FIN351: lecture 6

The cost of capital

The application of the portfolio theory and CAPM

FIN351: lecture 6

Today’s plan

What have we accomplished in the last lecture?

Cost of capital• Capital structure and WACC

• Calculate WACC without tax

• Calculate WACC with tax

The market efficiency concept

FIN351: lecture 6

What have we learned in the last lecture?

Beta (β): Measuring market risk or systematic risk of a security• Which is defined as the contribution of a

security to the risk on the market portfolio,

• Mathematically,

• How to understand β intuitively?

)~(

)~,~(

m

mii RVar

RrCov

FIN351: lecture 6

What have we learned in the last lecture? (1)

05 10 15

Number of Securities

Po

rtfo

lio

sta

nd

ard

dev

iati

on

Market risk

Uniquerisk

FIN351: lecture 6

What have we learned in the last lecture? (2)

The beta of a portfolio• The beta of a portfolio will be an weighted

average of the betas of the securities in the portfolio.

The expected return of a portfolio• The expected return of a portfolio will be an

weighted average of the expected returns of the securities in the portfolio.

FIN351: lecture 6

What have we learned in the last lecture? (3)

CAPM (Capital Asset Pricing Model) • The risk premium on each security is

proportional to the market risk premium and the beta of the security.

• That is, )( fmifi rRrr

portfoliomarkettheforpremiumriskrR

iurityforpremiumriskrr

fm

fi

sec

FIN351: lecture 6

What have we learned in the last lecture? (4)

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2

4

6

8

10

12

14

16

0 0.2 0.4 0.6 0.8 1 1.2

Beta

Exp

ecte

d R

etu

rn (

%)

. The graphic representation of CAPM in

the expected return and Beta plane

rf

Security Market Line

Rm

FIN351: lecture 6

What have we learned in the last lecture? (5)

We can use the Beta of the project cash flows to measure the risk of the project and use CAPM to get the discount rate or the expected return required by investors •

)( fmprojectfproject rRrr

FIN351: lecture 6

What have we learned in the last lecture? (6)

Some results• The Beta of the market portfolio is 1.

• The Beta of the risk-free asset is 0.

• The portfolio weights can be negative, but their sum must be 1.

FIN351: lecture 6

Example 1

You have $1 million of your own money to invest in stock A and B. You short-sell $1 million stock A and then invest in stock B. The expected returns for stock A and B are 15% and 20%, respectively. The risk-free rate is 5%. Stock A has a beta of 1.5 and stock B has a beta of 2.0.The expected rate of return for the market portfolio is 13%.

Please use two approaches to calculate the expected rate of return on your portfolio?

FIN351: lecture 6

Solution

%25%8*5.2%5

5.22*25.1*1

p

p

R

%252.0*215.0*1 pR

First, calculate the portfolio weight as follows:

(1)The expected rate of return of a portfolio is the weighted average of the

rates of return of the securities in the portfolio.

2;1 BA xx

(2) The beta of a portfolio is the weighted average of the betas of the securities in the portfolio. Then use CAPM to calculate the expected return

FIN351: lecture 6

The cost of capital

Cost of Capital • The expected return the firm’s investors

require if they invest in securities or projects with comparable degrees of risk.

FIN351: lecture 6

The cost of capital for the bond

The cost of capital for the bond• It is the YTM, the expected return required by

the investors.

• That is

• The expected return on a bond can also be calculated by using CAPM

tddd r

principalcpn

r

cpnr

cpn

111

P2bond

)( fmdfd rRrr

FIN351: lecture 6

Example 2

A bond with a face value of $2000 matures in 5 years. The coupon rate is 8%. If the market price for this bond is $1600.(a) What is the expected return on this bond or

what is the cost of debt or interest rate for this bond?

(b) Suppose that the YTM is 9%, what is the market value of this bond?

