journal man fin

Learning Objectives

After studying this chapter, you should be able to:

• Show how the discount rate is calculated and used.

• Explain how the weighted average cost of capital is calculated, and outline the significance of its components.

• Describe how to estimate the discount rate for individual projects and how risk factors into the process.

Associated Press8

Cost of Capital

byr80601_08_c08_225-252.indd 225 1/24/13 3:59 PM

CHAPTER 8Pre-Test

Introduction

Figure 8.0: Chapter 8 in focus

Investments made by the firm

Bank loans

Bonds

Preferred stock

Common stock

The Financial Balance Sheet

Cash returned to capital supplied $

Capital suppliers are exposed to risk and their returns must reflect that risk. The corporation’s cost of capital is the weighted average of the returns required by suppliers of capital. This weighted average cost of capital is the discount rate for corporate investments.

Chapter 6 described the various capital budgeting techniques employed by corporate managers. Among the techniques, net present value (NPV) emerges as the best measure of a project’s contribution to shareholder wealth. In NPV analysis, the present value of a project’s expected future cash flows is compared to the initial investment, and the proj- ect is accepted if the present value exceeds the initial investment. Calculation of NPV requires the analyst to estimate cash flows and an appropriate discount rate. Techniques for estimating cash flows were covered in Chapter 6. In this chapter, you will learn how to estimate the discount rate. The same estimates of cash flows and discount rate are also used in internal rate of return analysis. Used in IRR, the discount rate becomes a hurdle rate against which to compare the project’s IRR.

Pre-Test

1. The cash flows from a project are distributed to investors in order of the priority of their claims.

a. True b. False

2. The cost of preferred stock is found by solving for the required return of a perpetuity.

a. True b. False

byr80601_08_c08_225-252.indd 226 1/24/13 3:59 PM

CHAPTER 8Section 8.1 Estimating the Discount Rate

3. WACC is used as the discount rate for evaluating projects if they are riskier than the overall firm’s risk.

a. True b. False

Answers 1. a. True. The answer can be found in Section 8.1. 2. a. True. The answer can be found in Section 8.2. 3. b. False. The answer can be found in Section 8.3.

8.1 Estimating the Discount Rate

To illustrate the calculation and use of the discount rate, we elaborate on the Chapter 6 example of Pacific Offshore Ltd. (POL). Recall the NPV of POL’s Pogo harness project is $9,110, which was found by discounting the project’s net cash flows by 12.5% (the required rate of return). The project’s internal rate of return of 17.2% is greater than the 12.5% required rate of return on the harness project; therefore, whether we use NPV or IRR, the harness project appears to be acceptable because it meets the respective decision criteria. Had the required return been 20%, for example, the project would have been rejected using either criterion. Table 8.1 reviews the details of POL’s Pogo harness project from Chapter 6.

Table 8.1: Review of POL’s Pogo harness project details

Data Category Value

Project cost $64,384

Required rate of return 12.5%

Internal rate of return 17.2%

Net present value $9,110

We have referred to the 12.5% as the harness project’s required rate of return. To be more specific, 12.5% is the weighted average return demanded by the company’s investors. The weightings reflect the proportional values of their investments. From Chapter 6, the cost of the harness project is $64,384, meaning that Paula Bauer must raise that amount from her investors to fund tools, equipment, and working capital and to pay the cost of reconfiguring the plant. Paula has decided to fund future projects using the firm’s cur- rent proportional mix of debt and preferred and common stock. POL’s current capital mix is 28% debt, 7.8% preferred stock, and 64.2% common stock. POL, therefore, will raise about $18,000 in debt and about $5,000 in preferred stock. The balance of the funding will come from residual cash flows that belong to the firm’s shareholders. Table 8.2 shows how

byr80601_08_c08_225-252.indd 227 1/24/13 3:59 PM

CHAPTER 8Section 8.1 Estimating the Discount Rate

POL’s capital mix will fund the Pogo harness project. Later, in Section 8.2, we will show you how Paula came up with these numbers.

Table 8.2: POL’s capital mix

Capital component Proportion Cash Value

Debt 28% $18,028

Preferred stock 7.8% $5,022

Common stock 64.2% $41,334

Cash from the harness project will flow to these investors in order of the priority of their claims: first to bondholders, then to preferred stockholders, and finally to common stock- holders. Figure 8.1 illustrates the flow of capital and cash flows, assuming that the harness project produces its expected cash flows.

Figure 8.1: Pogo harness project

Harnesses

Cash Flows

$64,384

$18,028

$5,022

$41,334

Bondholders

Preferred stockholders

Common stockholders

Pogo Harness Project tools, equipment, working capital, plant

Consumers

Financing mix and cash flows for the Pogo harness project.

POL raises capital by selling these securities to investors, who expect to receive a return on their investment. Any investor purchasing POL’s securities must expect that the returns will be at least equal to, and preferably greater than, the required return on an investment having the same risk as the harness project. If expected returns were lower than required, investors would look elsewhere, or they may be persuaded to buy POL’s securities at a discount, which would increase their expected returns. Thus, Paula must be confident that the discount rate she uses to value the project will provide the required return to each class of POL’s investors. This discount rate is known as the cost of capital for the project

byr80601_08_c08_225-252.indd 228 1/24/13 3:59 PM

CHAPTER 8Section 8.2 The Weighted Average Cost of Capital

because the returns investors require are the cost, like rent, that is paid for the use of the capital.

8.2 The Weighted Average Cost of Capital

The cost of capital is a weighted average of the required returns for each capital source. In this section, we will show you how to calcu- late the weighted average cost of capital and its components.

Calculating the Weighted Average Cost of Capital For the Pogo harness project, the weighted average cost of capi- tal (WACC) is the after-tax required returns (interest on bonds or other types of debt is tax deductible; thus, it lowers the effective cost of debt to the firm) on POL’s bonds, preferred stock, and common equity, weighted by their proportional contribution to the project. As you can see in Table 8.3, of the $64,384 being raised, the bondholders contribute $18,028 (28%), the preferred stockholders contribute $5,022 (7.8%), and the common stockhold- ers contribute the remaining $41,334 (64.2%) in residual cash flows.

Later we will explain how Paula estimated the costs of debt, preferred stock, and common equity. First, though, we present her worksheet for computing POL’s cost of capital. Table 8.3 shows that she multiplied the proportion of each capital source by its after-tax required return. She then summed these results to arrive at the 12.5% cost of capital (or the project’s required rate of return).

