, then use scenario analysis/decision tree to yield

• E [N P V ∗] = 9.36, σ∗npv = 8.57, C V ∗ = 0.92

• Higher E [N P V ] with lower risk therefore the option to wait is valuable.

QUESTION: Should a higher or lower discount rate be used in Part 2? 18.3

• The appropriate discount rate for the “delay decision” is difficult to quantify.

• You could discount year two through four cash flows at 14% while discounting costs byRF = 6%.

• Result: lower NPV but still greater than “immediate” 1.08.

• What you can do when you can not define the appropriate discount rate: sensitivityanalysis.

18.2.4 Approach 4: Black-Scholes model• To use the B-S model 5 inputs are needed

1. Risk free rate: in this example, use 1-year T-bill rate of 6%

2. Time to expiration: one year

3 Exercise price $50M



3. Exercise price $50M

18.2. INVESTMENT TIMING OPTION 345

4. Current price of stock: The underlying asset for this real option is the delayed projectwith “current price” equal to the present value of all expected cash flows excluding the

50M exercise price

5. Variance of the project’s return. Three methods:

(a) Use educated guess based on variance of company’s stock which should be lower thanthe variance of average projects. σ2

avg stock = 12%, 18 ≤ σ2avg project ≤ 30%

QUESTION: Why?18.4

(b) Direct method: calculate variance of returns of each outcome. Use the PV at time

0 to compute returns. Note: (1) we are not using the IRR; (2) E [R] = WACC because PVs were discounted by WACC.

(c) Indirect method: Use CV of delayed project (excluding the exercise price) in thisformula:

σ2 = ln

CV 2 + 1

t (18.1)

Note: use expected value and standard deviation at the option expiration date tocompute CV. Why? You must read the article that derived the formula!

• Which variance to use? Use judgment.

QUESTION: Any other suggestions?18.5

• Conclusion: option to wait is worth more than proceeding immediately therefore wait.

• Lets look at how how sensitive the option value is to σ ...



p


18.2.5 Approach 5. Financial Engineering

• Use this approach when decision trees or B-S models do not map directly to the real option

• Includes “making up” a new model customized to the particular project

18.3 Growth option

Before this chapter we looked at decisions as either accept or reject. In the previous section the

decision was immediate or delay. Here we look at the option to grow or not to grow.

18.3.1 Approach 1. DCF ignoring the option

• In this case we are only considering running this project once

• Expected net cash flows are:

E [N CF ] = 0.25(34) + 0.5(20) + 0.25(2) = 19

• The expected NPV is 1.29

QUESTION: What about risk of the project vs. risk of project with the option?18.6



p j p j p

18.3. GROWTH OPTION 347

18.3.2 Approach 2: DCF and qualitative analysis

Is the option to produce more (the “follow on” project) valuable? If so, do not ignore the option(i.e., throw it away).

18.3.3 Approach 3: Decision tree

• Ignore option: E [N P V ] = 1.29, σnpv = 18.70, CV = 14.54 → positive E [N P V ] but “veryrisky”

• Consider option: E [N P V ∗] = 4.70, σ∗npv = 24.62, C V ∗ = 5.24 → less risk• E [N P V ∗] > E [N P V ] → the option is valuable

• Since C V ∗ < CV we may need to adjust the discount rate → sensitivity analysis (Note: costs,since they are known, are discounted at RF

18.3.4 Approach 4: Black-Scholes model

• t = 2 years, RF = 6%, X = 30

• S 0 = current “stock price” = PV of future cash flows of second generation project = 24.07

• QUESTION: What does S 0 < X imply?18.7

• σdirect = 17.8%, σindirect = 15.3%, both of which are greater than 12% of the average stockreturn. Thus consistent with the benefits of diversification




• Judgement: 15 ≤ σtrue ≤ 20 but will use sensitivity analysis.

• value >> 0 → accept project

18.4 Use of real options

• Real options are being used more and more for project evaluation.

• Real options impact risk and therefore the appropriate discount rate.

• Given the large number of financial derivatives, you should be able to find a financial derivativeanalogous to your seemingly obscure real option case.

• When you can not: insert financial engineering.



