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RISK, COST OF CAPITAL, AND VALUATION
Chapter 12
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
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KEY CONCEPTS AND SKILLS
• Measure a firm’s cost of equity capital• Grasp and interpret the impact of beta in
determining the firm’s cost of equity capital• Comprehend and calculate the firm’s overall cost
of capital• Incorporate the impact of flotation costs on
capital budgeting
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CHAPTER OUTLINE
12.1 The Cost of Equity Capital12.2 Estimating the Cost of Equity Capital with the
CAPM12.3 Estimation of Beta12.4 Determinants of Beta12.5 Dividend Discount Model12.6 Cost of Capital for Divisions and Projects12.7 Cost of Fixed Income Securities12.8 The Weighted Average Cost of Capital
12.9 Valuation of RWACC
12.10 Estimating Eastman Chemical’s Cost of Capital12.11 Flotation Costs and the Weighted Average Cost
of Capital
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WHERE DO WE STAND?
•Earlier chapters on capital budgeting focused on the appropriate size and timing of cash flows.•This chapter discusses the appropriate discount rate when cash flows are risky.
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Invest in project
12.1 THE COST OF EQUITY CAPITAL
Firm withexcess cash
Shareholder’s Terminal
Value
Pay cash dividend
Shareholder invests in financial
asset
Because stockholders can reinvest the dividend in risky financial assets, the expected return on a capital-budgeting project should be at least as great as the expected return on a financial asset of comparable risk.
A firm with excess cash can either pay a dividend or make a capital investment
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12.2 ESTIMATING THE COST OF EQUITY CAPITAL WITH THE CAPM
• From the firm’s perspective, the expected return is the Cost of Equity Capital:
)( FMFS RRβRR • To estimate a firm’s cost of equity capital, we need to
know three things:
1. The risk-free rate, RF
FM RR 2. The market risk premium,
2,
)(
),(
M
MS
M
MS
σ
σ
RVar
RRCovβ 3. The company beta,
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EXAMPLE: CALCULATING “R” USING CAPM
• Suppose the stock of Stansfield Enterprises, a publisher of PowerPoint presentations, has a beta of 2.5. The firm is 100% equity financed. • Assume a risk-free rate of 5% and a
market risk premium of 10%.• What is the appropriate discount rate for
an expansion of this firm?
)( FMF RRβRR
%)105.2(%5 R
%30R
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EXAMPLE: USING RS AND THE SML TO EVALUATE PROJECTS
Suppose Stansfield Enterprises is evaluating the following independent projects. Each costs $100 and lasts one year.
Project Project Project’s Estimated Cash Flows Next Year
IRR NPV at 30%
A 2.5 $150 50% $15.38
B 2.5 $130 30% $0
C 2.5 $110 10% -$15.38
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APPLICATION: USING THE SML FOR PROJECT SELECTION
An all-equity firm should accept projects whose IRRs exceed the cost of equity capital and reject projects whose IRRs fall short of the cost of capital.
Pro
ject
IRR
Firm’s risk (beta)
SML
5%
Good project
Bad project
30%
2.5
A
B
C
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THE RISK-FREE RATE
• Treasury securities are close proxies for the risk-free rate.• The CAPM is a period model. However, projects
are long-lived. So, average period (short-term) rates need to be used.• As a practical matter, the one year Treasury Bill
rate will be assumed as an accurate estimate of short term rates• CAPM suggests that we should use a Treasury
security whose maturity matches the time horizon of investors:• No one agrees on what that horizon is!
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THE MARKET RISK PREMIUM
• Method 1: Use historical data• Method 2: Use the Dividend Discount Model
• Market data and analyst forecasts can be used to implement the DDM approach on a market-wide basis
gPDR 1
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12.3 ESTIMATION OF BETA
Market Portfolio - Portfolio of all assets in the economy. In practice, a broad stock market index, such as the S&P 500, is used to represent the market.
Beta - Sensitivity of a stock’s return to the return on the market portfolio.
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ESTIMATION OF BETA
)(
),(
M
Mi
RVar
RRCovβ
• Problems
1. Betas may vary over time.2. The sample size may be inadequate.3. Betas are influenced by changing financial leverage and business
risk.
• Solutions
– Problems 1 and 2 can be moderated by more sophisticated statistical techniques.
– Problem 3 can be lessened by adjusting for changes in business and financial risk.
– Look at average beta estimates of comparable firms in the industry.
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STABILITY OF BETA
• Most analysts argue that betas are generally stable for firms remaining in the same industry.• That is not to say that a firm’s beta cannot
change.• Changes in product line• Changes in technology• Deregulation• Changes in financial leverage
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USING AN INDUSTRY BETA
• It is frequently argued that one can better estimate a firm’s beta by involving the whole industry.• If you believe that the operations of the firm
are similar to the operations of the rest of the industry, you should use the industry beta.• If you believe that the operations of the firm
are fundamentally different from the operations of the rest of the industry, you should use the firm’s beta.• Do not forget about adjustments for financial
leverage.
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12.4 DETERMINANTS OF BETA
•Business Risk• Cyclicality of Revenues•Operating Leverage
•Financial Risk• Financial Leverage
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CYCLICALITY OF REVENUES
• Highly cyclical stocks have higher betas.• Such firms do well in the expansion phase of the
economic cycle and more poorly in the contraction phase
• Cyclical industries include retail and automotive• Non-cyclical industries include transportation
• Note that cyclicality is not the same as variability• Stocks with high standard deviations need not
have high betas.• Price movement of such stocks is more dependent
on quality of performance than market movement• Example: Movie studio hits and flops.