Table 8.3: Worksheet for computing POL’s cost of capital

Capital component

A Targeted proportion or weight

B Project cost

A 3 B Dollars raised

D After-tax required returns

A 3 D Weighted Average

Debt (bonds) 28% $64,384 $18,028 6.93% 1.94%

Preferred stock 7.8% $64,384 $5,032 11.96% 0.93%

Common equity

64.2% $64,384 $41,334 15% 9.63%

Total 100% $64,384 12.5%

Cost of capital includes the rent a company pays in order to use its capital. What other expenses could be included in cost of capital?

Associated Press

byr80601_08_c08_225-252.indd 229 1/24/13 3:59 PM

CHAPTER 8Section 8.2 The Weighted Average Cost of Capital

Paula’s worksheet may be summarized by a formula for the weighted average cost of capital.

(8.1) WACC = (Wd)(after-tax cost of debt)

+ (Wpfd)(cost of preferred stock)

+ (We)(cost of common equity) where

Wd = the desired proportion of financing provided by debt

Wpfd = the desired proportion of financing provided by preferred stock

We = the desired proportion of financing provided by common equity

This formula is adaptable to any combination of financing sources. For example, if pre- ferred stock were not used, then Wpfd 5 0, and preferred stock would drop out of the formula. Some companies borrow from many sources, and they may have several bond issues and perhaps long-term loans from banks or insurance companies. The only source of capital that is common to all companies is common equity. The WACC formula for a company with no preferred stock, but with two types of debt, might look like this:

(8.2) WACC = (WB)(after-tax cost of bonds)

+ (WL)(after-tax cost of loan)

+ (We)(cost of equity)

No matter how many sources of capital there are, the weights always sum to 1 (WB 1 WL 1 We 5 1). This ensures that all capital sources have been included in the calculation of WACC.

Discounting expected cash flows by the weighted average cost of capital gives Paula the information she needs to make her investment decision on the Pogo harness project. If the NPV 5 0, then the project should provide all investors with their required returns but with nothing more. This is the minimally acceptable outcome. The harness project is expected to do better than that, meaning that it should add value because its NPV is $9,110.

To summarize, discounting project cash flows at the WACC ensures that the minimal needs of each class of investor are met. The WACC is the appropriate discount rate for the harness project if its risk is similar to that of the entire company, and it is being financed with a mix of debt and equity similar to that of the company’s financing.

We may rewrite the NPV and IRR equations from Chapter 6 to include WACC.

Recall Equation (6.1), the NPV equation, from Chapter 6:

byr80601_08_c08_225-252.indd 230 1/24/13 3:59 PM

CHAPTER 8Section 8.2 The Weighted Average Cost of Capital

(8.3) NPV 5 2II 1 a nt 5 1 OCFt

11 1 R1r2 2 t 1 TCFn

11 1 R1r2 2 n where

II 5 initial investment

OCFt 5 operating cash flows in year t

TCF 5 terminal cash flows

t 5 year

n 5 life span of the project (in years)

r 5 required rate of return

Rewritten to include WACC, the NPV equation becomes

(8.4) NPV 5 a nt 5 1 CFt

11 1 WACC2 t 2 II

where

CFt 5 total net cash flow for period t

The company should accept projects with NPV . 0.

Rewritten to accommodate WACC, the IRR equation becomes

(8.5) a nt 5 1 CFt

11 1 IRR2 t 2 II 5 0

The company should accept projects with IRR . WACC because such projects have expected returns (IRRs) greater than the investor’s required return (WACC).

Next, we explain how Paula estimated the cost of each capital component.

The Cost of Debt The cost of debt, or Kd, is the current yield to maturity on the company’s bonds or other long-term debt securities.

Cost of debt 5 Yield to maturity

or

Kd 5 YTM

YTM reflects current credit market conditions and investors’ expectations, and therefore it is the best indicator of returns investors require on the sale of new bonds. Recall from Chapter 4 that YTM is the discount rate applied to the expected cash flows from a bond. This discount rate is the cost of debt for the project.

byr80601_08_c08_225-252.indd 231 1/24/13 3:59 PM

CHAPTER 8Section 8.2 The Weighted Average Cost of Capital

Let’s assume the current market price of POL’s bonds is $1,003. The bonds mature in 6 years, bear a 9.5% coupon rate, make coupon payments semiannually, and their par value is $1,000. Given this information, Kd is found by solving for YTM in the following equation, which sets the price of the bonds equal to the present value of future cash flows. We may think of the YTM as the internal rate of return of a bond.

$1,003 5 $47.50

11 1 YTM2 1 1 $47.50

11 1 YTM2 2 1 . . . 1 $47.50

11 1 YTM2 12

1 $1,000

11 1 YTM212

Note that each coupon payment, $47.50, equals one-half of the coupon rate (9.5%) times par value ($1,000) because the bond pays coupons semiannually [(0.095)($1,000)/2 5 $47.50]. There are 12 payments because the bonds mature in 6 years and pay interest twice per year (semiannually). Similar to IRR, a financial calculator or computer will be needed to solve for YTM, but we will save you the work on this equation: The YTM on these bonds equals 4.72% semiannually, or 9.44% on an annual basis.

Because interest on debt is tax deductible, the YTM must be adjusted for the tax effect. The tax deduction lowers the effective cost of debt to the company. We adjust YTM for taxes by multiplying YTM by (1 – t), where t is the firm’s marginal tax rate. Substituting Kd for YTM gives us Equation (8.6):

(8.6) After-tax cost of debt 5 Kd (1 – t)

The Cost of Preferred Stock As you recall from Chapter 4, preferred stock combines features of debt and equity. Pre- ferred dividends are fixed, like bond interest, but also have an infinite life, like common stock dividends. We recognize this as a perpetuity (a perpetual annuity), which greatly simplifies the calculation. The cost of preferred stock, or Kpfd, equals its required rate of return, which is its annual dividend divided by its current market price.

Cost of preferred stock 5 Required rate of return 5 Annual dividend /Current market price

Again, let’s assume the dividend on POL’s preferred stock is $2.50 and its current mar- ket price is $21.50 per share. As Equation (8.7) shows, the required return on the stock is 11.63%.

(8.7) Kpfd 5 dividend

share price 5

$2.50 $21.50

5 0.1163 5 11.63%

byr80601_08_c08_225-252.indd 232 1/24/13 3:59 PM

CHAPTER 8Section 8.2 The Weighted Average Cost of Capital

No tax adjustment is necessary for preferred stock because dividends are paid with after- tax cash flows.