Chapter 19

Change Log

Second Edition

1. More examples are included throughout the text.

2. A list of tables and a list of figures has been added for easy lookup.

3. Numerous typos have been corrected.

4. Expanded illustrations and explanations have been included in chapter appendices 5.A, 5.B,11.A, and 14.A.

5. Greatly expanded Chapter 8, managerial accounting.



349

350 CHAPTER 19. CHANGE LOG



Bibliography

Angell, R. J. (2011). A note on the calculation of sustainable growth rates in finance texts. Journal

of Economics and Finance Education , 10(1):41–44.

Brigham, E. F. and Daves, P. R. (2007). Intermediate Financial Management . Thomson South-Western, ninth edition.

Brigham, E. F. and Daves, P. R. (2010). Intermediate Financial Management . Thomson South-Western, 10th edition.

Modigliani, F. and Miller, M. (1958). The cost of capital, corporation finance, and the theory of investment. American Economic Review , 53:261–297.

Modigliani, F. and Miller, M. H. (1963). Corporate income taxes and the cost of capital: a correction.American Economic Review , 53(3):433–443.

Parrino, R. and Kidwell, D. (2010). Fundamentals of Corporate Finance . John Wiley & Sone, Inc.,New Jersey.



351

352 BIBLIOGRAPHY

Ross, S. A., Westerfield, R., and Jaffee, J. (2010). Corporate Finance . Mcgraw-Hill Irwin, New York,NY, ninth edition.

Wildsmith, J. R. (1974). Managerial Theories of the Firm . Dunellen, New York.



Chapter 20

Answers to embedded questions

Answers1.1accounting, pollution, price gouging, employee treatment, OSHA. Google’s “don’t be evil.” 1.2product quality and choices1.3increase the size, reduce the time, and reduce the risk of FCFs1.4Intrinsic value since “the market” will eventually catch on.1.5

God1.6Long term, of course.1.7Sales data and forecasts, truthful or revised accounting statements, R&D info, clinical trial results, trades between companies, etc.1.8current assets less current liabilities1.9Limited to their initial investment1.10Corporation Advantages: Limited liability. Corporation disadvantages: Double taxation, disperse control1.11It’s easy. Just look at income statements and after-tax cash to owner/worker.1.12No. Talk about why not, conflict of interest, etc.1.13These guys and gals are golfing buddies, their children go to the same expensive private schools, they live in the same expensive

neighborhoods, etc.



353

354 ANSWERS

1.14Internal auditor deals with financial statements while the C&E director deals with state and federal regulations as well as ethicalconduct2.1(1) long-run allows time for the true financial statements to come out and (2) managers not encouraged to inflate next quarter’s

numbers2.2(1) How do you measure performance? (2) How much of that performance is due to manager’s decisions? (3) Short-term goals induce

“cooked books” while long-term goals can limit manager’s short-term pay2.3Not so much...2.4They also received money from the POFs they were auditing for other consulting contracts2.5Investment banks who employed the analysts also did other business with POFs2.6That is your decision but be mindful of the consequences.2.7Entrenched, egotistical, and greedy management2.8Could be a golfing buddy, board member may have consulting company therefore disagreement may result in a loss of a consulting

contract. Finally, could be interlocking boards2.9With cumulative voting you can concentrate your votes.see footnote on page 377 of Brigham and Daves (2007) or second paragraph

on page 387 of Brigham and Daves (2010).2.10A shift in ownership from a large number of small investors who are inactive to a smaller number of large investors who are active2.11Should Wall Street executives have received any performance-based bonuses for 2008?2.12Your ownership accrues 25% p er year typically. Executives work “accelerated vesting” into their contracts.2.13Illiquid due to exercise restrictions2.14Communism since employees (the workers) have more “power” than investors2.15Good question. I would venture more prevalent with larger companies due to the cost of initial setup and executing the plan. For

more information see The National Center for Employee Ownership2.16Who knows? Take a look at the “International corporate governance” green box on pages 380 and 381 of Brigham and Daves (2007)

or pages 394 and 395 of Brigham and Daves (2010).3.1

With Option 2 you make three payments of $12,000. If CD rates are 3% this translates into an NPV of -33,943. This means it ismore expensive to finance the car than to purchase it cash. If CD rates are 7% this translates into an NPV of -31,492. Therefore it ischeaper to finance the car at 0% and invest your $32,679 in 7% CDs.3.2Due to people’s impatience and risk aversion.3.3Try not paying your credit card off every month!3.49 years3.52, 4, 12, 365.25, ∞3.6It should, it is Eq. (3.3) rearranged.3.7Typically cash deposited today is out-of-pocket and treated negative. The withdrawal in the future is cash into your pocket and

treated positive. It is just a matter of perspective, but you must be mindful of the perspective.

