FInance Discussion Topic #3
jandregRisk, Cost of Capital, and Valuation
Chapter 13
Copyright © 2013 by the McGraw-Hill Companies, Inc. All rights reserved.
McGraw-Hill/Irwin
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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 the firm’s overall cost of capital
- 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 appropriate size and timing of cash flows.
- This chapter discusses the appropriate discount rate when cash flows are risky.
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The terms discount rate, required return, and cost of capital are all synonymous.
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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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Therefore, the discount rate of a project should be the expected return on a financial asset of comparable risk.
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The Cost of Equity Capital
- From the firm’s perspective, the expected return is the Cost of Equity Capital:
- To estimate a firm’s cost of equity capital, we need to know three things:
- The risk-free rate, RF
- The market risk premium,
- 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?
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You may want to note that this example assumes expansion into projects that are similar to the existing nature of the business. Also, point out that the firm is all equity, thus its discount rate is the cost of equity.
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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)
5%
Good project
Bad project
30%
2.5
A
B
C
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This, again, assumes independent projects. This is a good point at which to review the relation between IRR and NPV.
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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.
- 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.
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This approach follows Ibbotson.
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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
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13.3 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
- Problems
- Betas may vary over time.
- The sample size may be inadequate.
- 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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13.4 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.
- Empirical evidence suggests that retailers and automotive firms fluctuate with the business cycle.
- Transportation firms and utilities are less dependent on 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” 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
D Sales
Sales
D 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.
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:
bEquity =
2 × 0.90 = 1.80
bAsset = 0.90 =
1 + 1
1
× bEquity
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13.5 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.
- The CAPM explicitly adjusts for risk and it can be used on companies that do not pay dividends.
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Note that even if a firm pays no dividend, there is still a cost to equity, as investors expect to receive future payouts (i.e., the growth). Further, investors also face opportunity costs for investing in one firm versus another, implying that dividend yield is only a piece of the whole issue.
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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)
Hurdle rate
The SML can tell us why:
rf
bFIRM
Incorrectly rejected positive NPV projects
Incorrectly accepted negative NPV projects
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To estimate the cost of capital for a division, a “pure play” approach could be used, although finding exactly similar firms may be difficult, particularly considering underlying financial and operational structure.
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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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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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There is no tax adjustment because dividends are not tax deductible.
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13.8 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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With preferred stock:
WACC = (S/(B+P+S))RS + (P/(B+P+S))RP + (B/(B+P+S))RD(1-TC)
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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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Example: International Paper
- 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: 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:
= 3% + 0.82×8.4%
= 9.89%
RS = RF + bi × ( RM – RF)
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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. 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.
= 0.68 × 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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13.11 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?
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