The Cost of Common Equity, Ke The cost of common equity, or Ke, is the most difficult of the component costs to estimate. Chapter 7 presented the capital asset pricing model (CAPM) as one means of estimating investors’ required return for risky assets. Although this risk–return model is the most frequently used method for estimating returns to common stock, other models may also be used, most notably the discounted cash flow model introduced in Chapter 4. As a gen- eral rule, the analyst should approach the problem of estimating common stock returns from several directions and hope to generate a consensus estimate from these varying approaches. Here, we will cover three approaches: CAPM, the discounted cash flow model, and the equity-debt risk premium.

The CAPM Approach to Ke Chapter 7 built on portfolio theory to show the relationship between required returns on investments and their market risk. The CAPM states that the required return on a risky investment equals the risk-free rate plus the product of the asset’s beta and the market risk premium.

Required return on risky investment 5 Risk-free rate 1 Asset’s beta (Market risk premium)

Represented as an equation, the CAPM is

(8.8) R1r2 i 5 rf 1 bi 1market risk premium2

or

R1r2 i 5 ri 1 bi 3E1rm 2 2 rf 4

where

R(r)i 5 required return for asset i

Rf 5 risk-free rate of return

bi 5 beta of asset i

Now, let’s look at the individual components of the equation to find the information needed to solve the CAPM.

First, we examine the risk-free return. Although no asset is totally free of risk, U.S. govern- ment T-bonds are considered nearly riskless. Thus, T-bonds are a widely used proxy for the true risk-free rate. T-bond returns are widely available in print and on the Web.

byr80601_08_c08_225-252.indd 233 1/24/13 3:59 PM

CHAPTER 8Section 8.2 The Weighted Average Cost of Capital

Websites like Yahoo! are useful for obtaining beta information. What benefit is there to obtaining the information this way versus calculating it yourself?

Associated Press

Next, we need an estimate of the equity beta. Brokerage and other investment service firms estimate betas for many pub- licly traded stocks. Betas may be obtained on the Web and in print from Value Line, Stan- dard & Poor’s, Yahoo!, and Bloomberg. As we saw in Chap- ter 7, we may also estimate beta ourselves using data on past returns.

In place of market risk pre- mium, we use the historical market risk premium. This is found by calculating the aver- age amount by which the mar- ket return has exceeded T-bond returns. For example, the dif- ference between the S&P 500

return and the T-bond return for years 1931 through 2011 could be averaged and used as the historical market risk premium. In that 80-year period, the market risk premium has averaged about 7.6% per year (Damodaran, 2011). There are many other estimates of the markets risk premium (or equity risk premium). For more information, please see the Web Resources section at the end of the chapter.

For POL, Paula gathered estimates for the risk-free return, POL’s beta, and the market risk premium. These can be found in Table 8.4.

Table 8.4: POL’s cost of equity estimates using the CAPM

CAPM component Value

Risk-free return (T-bonds) rf 5 5%

BetaPOL (from POL’s investment banker) bPOL 5 1.2

Market risk premium (historical equity market risk premium)

7.6%

If we plug these numbers into Equation (8.8), Paula’s CAPM estimate is

R1r2 POL 5 rf 1 bPOL3market risk premium 4

5 5% 1 1.2(7.6%)

5 14.12%

The CAPM approach is the most popular among companies for determining their cost of equity.

byr80601_08_c08_225-252.indd 234 1/24/13 3:59 PM

CHAPTER 8Section 8.2 The Weighted Average Cost of Capital

The Discounted Cash Flow Approach to Ke In Chapter 4, the constant dividend growth model for valuing common stock was intro- duced. To find the cost of equity, we use a form of that constant growth formula.

(8.9) P0 5 D1

Ke 2 gn where

P0 5 today’s price of the stock

Ke 5 the required return on equity, also known as the cost of equity

gn 5 the normal, constant growth rate of dividends

D1 5 the next dividend that the firm is expected to pay

The current price equals next year’s dividend divided by the difference between equity’s required return and the long-run dividend growth rate.

This equation may also be adapted to allow us to solve for Ke:

(8.10) Ke 5 D1 P0

1 gn

The dividend growth model for estimating the required return on common stock reflects the discounted cash flow approach to valuation, as do the YTM for debt and the preferred stock perpetuity model.

This approach requires a current market price, an estimate of next year’s dividend per share, and an estimate of the long-run dividend growth rate. Prices for traded firms’ stock are easily obtained. Value Line and many brokerage firms forecast dividends and dividend growth rates for large and actively traded companies. For smaller companies, such as POL, published forecasts are generally not available, so we must rely on our own resources. Forecasts should begin by looking at a company’s dividend history. If we have enough data, we can calculate historical growth rates. The historical growth rate is the compound rate that equates a dividend paid several years ago with a recent dividend payment. This process is nothing more than an application of the future value of a single cash flow formula, as given in Chapter 3.

FVn 5 PV0 (1 1 r) n

where

FVn 5 the future value at the end of n time periods

PV0 5 the present value of the cash flow

r 5 the periodic interest rate

byr80601_08_c08_225-252.indd 235 1/24/13 3:59 PM

CHAPTER 8Section 8.2 The Weighted Average Cost of Capital

The difference is that rather than looking forward, we are looking back. To use the model, we must change the definition of its components. FVn becomes the most recent dividend, D0. PV0 becomes the beginning historical dividend, D–n (“–n” refers to n periods in the past). Finally, the rate of return, r, becomes the compound growth rate, gn. Equation (8.11) shows us what the new formula looks like:

(8.11) D0 5 D2n11 1 gn2 n

where

D0 5 the most recent dividend

D–n 5 the beginning historical dividend

gn 5 the compound growth rate

Fortunately, POL has paid a dividend for five years, so we are able to calculate a growth rate. The dividend five years ago (D–5,) was $0.60 and the most recent dividend (D0) was $0.84. Now, let’s solve for gn .

D0 5 D2n(1 + gn) n

D0 5 D25 11 1 gn2 5

0.84 5 0.60(1 1 gn2 5

11.42 15 5 1 1 gn 1.07 5 1 1 gn

0.07 5 gn

gn 5 7%

Now that we have solved for the compound growth rate, we can plug it into the constant growth formula. The current market price of POL’s common stock is $11.25. Next year’s dividend, D1, should equal D0 (1 1 gn). D1 5 $0.84(1.07) 5 $0.90. Now, we may solve for Ke.