http://www.nceo.org/articles/esop-employee-stock-ownership-plan

http://www.nceo.org/articles/esop-employee-stock-ownership-plan



ANSWERS 355

3.8You choose the option with the highest present value.3.9We need a couple volunteers in class to demonstrate.3.10That is a good deal for the lender given the high interest. However, there is a risk of being repaid zero.3.11Presuming those are end of year numbers there are a total of N = 39 years with P V = −203, 211, 926 and F V = 309, 162, 581.

Therefore i = g = 1.08%.3.12To determine if you have the resources to support the sales growth and to determine if the growth is profitable3.13Remember the ACE method: artwork, calculator, equation.3.14(1) Don’t mixing banking and friendship. (2) There is no interest associated with this loan.3.15Lower interest rates are generally better. You may want to look at total interest dollars over the life of the loan. This could make an

interesting extra credit assignment. At what loan amount, interest rate, term combination are you better off paying a higher rate ?3.16ACE method3.178%3.18N = 5 , I = 1.9/123.19No. The longer term translates into more interest and a higher interest rate paid.3.20$276.103.21The second approach looks easier to me.3.22∞3.23$500 million in dividends every year forever. Sounds like a good deal to me.3.24We will answer this in class3.25Otherwise P V A would be negative. If i < g then we would use another model3.26We will work this out in class.3.27Lender B has the lowest APR at 10.90%3.28This could make a good extra credit assignment4.1Corporations and governments issue bonds to finance projects4.2

Bond is selling at a premium therefore the current market yield must be less than 10%4.3Perform calculation using a financial calculator4.4We will do this in class4.5To reissue new bonds at the new and lower market rate4.6Callable yield should be a little bit higher than non callable.4.7Fewer bonds to mature → less money required4.8Duration matching can be used to hedge interest rate and reinvestment rate risk.4.9Via restrictive covenants such as dividend and additional debt restrictions4.10I am not a lawyer, but perhaps this solidifies specific bondholder claims4.11Corporations issue bonds with yields lower than normal since they are tax free. Think corporate welfare here



356 ANSWERS

4.12The credit worthiness of the insurance company. E.g., AIG.4.13Think about how AAA ratings were given to junky securities4.14Yes!4.15Uncle Sam!4.16U.S. Treasury Bonds are more marketable and therefore will have lower yields.4.17The risk that their bond will be called in at a time when they can purchase only lower yield bonds4.18The rate corresponding to the compensation necessary for one to postpone consumption.4.19It gets complicated, but, a downward sloping yield curve suggests the Fed will be lowering rates in the future. Why does the Fed

lower rates? When there is an economic slowdown. This is related to the expectations hypothesis to be covered in advanced financecourses.4.20Also note the slope and shape of the demand curve is dependent on the set of available projects.4.21When a positive technology shock occurs the return on investment will be higher, therefore a company will be willing to pay a little

more to take on project with new technology.4.22To the right.4.23It should not be. The nominal rate is a combination of the real rate and expected inflation.4.24It depends on what you believe rates will be next year. You can infer that information from the yield curve and application of the

expectations hypothesis.4.25r∗ = rRF − IP and thus you can obtain the inflation premium from quoted yields on non-indexed (nominal) T-bonds and indexed

(TIPS) T-bonds4.26Prior to the dysfunctional Congress there was no default risk. I don’t know what to say now.4.27Gold can be sold real quick (go to any pawn shop or jeweler). However, there are significant transaction costs. Therefore gold is

highly liquid but with low marketability.4.28Short term bonds must be reinvested in the future at then-current market rates whereas long-term bonds keep on paying the same

coupon. Thus, if rates fall in the future, long-term bond prices will rise more than short-term and pay better coupons to the new

short-term bonds5.1Someone (management or fellow disgruntled outside investor) who you grant permission to vote on your behalf 5.2With voting rights but how much more depends on level of shareholder protection. The value of the voting right diminishes with the

quality of shareholder protection. Less shareholder protection → voting is more important. Voting shares are about 4% to 6% higher invalue than non-voting shares in the U.S.5.3Inferior risk-adjusted returns5.4Capital gains5.5Buying and selling would occur until it did. Note the “marginal” investor sets the price5.6g again!5.7Rs ≈ Rs, in equilibrium Rs = Rs, Rs could be anything



