Cost of Capital and Risk in Valuation

8/12/2019 Cost of Capital and Risk in Valuation

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Risk, Cost of Capital, and Valuation


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Know how to determine a firms cost of equitycapital

Understand the impact of beta in determining thefirms cost of equity capital Know how to determine the firms overall cost ofcapitalUnderstand the impact of flotation costs oncapital budgeting


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The Cost of Equity Capital

Estimating the Cost of Equity Capital with the CAPM

Estimation of Beta

Determinants of BetaThe Dividend Discount Model Approach

Cost of Capital for Divisions and Projects

Cost of Fixed Income Securities

The Weighted Average Cost of Capital

Valuation with R WACC

Estimating Eastman Chemicals Cost of Capital

Flotation Costs and the Weighted Average Cost of Capital


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Earlier we had looked at the issue of capital

budgeting focused on the appropriate size andtiming of cash flows.

This chapter discusses the appropriate discountrate when cash flows are risky.


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Invest in project

Firm withexcess cash

ShareholdersTerminal

Value

Pay cash dividendShareholder

invests infinancial asset

Because stockholders can reinvest the dividend in risky financialassets, the expected return on a capital-budgeting project should beat least as great as the expected return on a financial asset ofcomparable risk.

A firm with excess cash can either pay adividend or make a capital investment


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From the firms perspective, the expected return isthe Cost of Equity Capital:

)( F M F s R R R R

To estimate a firms cost of equity capital, we needto know three things:

1. The risk-free rate, R F

F M R R 2. The market risk premium,

2,

)(

),(

M

M i

M

M ii

RVar

R RCov 3. The company beta,


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Suppose the stock of Stansfield Enterprises, apublisher of PowerPoint presentations, has a betaof 1.5. The firm is 100% equity financed.

Assume a risk-free rate of 3% and a market riskpremium of 7%. What is the appropriate discount rate for anexpansion of this firm?

)( F M F s R R R R

%75.1%3 s R

%5.13 s R


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Suppose Stansfield Enterprises is evaluating thefollowing independent projects. Each costsRs.100 and lasts one year.

Project Project b Projects EstimatedCash Flows Next Year IRR NPV at 13.5%

A 1.5 Rs.125 25% Rs.10.13

B 1.5 Rs.113.5 13.5% Rs. 0C 1.5 Rs.105 5% -Rs.7.49


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An all-equity firm should accept projects whose IRRs exceed the costof equity capital and reject projects whose IRRs fall short of the cost

of capital.

P r o

j e c t

I R R

Firms risk (beta)

5%

Good project

Bad project

30%

2.5

A

B

C


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Market Portfolio - Portfolio of all assets in theeconomy. In practice, a broad stock market index,

such as the S&P 500, is used to represent themarket.

Beta -Sensitivity of a stocks return to the return

on the market portfolio.


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)(),(

M

M i

RVar R RCov

Problems

1. Betas may vary over time.

2. The sample size may be inadequate.

3. Betas are influenced by changing financialleverage and business risk.


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)(),(

M

M i

RVar R RCov

Solutions

Problems 1 and 2 can be moderated by moresophisticated statistical techniques.

Problem 3 can be lessened by adjusting for changes in business and financial risk.

Look at average beta estimates of comparable firms inthe industry.


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Most analysts argue that betas are generally stable forfirms remaining in the same industry.

That is not to say that a firms beta cannot change. Changes in product line

Changes in technologyDeregulationChanges in financial leverage


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Business Risk

Cyclicality of RevenuesOperating Leverage

Financial RiskFinancial Leverage


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Highly cyclical stocks have higher betas.Empirical evidence suggests that retailers andautomotive firms fluctuate with the business cycle.Transportation firms and utilities are less dependenton the business cycle.

Note that cyclicality is not the same as variability stocks with high standard deviations

need not have high betas.Movie studios have revenues that are variable,depending upon whether they produce hits orflops, but their revenues may not be especiallydependent upon the business cycle.


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The degree of operating leverage measures howsensitive a firm (or project) is to its fixed costs.

Operating leverage increases as fixed costs rise and variable costs fall.Operating leverage magnifies the effect of cyclicalityon beta.The degree of operating leverage is given by:

DOL = EBIT D Sales

SalesD EBIT


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Sales

Rs.