Ke 5 D1 P0

1 gn

P0 5 $11.25

gn 5 7% 5 0.07

D1 5 $0.90

Ke 5 $0.90 11.25

1 0.07 5 0.15 5 15%

byr80601_08_c08_225-252.indd 236 1/24/13 3:59 PM

CHAPTER 8Section 8.2 The Weighted Average Cost of Capital

Having estimated Ke using the constant growth formula, we must remember that this formula assumes a constant growth rate into perpetuity. Therefore, this method may not be appropriate for firms whose growth is unstable or unsustainable. Cyclical firms, such as lumber companies, often have earnings that fluctuate dramatically with the business cycle. Exceptionally high initial growth rates of start-up companies will eventually fall to more sustainable levels as the industry matures. For these types of firms, the constant growth assumption is quite difficult to apply. In practice, companies appear to favor the CAPM approach to the discounted cash flow approach for determining their cost of equity.

The Equity-Debt Risk Premium Approach to Ke The final method for estimating the cost of equity is to add a risk premium to the cost of debt. Because equity is a residual claim with a lower priority than debt, equity is riskier than debt; therefore, investors require that Ke exceed Kd. The difference between Ke and Kd is the equity-debt risk premium.

(8.12) Ke 5 Kd 1 RP

The risk premium, RP, is generally in the range of 3% to 6%. The method is ad hoc but works fairly well as a benchmark because the necessary data are easily obtained. Esti- mates of Ke, using CAPM and discounted cash flow models, that fall outside the range [Kd 1 (3% to 6%)] should prompt the analyst to revisit her estimates. For POL, the equity-debt risk premium approach yields the following range for Ke.

1Kd 1 3%2 , Ke , 1Kd 1 6%2

(9.4% 1 3%) , Ke , (9.4% 1 6%)

12.4% , Ke , 15.4%

Recall that Paula’s estimates of Ke using the CAPM were 14.12%, and her discounted cash flow method produced a 15% cost of equity. Those estimates are within the range pre- scribed by the equity-debt risk premium, which more or less confirms Paula’s estimates. Weighing the results of the three approaches to estimating Ke, Paula elected 15% as POL’s cost of equity. As with preferred stock, no tax adjustment is necessary because dividends are not a tax-deductable expense.

The Cost of Selling Securities The cost of capital reflects returns required by investors who are supplying capital to the firm. These returns reflect the amount the investors paid for their respective securities. However, when a company raises funds by selling securities, it usually employs a company to assist it in marketing its securities. Companies that specialize in selling new securities issues, called investment banks, take a cut for marketing and underwriting the issue. A securities issue is underwritten when the investment bank buys securities from the com- pany and resells them to investors for a higher price. The difference between the price paid to the company and the sale price is called the underwriting spread. Of course, the sale price must approximate the security’s market value. For example, let’s assume that POL is selling bonds to pay for the harness project. Investors will buy the bonds for their current

byr80601_08_c08_225-252.indd 237 1/24/13 3:59 PM

CHAPTER 8Section 8.2 The Weighted Average Cost of Capital

Facebook is one of many promising companies that venture capital firms invested in. Do you think venture capital is a beneficial way for small companies to obtain the capital they need?

Associated Press

market price, $1,003. How- ever, the underwriting spread reduces POL’s proceeds from the bond sale and raises POL’s effective cost of debt above the 9.44% YTM.

Costs associated with selling securities are called flotation costs. Aside from the underwrit- ing spread, flotation costs include fees paid to the investment banker for consultation, docu- ment preparation, and so on. They also include costs of filing with regulators such as the Secu- rities and Exchange Commission, as well as legal and accounting fees. Here is a list of common fea- tures of flotation costs:

• They make up a greater percentage of the value of the securities issues for equity than those for debt, reflecting the increased risk of underwriting stocks.

• They are proportionally greater for issues of small dollar value. • There are significant scale economies to securities issues. • Some fees and other costs are relatively fixed.

With the high cost of issuing securities for smaller companies, it would seem that small firms might have a tough time raising outside capital. Historically, this has been the case with small firms having to rely largely on private sources of capital. However, the rapid development and dissemination of technology, and the deregulation of financial services, of transportation, and of telecommunications have bolstered entrepreneurial activity in the United States, creating new investment opportunities. As evidence, venture capital firms have sprung up by the hundreds to supply early financing to promising companies. One such company was Facebook, which went public in May of 2012. Unfortunately, the IPO was something of a flop for investors, though the investment bankers reportedly made over $170 million of fees plus possibly another $100 million trading the shares the first weeks after the IPO (venturebeat.com, 2012)!

Flotation costs siphon money from the securities issue, raising the effective cost of capital. Therefore, the cost to the company is greater than the return to the investor. This means that the cost of each component must be adjusted to reflect flotation costs. Net proceeds to the company equal the sale price to the investors minus flotation costs.

Net proceeds to company 5 Sale price – Flotation costs

or

(8.13) Pnet 5 P 2 1flotation costs2

byr80601_08_c08_225-252.indd 238 1/24/13 3:59 PM

CHAPTER 8Section 8.2 The Weighted Average Cost of Capital

Virtually all financing with bonds and preferred stock represents new issues and therefore includes flotation costs. Common equity financing may be done through stock sales, but more often it comes from retained earnings, which carry no flotation costs. In the case of POL, the company is selling bonds and preferred stock to finance the harness proj- ect. Common equity financing comes from retained earnings. POL’s investment banker estimates that flotation costs will be $20 for every bond sold and $0.60 for each share of preferred stock. Paula adjusts the cost of debt and preferred stock to reflect these flotation costs. Let’s look at each of these in turn.

Adjusting cost of POL’s debt (bonds) to reflect flotation costs:

(8.13) Kd new 5 YTM1YTM was calculated using Pnet for bonds2

(8.14) Pnet for bonds 5 $1,003 2 $20 5 $983

Based on the Pnet of $983, we recalculate YTM:

YTM* 5 4.94% semiannually

Knewd 5 9.9% annually

Knewd 11 2 t2 5 9.9%1.072 5 6.93%

Now we have calculated four numbers masquerading as the cost of debt for POL. Table 8.5 shows costs before and after the tax adjustment, and with and without flotation costs.

Table 8.5: POL’s cost of debt estimates before and after flotation costs

Floatation Costs Before tax After tax

Excluded 9.44% 6.61%

Included 9.88% 6.93%

As Table 8.5 shows, the actual YTM of the bonds is 9.44%, but after adjusting for taxes and flotation, the cost of debt to POL is 6.93%. The tax savings reduces the cost of debt, but flotation costs take back some of that savings. Now, let’s look at preferred stock.