ANSWERS 357

5.8Because if you buy the stock today you will not receive D0

5.9No. If you sell the stock in a couple years the sales price will include all expected future cash flows from year 2 onward5.10 Two ways to look at this. First (1 + g)t/ (1 + Rs)t > 1

∀ t therefore stock price is infinite. Second, Rs

−g < 0 and the stock price is

negative. Both ways are nonsensical In this case you would use a different model.5.1123.005.12No. Increasing dividends can have a negative impact of future growth. E.g., not investing in new equipment or R&D.5.1324.845.141. For liquidity reasons. 2. To partake in growing dividends, 3. To realize some capital gains. 4. To obtain voting rights. In sum:

to make more money.5.15 V ps = Dps

Rps

6.1Unlimited. When you write a call you expect the stock price to go down and the option never exercised. However, if the price goesup you or obligated to sell it cheap. If this is a naked call, you have to buy the stock on the open market then sell it cheap. Ouch!6.2Think of investing at rf to have cash in the future.6.3

The intrinsic value is $5.00 and the time value is $3.716.4Investors would sell options at this higher price until 8.71 were reached6.5Investors would construct “opposite” portfolio: short stock and buy option. buying would drive price from low value to higher 8.716.6Related to volatility of stock. would need to get into lognormal returns and CDF to elaborate.6.7Exercisable only on expiration date6.8Repay the debt or have no equity. More in chapters 16 and 20 of Brigham and Daves (2010)7.1Risk, return, diversification7.2Since both stocks have the same expected return, it is clear sale.com has more risk. However, if you used P r [R < 0] as your measure

the results may be different.7.3Probabilities should add up to 100% and we will see this later in the course when estimating future cash flows. E.g., when your

marketing VP provides demand estimates.7.415%7.5If the underlying returns are normally distributed, 99.730020% of the observations are with +/ − 3σ7.6No short selling7.7Intel/Dell positive, American/Exxon negative (or less positive).7.8wi gets smaller, and therefore w2

i gets even smaller7.9When fundamental equals market value. Also, in economic terms, when supply equals demand.7.10An asset that has guaranteed returns. Example: U.S. Treasury bill.7.11Because it offers the optimum risk-return trade off.7.1216%



358 ANSWERS

7.13Sell.7.1475.717.15Managers’ info already in price7.16International correlation information8.1Balance sheet, income statement, statement of cash flows, and sometimes statement of retained earnings8.2Liquidity but IFRS is opposite?8.3The order in which they must be paid8.4Cash, marketable securities, short term investments8.5Credit cards (short term) to buy food. Home mortgages (long term) to buy homes.8.6Net of accumulated depreciation.8.7The amount paid for a company in excess of the book value, thus an intangible asset8.8Pay packages for executives?8.9Revolving line of credit and accrued expenses such as employee bonuses.8.10All of the accounting trickery that happens on the income statement after (and including) “Sales.” 8.11Market value represents the present value of expected future cash flows. Book value represents the liquidation value of a company

based more on historical costs and accumulated depreciation.8.12The question almost answers itself. Synergy is where 1 plus 1 equals 3. Having the right equipment and the right people can facilitate

a higher market value than the sum of the parts.8.13Depreciation refers to tangible assets while amortization applies to intangible assets8.14Revenues have to b e recognized in the same fashion as costs are recognized.8.15To tell the IRS I did not make any money (and avoid taxes) and tell the shareholders I made lots of money (pay my bonus please).8.16For one they legally last only a finite time. Second, disruptive technologies will replace your fancy patented product soon anyway.8.17Balance sheet reduction in debt8.18Because interest is tax deductible8.19

Then ARE is also negative. In this scenario a company has reduced common equity via a reduction in assets.8.20Because non cash charges were taken out of net income and non cash revenues were added8.21(1) depreciation and amortization are typically the largest non cash items and (2) the smaller items typically cancel each other out.

