Risk And Capital Budgeting

Professor XXXXXCourse Name / Number

2

Choosing the Right Discount Rate

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r

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CFCFNPV

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The numerator focuses on project cash flows, covered in chapter 8:

The denominator is the discount rate, the focus of chapter 9.

The denominator

should:

Reflect the opportunity costs of the firm’s investors.

Reflect the project’s risk.

Be derived from market data.

3

A Simple Case

Firm is financed with 100% equity.

Project is similar to the firm’s existing assets.

Project discount rate is easy to determine if we assume :

In this case, the appropriate discount rate equals the cost of equity.

Cost of equity estimated using the CAPM

))(()( FmiFi RREβRRE

4

All Leather’s Cost of Equity

E(Re ) = Rf + (E(Rm) - Rf) = 10.5% cost of equity

All Leather Inc., an all-equity firm, is evaluating a proposal to build a new manufacturing facility.

– Firm produces leather sofas.– As a luxury good producer, firm very sensitive to

economy.– All Leather’s stock has a beta of 1.3.

• Managers note Rf = 4%, expect the market risk premium will be 5%.

5

Cost of Equity

Beta plays a central role in determining whether a firm’s cost of equity is high or low.

What factors influence a firm’s beta?

Operating leverage

The mix of fixed and variable costs

Sales

Sales

EBIT

EBITLeverageOperating

Financial Leverage

The extent to which a firm finances operations by borrowing

The fixed costs of repaying debt increase a firm’s beta in the same way that

operating leverage does.

6

All Leather Inc. and Microfiber Corp.

All Leather Inc Microfiber Corp

Sales volume 40,000 sofas 40,000 sofas

Price $950 $950

Total Revenue $38,000,000 $38,000,000

Fixed costs per year $10,000,000 $2,000,000

Variable costs per sofa

$600 $800

Total cost $34,000,000 $34,000,000

EBIT $4,000,000 $4,000,000

What if sales volume increases by 10% ?

44,000 sofas44,000 sofas

$41,800,000$41,800,000

$37,200,000$36,400,000

$4,600,000$5,400,000

The two firms are in the same industry

All Leather’s EBIT increases faster because it has high operating leverage.

7

Operating Leverage for All Leather and Microfiber:

Microfiber

All Leather 

EBIT

Sales

Other things equal, higher operating leverage means that All Leather’s beta will be higher than Microfiber’s beta.

8

The Effect of Leverage on Beta:

Firm 1 Firm 2Assets $250 million $250 millionDebt $0 $100 millionEquity $250 million $150 million

Case #1: Gross Return on Assets Equals 25 Percent.EBIT $62.5 million $62.5 millionInterest $0 $8.5 millionCash to equity $62.5 million $54 millionROE 62.5 ÷ 250 = 25% 54 ÷ 150 = 36%

Case #2: Gross Return on Assets Equals 5 Percent.EBIT $12.5 million $12.5 millionInterest $0 $8.5 millionCash to equity $12.5 million $4 millionROE 12.5 ÷ 250 = 5% 4 ÷ 150 = 2.7%

Financial leverage makes Firm 2’s ROE more volatile, so its beta will be higher.

9

The Weighted Average Cost of Capital (WACC)

Cost of equity applies to projects of an all-equity firm.

– But what if firm has both debt and equity?– Problem akin to finding expected return of portfolio

Use weighted average cost of capital (WACC) as discount rate:

%11%5.1215050

150%5.6

15050

50

ed r

ED

Er

ED

DWACC

• An example…– Comfy Inc builds houses.– Firm has $150 million equity (E), with cost of equity re =

12.5%.– Also has bonds (D) worth $50 million, with rd = 6.5%– Assume initially that there are no corporate taxes.

10

Finding WACC for Firms with Complex Capital Structures

pde rPDE

Pr

PDE

Dr

PDE

EWACC

%73.12%85.211

5.12%7

5.211

49%15

5.211

150

WACC

How do we calculate WACC if firm has long-term (D) debt as well as preferred (P) and common stock (E)?

An example....

Sherwin Co.Total value = 211.5 million

Has 10,000,000 common shares; price = $15/share; re = 15%.

Has 500,000 preferred shares, 8% coupon, price = $25/share, $12.5 million value.

Has $40 million long term debt, fixed rate notes with 8% coupon rate, but 7% YTM.

Notes sell at premium and worth $49 million.

11

Connecting the WACC to the CAPM

)( fMdfd RRRr

WACC consistent with CAPMCan use CAPM to compute WACC for levered firm.

Calculate beta for bonds of a large corporation:

– First find covariance between bonds and stock market.

– Plug computed debt beta (d), Rf and Rm into CAPM to find rd.

• Debt beta typically quite low for healthy, low-debt firms– Debt beta rises with leverage.

Any asset that generates a cash flow has a beta, and that beta determines its required return as per CAPM.

12

Calculating Asset Betas and Equity Betas

edA βED

Eβ

ED

Dβ )()(

• An asset beta is the covariance of the cash flows generated by a firm’s assets with RM, return on market portfolio, divided by variance of market’s return.– For all-equity firm, asset beta = equity beta.– For levered firm, asset beta will be less than equity beta

(still assuming no taxes).• If asset beta known, and debt beta is assumed to be 0, can

compute equity beta directly from A:)(E

D1ββ AE

The CAPM establishes direct link between required return on debt and equity and betas of these

securities.

13

Discount Rate for Unique Projects

What if a company has diversified investments in many industries?

In this case, using firm’s WACC to evaluate an individual project would be inappropriate.

Use project’s asset beta adjusted for desired leverage.