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OPERATING LEVERAGE
• The degree of operating leverage measures how sensitive 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
cyclicality on beta.• The degree of operating leverage is given by:
DOL = EBIT Sales
Sales EBIT×
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OPERATING LEVERAGE
Sales
$
Fixed costs
Total costs
EBIT
Sales
Operating leverage increases as fixed costs rise and variable costs fall.
Fixed costs
Total costs
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FINANCIAL LEVERAGE AND BETA
• Operating leverage refers to the sensitivity to the firm’s fixed costs of production.• Financial leverage is the sensitivity to a
firm’s fixed costs of financing.• The relationship between the betas of the
firm’s debt, equity, and assets is given by:
• Financial leverage always increases the equity beta relative to the asset beta.
Asset = Debt + Equity
Debt × Debt + Debt + Equity
Equity × Equity
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EXAMPLE
Consider Grand Sport, Inc., which is currently all-equity financed and has a beta of 0.90.The firm has decided to lever up to a capital structure of 1 part debt to 1 part equity.Since the firm will remain in the same industry, its asset beta should remain 0.90.However, assuming a zero beta for its debt, its equity beta would become twice as large:
Asset = 0.90 = 1 + 1
1 × Equity
Equity = 2 × 0.90 = 1.80
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12.5 DIVIDEND DISCOUNT MODEL
• The DDM is an alternative to the CAPM for calculating a firm’s cost of equity.
• The DDM and CAPM are internally consistent, but academics generally favor the CAPM and companies seem to use the CAPM more consistently. • This may be due to the measurement error
associated with estimating company growth.
gPDR 1
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12.6 CAPITAL BUDGETING & PROJECT RISK
A firm that uses one discount rate for all projects may over time increase the risk of the firm while decreasing its value.
Pro
ject
IR
R
Firm’s risk (beta)
SML
rf
FIRM
Incorrectly rejected positive NPV projects
Incorrectly accepted negative NPV projects
Hurdle rate
)( FMFIRMF RRβR
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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 market risk premium is 10%, and the firm’s beta is 1.3.
17% = 4% + 1.3 × 10% This is a breakdown of the company’s investment projects:
1/3 Automotive Retailer = 2.0
1/3 Computer Hard Drive Manufacturer = 1.3
1/3 Electric Utility = 0.6average of assets = 1.3
When evaluating a new electrical generation investment, which cost of capital should be used?
CAPITAL BUDGETING & PROJECT RISK
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CAPITAL BUDGETING & PROJECT RISK
Pro
ject
IR
R
Project’s risk ()
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 retailing should have higher discount rates.
SML
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12.7 COST OF DEBT
• Interest rate required on new debt issuance (i.e., yield to maturity on outstanding debt)
•Adjust for the tax deductibility of interest expense
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COST OF PREFERRED STOCK
•Preferred stock is a perpetuity, so its price is equal to the coupon paid divided by the current required return.
•Rearranging, the cost of preferred stock is:
•RP = C / PV
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12.8 THE WEIGHTED AVERAGE COST OF CAPITAL
• The Weighted Average Cost of Capital is given by:
• Because interest expense is tax-deductible, we multiply the last term by (1 – TC).
RWACC = Equity + Debt
Equity × REquity + Equity + Debt
Debt × RDebt ×(1 – TC)
RWACC = S + B
S× RS +
S + B
B× RB ×(1 – TC)
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12.9 FIRM VALUATION
•The value of the firm is the present value of expected future (distributable) cash flow discounted at the WACC
•To find equity value, subtract the value of the debt from the firm value
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12.10 EXAMPLE: EASTMAN CHEMICAL
• First, we estimate the cost of equity and the cost of debt.•We estimate an equity beta to estimate the cost of equity.•We can often estimate the cost of debt by observing the YTM of the firm’s debt.
• Second, we determine the WACC by weighting these two costs appropriately.
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EXAMPLE: EASTMAN CHEMICAL
• Eastman’s beta on Yahoo finance is 1.81, the risk free rate is .50%, and the market risk premium is 7%. • Thus, the cost of equity capital is:
RS = RF + i × ( RM – RF)
= .005 + 1.81×.07
= 13.17%
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EXAMPLE: EASTMAN CHEMICAL
• The yield on the company’s debt is 3.15%, and the firm has a 35% marginal tax rate.• The debt to value ratio is 29.4%
9.90% is Eastman’s cost of capital. It should be used to discount any project where one believes that the project’s risk is equal to the risk of the firm as a whole and the project has the same leverage as the firm as a whole.
= 0.706 × 13.17% + 0.294 × 3.15% × (1 – 0.35)
= 9.90%
RWACC = S + B
S× RS +
S + B
B× RB ×(1 – TC)
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12.11 FLOTATION COSTS
• Flotation costs represent the expenses incurred upon the issue, or float, of new bonds or stocks.• These are incremental cash flows of the project,
which typically reduce the NPV since they increase the initial project cost (i.e., CF0). Amount Raised = Necessary Proceeds / (1-% flotation cost)• The % flotation cost is a weighted average based
on the average cost of issuance for each funding source and the firm’s target capital structure:
fA = (E/V)* fE + (D/V)* fD
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QUICK QUIZ
• 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
of capital?• How do flotation costs affect the capital
budgeting process?