Use finance.google.com to illustrate NCF calculation8.22Operating, Investing, Financing8.23An increase in AR could be due to sales that have been made but cash not received.8.24The issuance of long term debt triggers an increase in cash. That cash is used to purchase PP&E. Therefore an increase in PP&E is

a use of cash.8.25Cash received.8.26Operating current liabilities: suppliers (accounts payable) and employees (accruals)



ANSWERS 359

8.27New building facade, computer upgrades, perquisites.8.28Taxes and net income.8.29Cash available to invest in growth or distribute to investors8.30Net income is reduced 0.40 (τ ) for every additional dollar of interest expense8.31By selling assets to offset operating losses.8.32See the ROIC equation.8.33The alternative with the highest after-tax cash flow. In this case the preferred stock with the (mostly) tax-deductible dividend income8.34(1) Dividends are not deductible from operating income and (2) shareholder has to pay taxes on them8.35Only single taxation.9.1It depends. We need to compare debt-to-asset and income available for interest payment ratios. If looking at just average interest

rates, Firm A: 11.4%, Firm B: 5.7%9.2It depends. creditor: high → firm is able to repay; shareholder: low → using your cash for growth rather than leaving it in cash and

marketable securities9.3(1) industry may have it all wrong and (2) might be something unique to your company (e.g., relationship with bank)9.4Is revenue recognized when invoiced, shipped, or cash received?9.5In their financial statement filings, p erhaps in the footnotes. You may also find the sales terms in internal documents.9.6High due to their JIT manufacturing process9.7Inventories are not moving too fast... therefore not “current.” You might be better off using the acid test ratio9.8Yes. older→ more depreciation → lower cost; newer → higher price due to inflation9.9Total assets includes current assets such as inventory (ITR) and log term assets such as PP&E (FATR)9.10Yes. home ownership9.11Lease payments are typically(?) deducted when calculating EBITDA.9.12Depreciation is a non-cash expense. Therefore whatever is depreciated can be considered cash available to repay short-term obligations.

Thus short-term lenders care about ECR. In the long term, these funds must be reinvested to maintain growth. Thus long-term investorscare about the measure that excludes depreciation funds (TIE)9.13Philosophically yes, the b orrower is servant to the lender. Financially, it could magnify gains. We will see the impacts of debt on

ROE while discussing the DuPont equation9.14P includes expectations of future FCFs, E is what they have now9.15P represents discounted future cash flows. higher risk → higher discount rate.9.16Less manipulated or adulterated.9.17B=cumulative value of what stockholders invested; M=present value of expected FCFs9.18To “make the case.” Some criticisms of Method X may not be present for Method Y, but if both say the same thing... Management

may prefer or require Method X. Also, people like to complicate things.9.19A = L + S.E.



360 ANSWERS

9.20Benchmark divisions9.21Deflate numbers or scale by assets or sales10.1strategy: a careful plan or method, tactic: a device for accomplishing an end10.2tech: apple newton (flop), profit: SUV (kill the environment, etc.) What happened to Tucker, Edsel, and betamax?10.3I (the investor) will handle diversification, you (the firm) do what you do best10.4assumes debt is constant for entire year10.5(1) charges full year of interest on debt that may have been incurred in November (2) circularity in spreadsheets10.6n bonds plus 1 current market yield10.7Because we are using beginning of year debt levels10.8Just a little algebra.10.9Treated as “backup” for times when there is a cash shortfall10.10Related to financial crisis of 2008-2009 when firms were unable to obtain short term loans or any loans for that matter. On 2009.10.21NPR morning radio had small business owner speaking of difficulty or inability to meet payroll due to unwillingness of banks to dish out

small business loans. Her business has been around 19 years and now it is the banks’ fault she can not make payroll. The firm may haveto close its doors. Do you buy that?10.11An artifact of the percent of sales method. γ varies; some assets and liabilities are unchanged (i.e., have no γ ).10.12Sales impacts everything via γ ’s and the sales forecast could be wrong10.13Better screening, hire repo-man, change credit terms, accept other forms of payment.10.14Talk to Dell about proper inventory management, read Chapter 21 of Brigham and Daves (2010)10.15Brigham and Daves (2010) says to reduce operating costs, but costs were already in-line with industry average. There may be otherundocumented reasons. Just be sure you don’t use the hatchet when a scalpel is needed.10.16Increased short-term investments10.17NP involves and action between the firm and creditor. AP and accruals are between the firm and customer10.18Profits from sales, cash, and short term investments.