FIN351: lecture 6

Solution

(a)

(b)

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)1(

2000

)1(

111601600

55

YTM

YTMYTMYTMYTM

922,1$09.1

2000

09.1*09.0

1

09.0

1160

55

bondP

FIN351: lecture 6

The cost of capital for a stock

The cost of capital for a stock is calculated by using • CAPM

• Dividend growth model

)r-(R+r=r fmfe i

gP

DIVr

gr

DIVP e

e

0

110

FIN351: lecture 6

Example 3

Sock A now pays a dividend of $1.5 per share annually, It is expected that dividend is going to grow at a constant rate of 2%. The current price for stock A is $25 per share. What is the expected return or the cost of capital by investing in this stock?

FIN351: lecture 6

Solution

%12.802.0

02.1*5.125

r

r

Using the dividend discount model, we have

FIN351: lecture 6

Capital structure

Capital Structure• The firm’s mix of debt financing and equity

financing.

• If we use D , E and V to denote the values of debt, equity and firm (asset), respectively.

• Then V=D+E

• The ratio of D/V or D/E can be used to measure the capital structure of the firm.

FIN351: lecture 6

Weighted Average Cost of Capital (WACC)

If you invest in a stock, you require a an expected rate of return, or the cost of capital for the stock

If you invest in a bond, you require a an expected rate of return, or the cost of capital for the bond

Then, if you invest in a a portfolio of all the firm’s securities (debt and stock), what is the expected rate of return you require?

The expected rate of return on a portfolio of all the firm’s securities is called the weighted average cost of capital(WACC). It is also called the expected return on the asset of the firm.

FIN351: lecture 6

WACC (continues)

According to portfolio theory, we know the expected return on a portfolio is the weighted average of the expected returns on the securities of the portfolio.

Thus, WACC for a firm with debt and equity is

de rVD

rVE

WACC

EDVwhere

FIN351: lecture 6

WACC (continue)

In calculating WACC, we have to use market values of debt and equity.

Even if you are given the book value of debt, you may convert this book value to market debt value to calculate WACC

Why do we use market values of debt and equity, but not book values of debt and equity, in calculating WACC?

FIN351: lecture 6

Example 4

Geothermal Inc. has two securities: debt and stocks. The market debt value is $194 million, but the firm’s market value is $647 million. Given that geothermal pays 8% for debt and 14% for equity, what is the Company Cost of Capital?

FIN351: lecture 6

Solution

%2.1214.0*647

45308.0*

647

194WACC

FIN351: lecture 6

Example 5

Executive Fruit has issued debt, preferred stock and common stock. The market value of these securities are $4mil, $2mil, and $6mil, respectively. The required returns are 6%, 12%, and 18%, respectively.• What is the WACC for Executive Fruit, Inc.?

FIN351: lecture 6

Solution

%13

18.0*12

612.0*

12

206.0*

12

4

12624

WACC

V

FIN351: lecture 6

Summary of WACC calculation

Three steps in calculating WACC• First step: Calculate the portfolio weight using

the market value.

• Second step: Determine the required rate of return on each security in the portfolio.

• Third step: Calculate a weighted average of these returns, or the expected return on the protfolio.

FIN351: lecture 6

The impact of tax on WACC

Taxes are an important consideration in the company cost of capital because interest payments are deducted from income before tax is calculated.

Tc)-(1r=

rate)tax -(1 timesdebt) ofcost (pretax =debt ofcost tax -After

d

FIN351: lecture 6

WACC with tax

Weighted -average cost of capital=

eVE

dVD r +Tc)r-(1 =WACC

FIN351: lecture 6

A summary example John Cox, a recent MBA student of SFSU, was asked by his

boss in Geothermal to decide whether the firm should take an expansion project: the cost of the project is $30 million, and the project is expected to generate a perpetual incremental cash flow of $4.5 million. Currently, Geothermal has 20 million shares of common stocks outstanding, with a market price of $22.65 per share. The Beta of the firm’s equity is 1.1. The risk free rate is 4% and the market risk premium is 5.6%. The firm also has long-term debt, with the YTM of 9%. John also got the following information from the firm’s balance sheet:• Debt (12 years maturity, 8% coupon): $200 million

• Common stocks:$110 million If the tax rate is 35%, should John suggest to his boss to take

the project or not?