Adjusting cost of POL’s preferred stock to reflect flotation costs:

Pnet 5 $21.50 2 $0.60 5 $20.90

K newd 5 D

Pnet 5

$2.50 $20.90

5 11.96%

Because there are no flotation costs associated with retained earnings, POL’s cost of com- mon equity remains at 15%.

Kre tearn 5 15%

byr80601_08_c08_225-252.indd 239 1/24/13 3:59 PM

CHAPTER 8Section 8.2 The Weighted Average Cost of Capital

For the record, the following equation shows how flotation costs would affect the cost of a new stock issue. The effect of flotation cost is most easily illustrated with the constant dividend growth model. As with the preferred stock adjustment, we reduce the stock price by the amount of the flotation costs, which raises the cost of equity to the company.

(8.15) Knew stock 5 D1 Pnet

1 gn

where

Pnet 5 P 2 1flotation costs2

Note that POL ‘s after-tax cost of debt (6.93%), the cost of preferred (11.96%), and the cost of equity (15%) are the component costs that Paula used in her WACC worksheet, Table 8.3. Using Equation (8.1), she multiplied these component costs by their desired propor- tions to derive the WACC. Next, we describe how Paula selected the mix outlined in Table 8.2 of common equity, preferred stock, and bonds to finance the harness project.

The Financing Mix and Weights in the WACC The financing mix is called capital structure. Capital refers to long-term financing, such as that used to fund POL’s Pogo harness project. Determining the best capital structure for a company raises some rather complicated issues, which we leave for Chapter 9.

The weights in the WACC formula could reflect any target or desired financing mix. Paula has chosen to finance the harness project using POL’s current mix of capital: 28% debt, 7.8% preferred stock, and 64.2% common stock. Generally, firms that are satisfied with their current capital mix will attempt to maintain those proportions.

The existing mix of capital can be determined by examining the right-hand side of the financial balance sheet. Recall that the financial balance sheet reflects market values, unlike the accounting balance sheet’s book values. Current market values are certainly closer to actual values than are historical accounting values. A company’s common stock with a book value of $5 may have a current market value of $100. If it decides to sell stock to finance an investment, it will surely not sell new shares for $5.

Paula determined the current financing mix by estimating the market values for each of POL’s capital sources. First, she obtained the current prices for the company’s bonds, pre- ferred stock, and common stock. Next, she multiplied these prices by the number of bonds or shares of stock outstanding to compute the market value of each component. Summing these market values gave her the total market value of POL’s capital. These calculations are shown in Table 8.6.

byr80601_08_c08_225-252.indd 240 1/24/13 3:59 PM

CHAPTER 8Section 8.2 The Weighted Average Cost of Capital

Table 8.6: Calculating market weightings of each capital source

Capital component Price/unit Number outstanding

Total market value of component

Proportion

Debt (bonds) $1,003.00 1,537 $1,541,611 28%

Preferred stock $21.50 20,068 $431,462 7.8%

Equity (retained cash) $11.25 313,867 $3,531,004 64.2%

Total $5,504,077 100%

Paula calculated the proportion for each component by dividing its market value by the total market value of capital, $5,504,077.

Proportion of common equity financing 5 3,531,004 5,504,077

5 64.2%

Proportion of preferred stock financing 5 431,462

5,504,077 5 7.8%

Proportion of debt financing 5 1,541,611 5,504,077

5 28.0%

Paula intends to finance the harness project using capital from these three sources in these proportions. As we saw in Table 8.3, the WACC for the harness project is 12.5%. We may confirm this with the WACC formula:

(8.16) WACC 5 1Wd 2 1Knewd 2 11 2 t2 1 1Wpfd2 1Kpfdnew2 1 1Wret earn 2 1Kret earn 2

5 (0.28)(9.9)(1 2 0.30) 1 (0.078)(11.96) 1 (0.642)(.15)

5 1.94% 1 0.93% 1 9.63%

5 12.5%

Glancing at Equation (8.16), you may wonder why Paula doesn’t finance the entire proj- ect with debt and discount it at the after tax cost of debt. The after-tax cost of debt is only (9.9%) (1 – 0.30) 5 6.93%. Discounting at 6.93% rather than 12.5% would certainly raise the harness project’s NPV. The problem with this scheme is that POL must maintain some balance between debt and equity. If debt were used this year, equity may have to be used next year to achieve the desired balance. If POL financed next year’s project with equity, then to be consistent, it would discount that project at the 15% cost of equity. In this case, projects considered in years when debt financing is used have a great advantage over those being evaluated in years when equity financing is used. More projects would be rejected, for example, in equity-financed years even though they may actually be superior

byr80601_08_c08_225-252.indd 241 1/24/13 4:00 PM

CHAPTER 8Section 8.3 Estimating the Discount Rate for Individual Projects

Field Trip: Cost of Capital Data

Ibbotson provides financial data for commercial and academic use.

Visit the Ibbotson Cost of Capital Resources Center: http://corporate.morningstar.com/ib/asp/subject.aspx?xmlfile55532.xml

and the Ibbotson Cost of Capital Yearbook: http://corporate.morningstar.com/ib/asp/subject.aspx?xmlfile51420.xml

Reflection Questions

1. Why do you think clients would be willing to pay for this information? What might they use it for? 2. Look at the module overviews on the Cost of Capital Resources Center. Is there more focus on cost

of debt or cost of equity? Why do you think this is?

projects if all projects were consistently evaluated. This illustrates why it is important to discount all projects at the cost of capital and not at the cost of debt one time and the cost of equity the next time, regardless of how a particular project is financed. We separate the investment decision from the financing decision; that is, we evaluate investment decisions like the Pogo harness project using the long-term mix of debt and equity that we expect over the project’s life, not the specific type of securities (debt, preferred stock, or common stock) that were most recently issued.

WACC reflects the firm’s long-term capital mix. A firm that finances a project with either debt or equity will temporarily unbalance its capital structure and, we can assume, will attempt to rebalance it the next time around. Firms often unbalance their capital structure temporarily to take advantage of scale economies of large securities issues. In reality, POL would never fund such a small project by selling both preferred stock and bonds because flotation costs would be prohibitive. This project would probably be funded entirely from retained earnings, meaning that POL would temporarily unbalance its capital structure.