10.19Stocks and bonds.10.20REV actual,t

U actual,t= REV full,t

1

11.1Debt11.2Debt will be invested in a project and everyone (past creditors, current creditors, and current stock holders) all have a claim to the

cash flows generated by that project. The returns on the project should satisfy al l stakeholders, not just the new bondholder.11.3(1) can not pay common stock dividends until preferred are paid; (2) difficult to raise additional funds; and (3) preferred stock holders

may be able to seize control of the firm11.4(1) Management thinks stock is over-valued or (2) firm needs to raise cash. But what about Cisco back in the day?11.5401k, pension funds, mutual funds, etc.



ANSWERS 361

11.6DY=D/P11.7Historical dividend growth rates or analysts’ forecasts11.8(1) they vary over time; (2) some firms repurchase stock instead of paying dividends11.9(1) accuracy and truthfulness (analysts and the earnings numbers) and (2) different opinions → different estimates. Now is a time

for mentioning “Wisdom of Crowds” 11.10Based on info available today: D0/P 011.11Out of the air. could use historical averages...11.12Scared of stocks → buy bonds → drives up price (lowers yield) of bonds11.13Because the firm receives less money for each bond when F > 011.14PMT=60, FV=1000, PV=-990, N=30 → I=6.0712.1(1) not everyone pays dividends; (2) difficult to trace increase in dividend to a project if the firm has multiple projects and therefore

multiple cash flows.12.2As a shareholder, I want Ford to focus on building cars or give that extra money for me to invest. Recall the “required” return from

the previous chapter. However, they appear to have weathered the market meltdown well.12.3EBIT (1 − τ )12.4(1) to have assets necessary to support forecasted sales growth, MagnaVision needs 69M dollars, 51M of which will come from profits.

The remainder from investors, and in MagnaVision’s case, from increased NP, LTD, and PS. Funds are raised via debt and preferred stockto maintain a constant capital structure (see Chapter 15). I believe retained earnings could also be reduced via the sale of marketablesecurities.12.5Marketable securities which are reported at their market value (approximately)12.6V debt = N P + LT D, V PS is obvious12.7In equilibrium, the market values common equity the way we just described! This is my value add... that statement is not in the

book, I believe.12.8Look at

−CR(Salest)(g).

12.9By increasing ROIC or reducing WACC . Regarding the former, ROIC can be increased by reducing required operating capital orincreasing NOPAT 12.10(1) may not have funds to improve all deficiencies at the same time; (2) some improvements may have little (or adverse) affects onMVA12.11no12.12Since ROIC < WACC for the memory division13.1Eq. (13.1) is essentially a market value balance sheet.

MV A = M V L + M V E



362 ANSWERS

In English, assets are purchased with money raised from debt and stock issuances.13.2Market interest rates impacts the market value of debt D . The market risk premium impacts the cost of equity S . And the market

value of the firm V is based on the expected future cash flows. More precisely, V should be referred to as the market value of assets .13.3In general, V 0 = F CF 1/WACC −g. So if F CF and g are the same for the levered and unlevered firm then WACC L = WACC U .13.4(1) leverage = D/S and it increases when D increases. (2) rsU > rdL since equity is more risky than debt.13.5Interest payments are tax deductible but dividends are not. Therefore a firm financed with debt will have more after tax cash flow.

That is, the firm will have a lower tax bill than a comparable firm financed by equity.13.6100% debt!13.7Because of the (1 − tc) in Eq. (13.7) that is not present in Eq. (13.4)14.1money, people, more on this later14.2so we can establish the year before full recovery14.3Shorter payback is better, therefore choose project S.14.4If you discount cash flows, it takes longer to recoup the current costs14.5

