Chap012

McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved

CHAPTER

12 Risk, Cost of Capital, and

Capital Budgeting

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Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved

McGraw-Hill/Irwin

Chapter Outline

12.1 The Cost of Equity Capital

12.2 Estimation of Beta

12.3 Determinants of Beta

12.4 Extensions of the Basic Model

12.5 Estimating Eastman Chemical’s Cost of Capital

12.6 Reducing the 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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The Cost of Equity Capital

• From the firm’s perspective, the expected return is the Cost of Equity Capital:

)( FMiFi 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

Mi

M

Mii σ

σ

RVar

RRCovβ 3. The company beta,

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12.2 Estimation of Beta

Market Portfolio - Portfolio of all assets in the economy. In practice, a broad stock market index, such as the S&P Composite, 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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Real-World Betas

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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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12.3 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.

–Empirical evidence suggests that high-tech firms, retailers and automotive firms fluctuate with the business cycle.

–Transportation firms and utilities are less dependent upon the business cycle.

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• 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” or “flops,” but their revenues may not be especially dependent upon the business cycle.

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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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• If one cannot estimate a project’s beta in another way, one can examine the project’s revenues and operating leverage.

• Strongly cyclical and high operating leverage high betas, and vise versa. (qualitative approach)

• Start-up projects have little data, quantitative estimates of beta generally are not feasible.

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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.

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Financial Leverage and Beta• The relationship between the betas of the

firm’s debt, equity, and assets is given by:

Asset = Debt + Equity

Debt × Debt + Debt + Equity

Equity × Equity

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Financial Leverage and Beta

• The beta of debt is very low in practice, if we assume that the beta of debt is zero, we have βAsset = 【 Equity/(Debt + Equity) 】 *βEquity

βEquity = βAsset (1+Debt/Equity)

– The equity beta will always be greater than the asset beta with financial leverage.

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12.4 Extensions of the Basic Model

• The Firm versus the Project

• The Cost of Capital with Debt

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The Firm versus the Project

• Any project’s cost of capital depends on the use to which the capital is being put—not the source.

• Therefore, it depends on the risk of the project and not the risk of the company.

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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

The SML can tell us why:

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• In D. D. Ronnelley case, if they use the average beta of a portfolio of publicly traded software firms, the beta of a new project may be greater than the beta of existing firms in the same industry. So the new venture should be assigned a somewhat higher beta than that of the industry to reflect added risk.

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• What beta should be used in the rare case when an industry-wide beta is not appropriate? Consider the determinants of the project’s beta, but only qualitative in nature.

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The Cost of Capital with Debt• The Weighted Average Cost of Capital （ WACC)

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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S and B are market values of stock and debt, respectively. Market-value weights are more appropriate than book-value weights because the market values of the securities are closer to the actual dollars that would be received from their sale.

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• Actually, it is useful to think in terms of “target” market weights.

• It is usually referred to as the Weighted Average Cost of Capital, rWACC.

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12.6 Reducing the Cost of Capital

• What is Liquidity?

• Liquidity, Expected Returns and the Cost of Capital

• Liquidity and Adverse Selection

• What the Corporation Can Do

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• Both the expected return on a stock and the cost of capital of the firm are positively related to risk. Expected return and cost of capital are negatively related to liquidity as well.

What is Liquidity?

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• It is quite difficult to lower the risk of a firm, it is much easier to increase the liquidity of the firm’s stock.

• A firm can actually lower its cost of capital through liquidity enhancement.

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What is Liquidity?

• Liquidity: the cost of buying and selling stocks. Those stocks that are expensive to trade are considered less liquid than those that trade cheaply.

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• There are three costs here: – Brokerage fees – The bid-ask spread: the specialist makes money

here. The gain to the specialist is a cost to you. – Market-impact costs: the price drop associated

with a large sale and the price rise associated with a large purchase are the market- impact costs.

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Liquidity, Expected Returns, and the Cost of Capital

• Investors demand a high expected return when investing in stocks with high trading costs (i.e., low liquidity). And, this high expected return implies a high cost of capital to the firm.

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Liquidity and the Cost of Capital

Cos

t of

Cap

ital

LiquidityAn increase in liquidity (i.e., a reduction in trading costs) lowers a firm’s cost of capital.

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Liquidity and Adverse Selection

• There are a number of factors that determine the liquidity of a stock.

• One of these factors is adverse selection.• This refers to the notion that traders with better

information can take advantage of specialists and other traders who have less information.

• The greater the heterogeneity of information, the wider the bid-ask spreads, and the higher the required return on equity.

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What the Corporation Can Do?

• Bringing in more uninformed investors: stock splits ； facilitating stock purchases through the Internet.

• Disclosing more information: Companies can also disclose more information, especially to security analysts to narrow the gap between informed and uninformed traders. This should reduce spreads.

DOL =△ EBIT / EBIT

△ Q / Q=

Q(P–V)Q(P–V)–F

=S–VC

S –VC–F

DFL =△ EPS / EPS△ EBIT / EBIT

=EBIT

EBIT–I

DTL =△ EPS / EPS△ Q / Q

=Q(P–V)

Q(P–V)–F –I

=S–VC

S–VC–F –I(=DOL*DFL)

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Chap012

Economy & Finance

industry beta

equity equity equity

projects beta

company beta

stability of beta

beta operating leveragerefers

usethe firms beta

beta thebeta of debt