8.3 Estimating the Discount Rate for Individual Projects

For many projects, the appropriate discount rate to use in the NPV calculation is the firm’s WACC, as outlined in the previous section. However, there are circumstances in which WACC is not the appropriate discount rate. Every company is risky, and this risk is reflected in its WACC. Investors in a particularly risky company demand higher returns on their securities, which increases the company’s WACC. In project analysis, we are actually interested in the risk of the particular project rather than the company as a whole, and we would like the discount rate to reflect the risk of the project. When we discount a project by the company’s WACC, we implicitly assume that project risk and company risk are identical. If they are not, then we should adjust the project discount rate up or down accordingly. For example, if a company increases its risk by investing in high- risk projects, investors expect a higher return; therefore, these risky projects should carry a higher discount rate.

In POL’s case, Paula believes that the Pogo harness project has the same risk as the com- pany’s existing business. Paula reasons that the harness is simply another product to add to POL’s existing line of hardware and sailing gear. Therefore, the business risk of the

byr80601_08_c08_225-252.indd 242 1/24/13 4:00 PM

CHAPTER 8Section 8.3 Estimating the Discount Rate for Individual Projects

Project and company risk can differ significantly. Do you think a Campbell’s Soup cafe would be a successful venture for the company?

Associated Press

Pogo harness project is essentially identical to that of the company’s existing products. Of course, she understands that there are uncertainties in producing a new product, but no more than in the normal course of extending and upgrading an existing line of products. Paula also realizes that the relevant risk for estimating required returns is the market- wide or nondiversifiable risks of the business (as discussed in Chapter 7). The new har- ness is probably about as sensitive to market-wide forces as are POL’s current products. All are sensitive to economic recession (in which case sales of discretionary products will decline), changing tastes, changes in tax codes, and so on.

Why a Project’s Risk May Differ From the Company’s Overall Risk While the harness fits neatly into POL’s existing product line, there are many occasions when this is not the case. In such instances, we must estimate a discount rate that reflects the project’s risk. Here, we explain why differences in risk might arise and how discount rates for individual projects might be estimated. Consider Campbell Soup. The company has a domi- nant position in its industry and produces a product for which there is fairly constant demand. Thus, we would expect that Campbell Soup has average or slightly below-average risk. Now suppose that Campbell’s managers propose two hypo- thetical projects. The first is a tomato soup with a spicy Mexican taste. The second proposal is to start a chain of small soup cafes—tentatively called “17 Flavors Soup Cafes.” The cafes would feature 17 flavors (hence the name) of Campbell’s soups ready for immediate serving.

Do these two proposals have the same risk? Let’s consider them both individually. The spicy Mexican soup is a standard Campbell’s product. Campbell Soup has enormous experience evaluating, producing, marketing, and distributing such products. By con- trast, a chain of fast-food restaurants differs markedly from any of Campbell’s other busi- nesses. The fast-food industry is very competitive, with several dominant chains vying for market share. Campbell’s managers have little experience in this industry. Also, the two projects will probably respond differently to economy-wide risk factors. For example, in a recession individuals tend to eat out less but may consume more canned soup at home.

Campbell’s managers may reasonably conclude that the new soup flavor project should be discounted at the company’s WACC. The new soup is analogous to POL’s Pogo har- ness project. On the other hand, Campbell’s managers would judge that the soup cafes add risk to company, and therefore should take a higher discount rate.

byr80601_08_c08_225-252.indd 243 1/24/13 4:00 PM

CHAPTER 8Section 8.3 Estimating the Discount Rate for Individual Projects

Estimating a Risk-Adjusted Discount Rate for NPV Analysis Chapter 7 introduced the capital asset pricing model and the idea that the capital markets price only market risk. This follows from the notion that unique risk is generally absent from well-diversified portfolios. Projects also contain mostly market risk; therefore, we may use the CAPM to determine a project’s discount rate.

(8.17) Required return on a project 5 Risk-free rate 1 Project beta (Market risk premium)

The project beta, commonly called an asset beta, is not the same as the common stock beta. As introduced in Chapter 7, asset beta measures the project’s market risk. Next, we discuss how to estimate a beta that is appropriate for evaluating the Campbell Soup “17 Flavors Soup Cafes” initiative.

Estimating a Project’s Beta Recall from Chapter 7 that beta is a measure of the extent to which the returns on a stock move with changes in the returns of a market portfolio, such as the S&P 500. One widely used technique for estimating a project’s cost of capital is the pure-play method. A pure-play is a publicly traded firm that engages primarily in the same line of business as the project being considered. If the pure-play firm has close to the same financing mix as the project, then the beta of this pure-play’s assets may then be found and used as a proxy for the project’s beta. The pure-play’s beta can be used as the beta in the CAPM to estimate the appropriate risk-adjusted discount rate (RADR) for the project.

Identifying a publicly traded pure-play firm is seldom easy. For the soup cafes, Camp- bell’s managers may begin with small chains of specialized fast-food restaurants. Another chain of soup cafes would be ideal, but what if none exist? We would then look to other small chain restaurants that fit the profile. Wendy’s would likely be a better proxy than McDonald’s because of size. Perhaps Baskin-Robbins would be better yet: Baskin-Robbins is not too large, and has a specialized menu, and ice cream is somewhat seasonal, as is soup. Ideally, several publicly traded pure-play firms would be identified.

Aside from identifying appropriate business lines for the pure-play firms, Campbell’s managers must also consider their capital mix. We said that to use the pure-play com- pany’s beta directly, the pure-play’s risk and financing must be close to that of the project. Financing is an issue because the equity betas of companies with the same business risk (same asset beta) will differ according to how much debt each company has. The more debt a company has, the higher the equity beta will be. The intuition behind this result (more debt, higher beta, all else being equal) is that the risk of the assets is fixed, so as low-risk debt replaces equity in a company’s financing mix that asset risk has to go some- where. If the debt is safe because of priority payments and contractual obligations, then the equity absorbs more and more of the risk producing a higher beta.

To avoid the effect of leverage on beta, the best choice for a pure-play comparison firm is an all equity-financed firm. The beta of an all equity-financed firm is identical to its asset beta. If a pure-play can be found with no debt, the project’s required return may be estimated directly using the CAPM. The project’s required return could then be used as the discount rate for NPV or as the hurdle rate for IRR. Suppose, for example, there

byr80601_08_c08_225-252.indd 244 1/24/13 4:00 PM

CHAPTER 8Section 8.3 Estimating the Discount Rate for Individual Projects

exists a chain of soup cafes that is all equity financed, and the beta for this company is 1.3. This beta may then be transferred to Campbell’s cafe project, and a RADR could then be estimated.