To determine the appropriate discount rate.14.6Better cash flow reinvestment assumption. In reality, you will use a combination of metrics and throw in some judgment14.7When r < crossover14.8Could choose the one with the higher IRR but ultimately some judgment will be needed. We will discuss a little bit more later.14.9Think zero-coupon bond!14.10When WACC < crossover rate14.11When there are multiple changes of sign in cash flows. That is, when cash flows are non-normal.14.12NP V small = 5, 000 and N P V big = 5, 00014.1311,000 and 1110,00014.14higher IRR, NPV more likely to be > 014.15Quit being lazy, be thorough, do the calculation, it is not that bad with Excel, are you a survivor or an achiever?14.16In this example, I would not have bothered with the common life calculation since I RRF > IRRC 14.17Economic life is 2 years while physical life is 314.18If they are compensated based on EVA, lower WACC means more money in their pocket14.19Perform further analysis with more employees14.20Managers will still inflate their results, perhaps even more15.1Depreciation is a non-cash expense that was removed prior to arriving at EBIT and in the long run equipment must be replaced and

maintained.15.2Larger depreciation expense15.3That demand for additional units exists



ANSWERS 363

15.4Simply, to minimize tax liability and maximize reported earnings. The manager wants to report lower expenses (lower depreciation)to increase income to shareholders but higher expenses (higher depreciation) to decrease taxable income for tax reporting15.5Operating income for year 3 is adjusted by 90, 000

−0.29

∗(180, 000) = +37, 800

15.6The net effect of cost reductions and/or additional sales15.7Depreciation schedule15.8Estimated based on past experience (read: a guess). Could verify by projecting cash flows beyond 4 years (including revenues, costs,

and salvage values) and checking if NPV is larger15.9Input from marketing, engineering, accounting, etc.15.10Somehow, the company must retain the land the building is sitting on, but sells the building. Cisco did something like this in “CiscoCity” in Santa Clara. Step 1: buy the land and build a building. Step 2: Use the building until book value exceeds market value. Step3: sell the building (at a loss) and then lease from the company you just sold the building to (tax deduction)15.11Costs and depreciation are fairly straightforward sans costs that are heavily impacted by commodity price fluctuations (such as oil).The marketing inputs are forecasts of what will people will do, which may be more difficult. Maybe if we take some advanced marketingclasses we can find the marketing estimates to be more reliable than accounting estimates of costs15.12Quoted bond rates are nominal and computations of Rs and R ps typically based on nominal values16.1PMT=1, N=n, I=r, FV=0, PV=-PVA[r,n].16.2You may have to obtain some financing for project and would be difficult to explicitly specify the dollar costs of debt and equity

financing. Thus with AEC you obtain a picture of the annual cost of capital in dollar amounts.16.3Machine has been fully depreciated and pretty reliable since it is worthless and can run 10 more years16.4Yes16.5Yes16.6-2.5735, not -2.6016.78,000 lost write-off right off the bat (market value of zero is larger than the book value of 8,000) but 800 less in incremental depreciation16.8Yes16.9The more valuable the old machine (i.e., the higher the book value), the more likely you are to replace it16.10Yes16.11Good example to do in class16.12According to our qualitative counter-intuitive statement, the better the old equipment the more likely to replace it... therefore higherNPV and per-unit differential.16.13Yes16.14The better the old machine (i.e., the higher the salvage value), the more likely you are to replace it16.15Yes16.16Another good example to do in class17.1They are random variables and therefore have some sort of distribution (PDF)



364 ANSWERS

17.2(1) correlation among the inputs, (2) ability for more than one input to change, (3) what is the probability of a 20% price decline?17.3(2) ability of multiple inputs to change simultaneously; (3) incorporates probability17.4Define a discrete PDF17.5

This is a discrete distribution17.6Either price is fixed or distribution is altered17.7normal distributions have no limits whereas the triangular distribution does17.8The number of units sold today gives some indication of the number of units to be sold next year17.9More risk therefore use higher discount rate (WACC)17.10Recalculate NPV for base case, perhaps re-run Monte-Carlo and check P r[N P V ≥ 0] and E [NP V ]18.1E [CF ] =

P Ri × CF i

18.2Estimate adding the $50M initial cost back in18.3Lower since there is less uncertainty (demand is either average or high). Perhaps we should discount the investment at the risk free

rate since the amount is known and the cash flows at something less than 14%18.4Diversification18.5Use range of values in sensitivity or Monte Carlo analysis18.6A good in-class example18.7The option is out of the money, in other words, has no intrinsic value

Corporate Finance FlexText™ 3e

Documents

Transcript of Corporate Finance FlexText™ 3e