• An example…– Assume GE is evaluating an investment in oil

and gas industry.– GE would examine existing firms that are pure

plays (public firms operating only in oil and industry).

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Data for Berry Petroleum and Forest Oil

0.550.56Asset beta *

0.640.16D/E ratio

0.610.86Fraction Equity

0.390.14Fraction Debt

0.900.65Stock beta

Forest OilBerry Petroleum

* Assumes debt beta = 0 and no taxes

Say GE selects Berry Petroleum & Forest Oil as pure plays:

Operationally similar firms, but Berry Petroleum’s E = 0.65 and Forest Oil’s E = 0.90

Why so different? Reason: Forest Oil uses debt for 39% of financing; Berry Petroleum: 14%.

15

Converting Equity Betas to Asset Betas for Two Pure Play Firms

69.025.0155.01

E

DAGE

To determine correct A to use as discount rate for the project, GE must convert pure play E to A, then

average.

– Previous table lists data needed to compute unlevered equity beta.

– Unlevered equity beta (same as A when taxes are zero) strips out effect of financial leverage, so always less than or equal to equity beta.

– Berry’s A = 0.56, Forest’s A = 0.55, so average A = 0.55• GE capital structure consists of 20% debt and 80% equity

(D/E ratio = 0.25). Compute relevered equity beta:

16

Converting Equity Betas to Asset Betas for Two Pure Play Firms

%96.9%)20%(5.6%)80%(83.10

de r

ED

Dr

ED

EWACC

One more step to find the right discount rate for GE’s investment in this industry: calculate project

WACC.

Using CAPM, compute rate of return GE shareholders require for the oil and gas investment.

• Assume risk-free rate of interest is 6% and expected risk premium on the market is 7%:

E(R) = 6% + 0.69(7%) = 10.83%.

– GE’s financing is 80% equity and 20% debt. Assume investors expect 6.5% on GE’s bonds:

17

Accounting for Taxes

• Have thus far assumed away taxes– Tax deductibility of interest payments favors use of debt.– Accounting for interest tax shields yields after-tax WACC.

ed rED

ErT

ED

DWACC

)1(

• After-tax formula for equity beta changes to:– We are still assuming debt beta = 0.

E

DTUE )1(1

βU is the beta of an unlevered firm.

Analogous to asset beta, but not strictly equal to βA due to taxes

18

Summary: Finding Discount Rate for Unique Projects

1) Identify pure play firms.

2) Calculate after-tax, unlevered betas for these firms and average them.

3) Relever beta to reflect the investing firm’s capital structure.

4) Plug relevered beta into CAPM to obtain re..

5) Use re, rd, and capital structure weights to obtain after-tax project WACC.

19

A Closer Look at RiskBreak-Even Analysis

Managers often want to assess business’ value drivers:

Useful to assessing operating risk is finding break-even point.

Break-even point is level of output where all operating costs (fixed and variable) are

covered.

20

Sensitivity Analysis

• Sensitivity analysis allows mangers to test importance of each assumption underlying a forecast.– Test deviations from “base case” and associated NPV.

• Best Electronics Inc has new DVD players project. Base case assumptions (below) yields Exp NPV = $1,139,715.1.   The project’s life is five years.2.   The project requires an up-front investment of $41 million.3.   BEI will depreciate initial investment on S-L basis for five

years.4.   One year from now, DVD industry will sell 3,000,000 units.5.   Total industry unit volume will increase by 5% per year.6.   BEI expects to capture 10% of the market in the first year.7. BEI expects to increase its market share one percentage

point each year after year one.

8. The selling price will be $100 in year one.9.   Selling price will decline by 5% per year after year one.10. Variable production costs will equal 60% of the selling price.11. The appropriate discount rate is 14 percent.

21

Sensitivity Analysis of DVD Project

NPV Pessimistic Assumption Optimistic NPV

-$448,315 $43,000,000 Initial investment $39,000,000 +2,727,745

-$1,106,574

2,800,000 un Market size in year 1 3,200,000 un +3,386,004

-$640,727 2% per year Growth in market size 8% per year +3,021,884

-$4,602,832

8% Initial market share 12% +6,882,262

-$3,841,884

Zero Growth in market share

2% per year +6,121,315

-$2,229,718

$90 Initial selling price $110 +4,509,149

-$545,002 62% of sales Variable costs 58% of sales +2,824,432

-$2,064,260

-10% per yr Annual price change 0% per year +4,688,951

-$899,413 16% Discount rate 12% +3,348,720

If all optimistic scenarios play out, project’s NPV rises to $37,635,010.If all pessimistic scenarios play out, project’s NPV falls to -$19,271,270!

22

Real Options in Capital Budgeting

Embedded options arise naturally from investment;

Called real options to distinguish from financial options.

Option pricing analysis helpful in examining multi-stage projects

Can transform negative NPV projects into positive NPV!

Value of a project equals value captured by NPV, plus option.

23

Real Options in Capital Budgeting

Expansion options

• If a product is a hit, expand production.

Abandonmen

t options • Can abandon a project if not

successful.• Shareholders have valuable option to

default on debt.Follow-on

investment

options

• Similar to expansion options, but more complex (Ex: movie rights to sequel)

Flexibility options

• Ability to use multiple production inputs (Ex: dual-fuel industrial boiler) or produce multiple outputs

All-equity firms can discount their standard investment projects at cost of equity.

Firms with debt and equity can discount their standard investment projects using WACC.

WACC and CAPM are connected. Cost of debt and equity are driven by debt and equity betas.

Use pure play equity betas when invest in unique projects.

Risk And Capital Budgeting