We will assume rf 5 4% and the market risk premium is 9%

RADR 5 Required returnsoup cafes 5 rf 1 basset1MRP2

RADR 5 4% 1 1.3(9%)

RADR 515.7%

If the capital structure of the pure-play firm includes debt, we may estimate the asset beta using the Hamada (1972) equation:

(8.18) basset 5 bequity

1 1 1D@E2 11 2 t2 where

bequity 5 beta of the pure-play’s common stock

t 5 the pure-play’s tax rate

D/E 5 ratio of the firm’s debt to equity, both at market value

If we find a pure-play with debt of $1 million and equity worth $2 million, a tax rate of 30%, and bequity equal to 1.5, we can estimate its asset beta as follows:

basset 5 1.5

1 1 11 2 0.32 1 12 2 5 1.11

This beta could then be plugged into Equation (8.18) and used to estimate the project’s appropriate discount rate.

RADR 5 4% 1 1.11(9%) 5 13.99% or 14%

Of course, for many projects a pure-play cannot be found. The methods for estimating the RADR under such circumstances range from ad hoc techniques (like adding or sub- tracting a few percentage points to the firm’s existing WACC) to developing betas based on accounting information. Ad hoc estimates require careful judgment on the part of the analyst. Should Campbell Soup, for example, add 2% to its current WACC to reflect the added risk of the cafes, or should it add 5%? Other new projects may be perceived as being less risky than existing lines of business, so a few percentage points would be subtracted from the current WACC. The difficulties encountered using this method are obvious, but at times there is no choice. Accounting betas are found by measuring the co-movement of an accounting-based standard of performance for a pure-play firm with a benchmark performance standard from a broad sample of other firms. This technique is beyond the scope of this text but is useful when a pure-play firm does not have publicly traded stock.

byr80601_08_c08_225-252.indd 245 1/24/13 4:00 PM

CHAPTER 8Post-Test

Use and Misuse of Risk-Adjusted Discount Rates

The risk-adjusted discount rate calculation depends on identifying pure-play companies. Because such companies are illusory, the calculation is subject to second-guessing and criticism, especially by those units in the company that are assigned a high RADR. Unit managers may cry foul and claim that the calculation is unreliable and discriminatory. The only defense against such charges is to make explicit the assumptions and calculations used to generate the RADR. Although the process is inevitably flawed, it must be shown to be as free of bias as possible. Top managers may also use arbitrary RADRs as a pretext for altering the allocation of resources within the company. In this case, the distrust of the technique by unit managers is fully justified.

Critical Thinking Questions

1. Why do you think managers continue to use RADR, despite its flaws? 2. What kind of information would you include in your defense of a high RADR?

Ideally, each project will have its own discount rate reflecting its risk. In practice, large companies use divisional hurdle rates, so that, for example, projects in a home appliances division carry a different RADR than do projects in broadcasting division.

Conclusion

Choosing the correct rate at which to discount project cash flows is crucial to valuing a capital project. The discount rate is the weighted average of the required return for each class of investor. The principal investor classes are the bondholders, preferred stockholders, and common stockholders. Each of these investor classes contributes capital to the firm as a whole, rather than to individual projects, and each is compensated for the risk that it incurs by investing in the firm. The discount rate that provides each investor class with its required rate of return is the weighted average cost of capital (WACC).

The WACC is the appropriate discount rate for a project whose risk is equal to that of the firm as a whole. However, the cash flows of projects that increase firm risk—and, there- fore, the risk of its investors—should be discounted at a rate greater than the WACC. In the same way, cash flows of projects that reduce firm risk should be discounted at a rate less than the WACC. The rate that reflects project-specific risk is the risk-adjusted discount rate (RADR).

Post-Test

1. The cash flows from a project are distributed to investors in order of the priority of their claims.

a. True b. False

2. The cost of preferred stock is found by solving for the required return of a perpetuity.

a. True b. False

byr80601_08_c08_225-252.indd 246 1/24/13 4:00 PM

CHAPTER 8Key Ideas

3. WACC is used as the discount rate for evaluating projects if they are riskier than the overall firm’s risk.

a. True b. False

4. What is the proper order in which a project’s investors can expect to be paid, based on the priority of their claim?

a. common stockholders, preferred stockholders, bondholders b. preferred stockholders, bondholders, common stockholders c. preferred stockholders, common stockholders, bondholders d. bondholders, preferred stockholders, common stockholders

5. Suppose a stock just paid a dividend of $3.00 a share. Dividends are expected to increase by 4% per year in the future. If the stock is selling for $50 a share, then what is the cost of equity?

a. 10% b. 46.24% c. 16.5% d. 10.24%

6. For which of the following projects is the WACC probably most appropriate for use as the discount rate when calculating the project’s NPV?

a. Boeing is considering using its expertise in aerodynamics and metals to make new metal water skis.

b. Boeing is considering the replacement of a crane for lifting airplane bodies into place in its 747 construction facility.

c. Boeing is required by law to install wastewater treatment facilities in its factory to treat runoff from the paint shop.

d. Boeing is considering entering the model airplane business.

Answers 1. a. True. The answer can be found in Section 8.1. 2. a. True. The answer can be found in Section 8.2. 3. b. False. The answer can be found in Section 8.3. 4. d. bondholders, preferred stockholders, common stockholders. The answer can be found in Section 8.1. 5. d. 10.24%. The answer can be found in Section 8.2. 6. b. Boeing is considering the replacement of a crane for lifting airplane bodies into place in its 747 construc-

tion facility. The answer can be found in Section 8.3.

Key Ideas

• The required return on an investment is the weighted average of the returns demanded by the company’s investors.

• The basic discount rate for capital investments is the company’s cost of capital. • The weighted average cost of capital (WACC) is the weighted average of the

required returns for each capital source. Weightings are the proportional contri- butions from each capital source.

• Discounting project cash flows by the WACC means that projects will be accepted only if they are expected to provide at least the required returns to all investors.

byr80601_08_c08_225-252.indd 247 1/24/13 4:00 PM

CHAPTER 8Critical Thinking Questions

• The cost of debt is the yield to maturity (YTM) on the company’s bonds or other long-term debt securities.

• The cost of preferred stock is its annual dividend divided by its current market price.

• The cost of common equity may be estimated using the CAPM, a discounted cash flow (dividend growth) model, or an equity-debt risk premium.

• The difference between returns to equity and returns to debt is the equity-debt risk premium.

• Investment banks assist companies in marketing new securities offerings. When an investment bank buys securities from the issuing company and resells them to investors, it is underwriting the securities offering. The difference between the price paid to the company and sale price to investors is the underwriting spread.

• Venture capital firms supply high-risk capital to small firms prior to an initial public offering of stock.