Fixed costs

Totalcosts

D EBIT

D Sales

Operating leverage increases as fixed costs riseand variable costs fall.

Fixed costs

Totalcosts


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Operating leverage refers to the sensitivity to the firmsfixed costs of production .Financial leverage is the sensitivity to a firms fixed costsof financing .The relationship between the betas of the firms debt,equity, and assets is given by:

Financial leverage always increases the equity betarelative to the asset beta.

b Asset = Debt + EquityDebt b Debt + Debt + EquityEquity

b Equity


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Consider Grand Sport, Inc., which is currently all-equityfinanced and has a beta of 0.90.The firm has decided to lever up to a capital structure of1 part debt to 1 part equity.Since the firm will remain in the same industry, its assetbeta should remain 0.90.However, assuming a zero beta for its debt, its equity

beta would become twice as large:

b Asset = 0.90= 1 + 1

1 b Equity b Equity = 2 0.90 = 1.80


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The DDM is an alternative to the CAPM for calculating afirms cost of equity.

The DDM and CAPM are internally consistent, butacademics generally favor the CAPM and companies seem touse the CAPM more consistently.

The CAPM explicitly adjusts for risk and it can be used oncompanies that do not pay dividends.

g P

R D s 1


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A firm that uses one discount rate for all projects may over timeincrease the risk of the firm while decreasing its value.

P r o

j e c t

I R R

Firms risk (beta)

r f

b FIRM

Incorrectly rejected positive NPV projects

Incorrectly accepted

negative NPV projectsHurdle

rate)( F M F IR M F R R R

The SML can tell us why:


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Suppose the Conglomerate Company has a cost of capital,based on the CAPM, of 17%. The risk-free rate is 4%, the marketrisk premium is 10%, and the firms beta is 1.3.17% = 4% + 1.3 10%This is a breakdown of the companys investment projects:

1/3 Automotive Retailer b = 2.0

1/3 Computer Hard Drive Manufacturer b = 1.3

1/3 Electric Utility b = 0.6average b of assets = 1.3

When evaluating a new electrical generation investment,

which cost of capital should be used?


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P r o

j e c t

I R R

Projects risk ( b)

17%

1.3 2.00.6 R = 4% + 0.6 (14% 4% ) = 10%

10% reflects the opportunity cost of capital on an investment

in electrical generation, given the unique risk of the project.

10%

24% Investments in hard

drives or auto retailingshould have higherdiscount rates.

SML


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Interest rate required on new debt issuance

(i.e., yield to maturity on outstanding debt)

Adjust for the tax deductibility of interestexpense


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Preferred stock is a perpetuity, so its price isequal to the coupon paid divided by thecurrent required return.

Rearranging, the cost of preferred stock is:R P = C / PV


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The Weighted Average Cost of Capital is given by:

Because interest expense is tax-deductible, wemultiply the last term by (1 T C ).

RWACC =Equity + Debt

Equity R Equity +

Equity + Debt

Debt R Debt (1 T C )

RWACC = S + B

S RS + S + B

B R B (1 T C )


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The value of the firm is the present value ofexpected future (distributable) cash flowdiscounted at the WACC

To find equity value, subtract the value of thedebt from the firm value


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First, we estimate the cost of equity andthe cost of debt.

We estimate an equity beta to estimate the

cost of equity. We can often estimate the cost of debt byobserving the YTM of the firms debt.

Second, we determine the WACC by weighting these two costs appropriately.


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The industry average beta is 0.82, the risk free rateis 3%, and the market risk premium is 8.4%.

Thus, the cost of equity capital is:

RS = R

F + b

i ( R

M R

F )

= 3% + 0.82 8.4%

= 9.89%


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The yield on the companys debt is 8%, and thefirm has a 37% marginal tax rate.The debt to value ratio is 32%

8.34% is Internationals cost of capital. It should be used todiscount any project where one believes that the projects riskis equal to the risk of the firm as a whole and the project has

the same leverage as the firm as a whole.

= 0.68 9.89% + 0.32 8% (1 0.37)

= 8.34%

RWACC = S + BS

RS + S + B B

R B (1 T C )


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How do we determine the cost of equity capital?How can we estimate a firm or project beta?How does leverage affect beta?How do we determine the weighted average cost ofcapital?

How do flotation costs affect the capital budgetingprocess?

Cost of Capital and Risk in Valuation

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