Chapter 13 Risk, Cost of Capital, and Valuation 13-0 Key Concepts - - PowerPoint PPT Presentation

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Risk, Cost of Capital, and Valuation

Chapter 13

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Key Concepts and Skills

• Know how to determine a firm’s cost of equity

capital

• Understand the impact of beta in determining

the firm’s cost of equity capital

• Know how to determine a firm’s cost of debt
• Know how to determine the firm’s overall cost of

capital

• Understand how to find the appropriate cost of

capital for any given capital project

• Understand the impact of flotation costs on

capital budgeting

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Chapter Outline

13.1 The Cost of Equity Capital 13.2 Estimating the Cost of Equity Capital with the CAPM 13.3 Estimation of Beta 13.4 Determinants of Beta 13.5 The Dividend Discount Model Approach 13.6 Cost of Capital for Divisions and Projects 13.7 Cost of Fixed Income Securities 13.8 The Weighted Average Cost of Capital 13.9 Valuation with RWACC 13.10 Estimating Eastman Chemical’s Cost of Capital 13.11 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 identification of relevant (incremental) cash flows and their timing, evaluating, say, NPV using a given discount rate.

• This chapter discusses how to find the

appropriate discount rate or required rate of return or the cost of capital when cash flows are risky.

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4

Invest in project

13.1 The Cost of Equity Capital

Firm with excess 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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5

Cost of Equity Capital

• Implication: Discount rate needs to be

appropriate for project’s risk (not necessarily the same as the firm’s overall risk)

• Let’s begin by considering how to estimate a

firm’s cost of equity capital.

• Two approaches for finding a firm’s equity cost
• f capital:

– From last time, CAPM – Dividend Discount Model (DDM)

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The Cost of Equity Capital

• The cost of equity capital is the required return on the

stockholders’ investment in the firm. CAPM can be used to estimate the required return. From the firm’s perspective, the expected return is the Cost of Equity Capital:

) (

F M i F i

R R β R R   

• To estimate a firm’s cost of equity capital, we need to

know three things:

• 1. The risk-free rate, RF

F M

R R 

• 2. The market risk premium,

2 ,

) ( ) , (

M M i M M i i

σ σ R Var R R Cov β  

• 3. The company beta,

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Example

• Suppose the stock of Stansfield Enterprises, a

publisher of PowerPoint presentations, has a beta of 1.5. The firm is 100% equity financed.

• Assume a risk-free rate of 3% and a market

risk premium of 7%.

• What is the appropriate discount rate for an

expansion of this firm?

) (

F M F s

R R β R R    % 7 5 . 1 % 3   

s

R % 5 . 13 

s

R

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Example

Suppose Stansfield Enterprises is evaluating the following independent projects. Each costs $100 and lasts one year.

Project Project b Project’s Estimated Cash Flows Next Year IRR NPV at 13.5% A 1.5 $125 25% $10.13 B 1.5 $113.5 13.5% $0 C 1.5 $105 5%

• $7.49

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Using the SML

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.

Project 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.

• Although the T-Bill rate is theoretically risk free, it is

frequently distorted by Fed Policy.

• The CAPM is a period model. However, projects are

long-lived. So, average period (short-term) rates need to be used.

• The historic premium of long-term (20-year) rates over

short-term rates for government securities is 2%.

• So, the risk-free rate to be used in the CAPM could be

estimated as 2% below the prevailing rate on 20-year treasury securities.

• Or use short term T-Note rates instead, say, 10 years.
• http://finance.yahoo.com/q?s=^TNX

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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. – Will not be stable. Also subject to growth assumption

• Method 3. Use forecasts

g P D R  

1

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Historical Market Risk Premium

• From SBBI Data:1926-2010

– Small Stocks: 12.22% – S&P 500: 9.85% – US LT Gov Bonds: 5.45% – US 30 Day T Bills: 3.62% – US Inflation: 3.04%

• Risk Premium:

– SP500-LT Bonds = 9.85%-5.45%= 4.4% – SP500-T Bills = 9.85%-3.62%= 6.23%

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Implied Risk Premium using the S&P 500

• http://pages.stern.nyu.edu/~adamodar/
• D1/P is the dividend yield. Because firms also buyback shares, we can use

in its place the dividend yield plus the buyback yield.

– 1.81%+2.08% = 3.88%

• g is the growth rate of dividends. For simplicity use the historic growth rate.

– Dividend in 2001 = 15.74, in 2010 = 22.73. g=(22.73/15.74)(1/9)-1 = 4.2%

% 08 . 6 % 2 % 08 . 8 % 08 . 8 % 2 . 4 % 88 . 3

1

            RF R ERP ERP RF R R R g P D R

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Survey data on the risk premium

• Most survey data is of academics and industry

professionals.

– Average is about 5.5%. – Has fallen in recent years from above 6%.

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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

• n the market portfolio.

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Estimation of Beta

) ( ) , (

M M i

R Var R R Cov β 

• 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. (see Rolling Beta for TGT.xlsx)

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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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Determinants of Beta

• Business Risk

– Cyclicality of Revenues – Operating Leverage

• Financial Risk

– Financial Leverage

• Highly cyclical stocks have higher betas.

– Retailers, auto makers

• Less cyclical

– Utilities.

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Example

• 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
• f this firm?

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Example

Suppose Stansfield Enterprises is evaluating the following independent projects. Each costs $100 and lasts one year.

Project Project b 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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Using the SML

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.

Project IRR Firm’s risk (beta)

SML

5% Good project Bad project 30% 2.5 A B C

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What if project betas vary?

• If the firm has a single cost of capital, but

considers projects of varying risk, adjustments should be made.

– Different risk adjusted costs of capital should be used for each project.

• Otherwise the firm will over invest in risky

projects.

– Why? - See the following example.

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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 b = 2.0 1/3 Computer Hard Drive Manufacturer b = 1.3 1/3 Electric Utility b = 0.6 average b 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

Project IRR Project’s risk (b) 17% 1.3 2.0 0.6 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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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. Project IRR Firm’s risk (beta)

SML

rf bFIRM Incorrectly rejected positive NPV projects Incorrectly accepted negative NPV projects Hurdle rate

) (

F M FIRM F

R R β R  

The SML can tell us why:

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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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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
• In practice, finding new debt issuances is tricky.
• For companies with publicly traded debt, we can rely on

the yield to maturity of the debt.

– Note that the coupon rate is NOT a measure of the cost of debt today.

• http://finance.yahoo.com/bonds

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Example: Target Corp

• First, we estimate the cost of equity and the cost
• f 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: International Paper

• The industry average beta is 0.82, the risk free rate is

3%, and the market risk premium is 8.4%.

• Thus, the cost of equity capital is:

RS = RF + bi × (RM – RF) = 3% +.82×8.4% = 9.89%

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Example: International Paper

• The yield on the company’s debt is 8%, and

the firm has a 37% marginal tax rate. The debt to value ratio is 32%

8.34% is International’s cost of capital. = 0.68 × 9.89% + 0.32 × 8% × (1 – 0.37) = 8.34% RWACC = S + B S × RS + S + B B × RB ×(1 – TC)

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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.

bAsset = Debt + Equity Debt × bDebt + Debt + Equity Equity × bEquity

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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: bAsset = 0.90 = 1 + 1 1 × bEquity bEquity = 2 × 0.90 = 1.80