FIN351: lecture 6

Solution

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7.18509.1

200)

09.1*09.0

1

09.0

1(*16

45365.22*20

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%9

1212

ed

e

d

rED

Ert

ED

DWACC

D

E

r

r

FIN351: lecture 6

Investment vs. Financing

Investment decisions or capital budgeting is about how to take projects to maximize V.

Financing decisions are about how to raise capital (E or D) to finance the projects to be taken

Asset Liabilities and equity

VDebt: D

Equity: E

FIN351: lecture 6

Market Efficiency

Market efficiency is concerned about whether capital markets have all information about the cash flows and risk of projects.

Financing and market Efficiency

FIN351: lecture 6

Efficient capital markets

Efficient Capital Markets – If capital markets are efficient, then security prices reflect all relevant information about asset values ( cash flows and risk)

FIN351: lecture 6

Market efficiency and random walk

Market efficiency concepts are very abstract.

How can we use a simple way to check whether the stock market (one of the capital markets) is efficient or not?• If the stock price follows a random walk, then

the stock market is efficient.

FIN351: lecture 6

What is a random walk of stock prices?

The movement of stock prices from day to day DO NOT reflect any pattern.

Statistically speaking, the movement of stock prices is random.

FIN351: lecture 6

A Random Walk example

$103.00

$100.00

$106.09

$100.43

$97.50

$100.43

$95.06

Coin Toss Game

Heads

HeadsHeads

Tails

Tails

Tails

FIN351: lecture 6

Three forms of market efficiency

The random walk concept is still abstract Financial economists have used three

more specific forms to characterize or judge market efficiency.• Weak-form

• Semi-strong form

• Strong form

FIN351: lecture 6

Weak-form of market efficiency

Weak Form Efficiency - Market prices reflect all information contained in the history of past prices, or you cannot use past stock prices to predict future prices

Technical Analysts - Investors who attempt to identify over- or undervalued stocks by searching for patterns in past prices.

FIN351: lecture 6

Efficient Market Theory

Last Month

This Month

Next Month

$90

70

50

EI’s Stock Price

Cycles disappear

once identified

FIN351: lecture 6

Semi-strong form of market efficiency

Semi-Strong Form Efficiency - Market prices reflect all publicly available information such as earnings, price-to-earnings ratios,etc.

Fundamental Analysts - Analysts who attempt to fund under- or overvalued securities by analyzing fundamental information, such as earnings, asset values, and business prospects.

FIN351: lecture 6

Efficient Market Theory

-16

-11

-6

-14

9

14

19

24

2934

39

Days Relative to annoncement date

Cu

mu

lati

ve A

bn

orm

al R

etu

rn

(%)

Announcement Date

FIN351: lecture 6

Market Efficiency

0

5

10

15

20

25

Av

era

ge

re

turn

, pe

rce

nt

Highest

Book-Market Ratio

Fama & FrenchReturn vs. Book-Market

FIN351: lecture 6

Strong form of market efficiency

Strong Form Efficiency - Market prices reflect all information that could in principle be used to determine true value.

Inside trading• Investors use private information to predict

future price movements

FIN351: lecture 6

Efficient Market Theory

-16

-11

-6

-14

9

14

19

24

2934

39

Days Relative to annoncement date

Cu

mu

lati

ve A

bn

orm

al R

etu

rn

(%)

Announcement Date

FIN351: lecture 6

Some exercises

1. If stock markets are efficient, what should the correlation between stock returns for two non-overlapping periods?

2. Which is the most likely to contradict the weak-form of efficiency

a. Over 25% of mutual funds outperform the market on average

b. Insiders can make abnormal profits

c. Every January, the stock market earns abnormal return

FIN351: lecture 6

Several types of securities

Three types of securities• Common Stock

• Preferred stock

• Corporate debt

FIN351: lecture 6

Common Stock

Common stocks have the following forms:• Treasury stock

• Issued shares

• Outstanding shares

• Authorized share capital

• Par value

Ownership of the corporation

FIN351: lecture 6

Corporate debt

Corporate bonds• Primary rate

• Funded debt

• Sink fund

• Callable bond

• Subordinate debt

• Secure debt

FIN351: lecture 6

Preferred stock

Preferred stock and common stock• Priority and voting rights

Preferred stock and bond• Obligation and bankruptcy