• Capital structure is the mix of debt, preferred equity, and common equity. Short- term financing is excluded. When possible, the proportions of each component in the capital structure should be calculated using market rather than book weights.

• A project should be discounted at the WACC, rather than at the costs of individ- ual capital components, regardless of how the project is financed. WACC is the appropriate discount rate for projects whose risk is about equal to the risk of the company as a whole.

• A pure-play is a publicly traded firm that engages primarily in the same line of business as the project being considered. The Hamada equation may be used to convert the equity beta of a pure-play firm into an asset beta.

• The risk-adjusted discount rate (RADR) applies to projects whose risk is substan- tially different from company risk.

Critical Thinking Questions

1. A fellow student comments that if a project has an NPV equal to zero, then the project will generate no cash flows for the common stockholders. You argue that it will produce such cash flows. What is your argument? (By the way, you are correct. It will produce cash for the common stockholders.)

2. Accounting balance sheets reflect the book values of claims, based on the histori- cal contributions of capital suppliers. Suppose a firm raised its initial capital 10 years ago, and its accounting statements currently reflect a capital mix of half debt and half equity. No more debt has been issued since the original bonds were sold. Interest rates have not changed, but the firm has been exceptionally successful.

a. Do you think common stockholders would be willing to sell their stock today for its book value?

b. Interest rates have not changed, but the firm’s bonds are selling at a premium, above their book values. Why?

c. If the firm has been wildly successful, and given your answers to parts (a) and (b), what do you think has happened to the total market value of the firm? Is it above or below its total book value?

d. How do you think the firm’s capital mix, based on market values, compares to the 50–50 mix reflected on the accounting balance sheet?

byr80601_08_c08_225-252.indd 248 1/24/13 4:00 PM

CHAPTER 8Key Terms

asset beta Refers to the systematic or mar- ket risk of an investment asset.

capital structure The mix of debt and pre- ferred equity in a company’s portfolio.

cost of capital The rate of return that must be earned in order to satisfy investors.

cost of common equity The investors’ required return on common equity.

cost of debt The required return of inves- tors in the company’s bonds. Usually, the cost of debt is measured by finding the yield to maturity of outstanding bonds.

cost of preferred stock The investors’ required return on preferred stock.

equity-debt risk premium A representa- tion of the difference between returns to equity and returns to debt.

flotation costs The transaction costs incurred when raising capital externally, for example, when selling newly issued stock or bonds.

investment bank A financial services company that specializes in selling new securities issues for client firms.

pure-play An actively traded firm whose sole product is similar to an investment project being analyzed. By finding the required return for the pure-play, the appropriate return requirement for the investment project can be estimated.

risk-adjusted discount rate (RADR) A rate of return that has been adjusted to reflect the risk in a new investment proj- ect vis-à-vis the risk of the firm’s existing projects.

underwriting A method of selling securi- ties in which the investment bank buys the securities from the client firm and resells them to investors.

underwriting spread The price at which the investment bank sells securities to the public minus the price paid to the client firm.

venture capital firms Businesses and individuals that finance high-risk start-up ventures, usually before an initial public offering of stock.

weighted average cost of capital (WACC) The discount rate that may be found by incorporating the required returns (costs) for each capital source used to finance the firm.

3. Explain why (1 – t) does not appear in the cost of preferred and the cost of com- mon equity formulas.

4. Suppose a firm uses all equity financing, but half that financing is internal equity and half is external equity.

a. Name the capital components for the firm. b. What will be the weights for each component? c. Write the firm’s WACC formula.

5. A project with an NPV 5 0 provides all corporate investors with their required return; therefore all investors are satisfied. Do you agree or disagree with this statement? Explain.

6. There are three methods of estimating the cost of corporate equity. Name or briefly describe these methods.

Key Terms

byr80601_08_c08_225-252.indd 249 1/24/13 4:00 PM

CHAPTER 8Key Formulas

Key Formulas

Weighted average cost of capital

(8.1) WACC = (Wd)(after-tax cost of debt)

+ (Wpfd)(cost of preferred stock)

+ (We)(cost of common equity)

(8.2) WACC = (WB)(after-tax cost of bonds)

+ (WL)(after-tax cost of loan)

+ (We)(cost of equity)

Net present value

(8.3) NPV 5 2II 1 a nt 5 1 OCFt

11 1 R1r2 2 t 1 TCFn

11 1 R1r2 2 n

After-tax cost of debt

(8.4) NPV 5 a nt 5 1 CFt

11 1 WACC2 t 2 II

(8.5) a nt 5 1 CFt

11 1 IRR2 t 2 II 5 0

(8.6) Kd (1 – t)

Cost of preferred stock

(8.7) Kpfd 5 dividend

share price

(8.8) R1r2 i 5 rf 1 bi 1market risk premium2

or

R1r2 i 5 ri 1 bi 3E1rm 2 2 rf 4

Cost of common equity; dividend growth

(8.10) Ke 5 D1 P0

1 gn

(8.11) D0 5 D2n11 1 gn2 n

byr80601_08_c08_225-252.indd 250 1/24/13 4:00 PM

CHAPTER 8Web Resources

Cost of common equity; equity-debt risk premium

(8.12) Ke 5 Kd 1 RP

Cost of preferred stock

(8.13) Pnet 5 P 2 (flotation costs)

Cost of common equity; equity-debt risk premium

(8.15) Knew stock 5 D1 Pnet

1 gn

Weighted average cost of capital

(8.16) WACC 5 1Wd 2 1Knewd 2 11 2 t2 1 1Wpfd2 1Kpfdnew2 1 1Wret earn 2 1Kret earn 2

Calculating the asset beta (the Hamada equation)

(8.18) basset 5 bequity

1 1 1D@E2 11 2 t2

Web Resources

For more information on other estimates of the market’s risk premium (or equity risk premium), read Pablo Fernandez’s paper “Equity Premium: Historical, Expected, Required and Implied.” Available at SSRN: http://ssrn.com/abstract5933070 or http://dx.doi.org/10.2139/ssrn.933070.

A very simple cost-of-capital calculator is available at the following website. To test your skill, you could make up a simple set of assumptions and see if you and the online calcu- lator get the same answer for the WACC. http://www.wacccalculator.com/

Morningstar is a well-known financial information provider that produces cost-of- capital estimates that are published in an annual yearbook. These yearbooks are costly; nevertheless, it is instructive to peruse their website to see the scope of issues and infor- mation that surrounds estimating the cost of capital. http://corporate.morningstar.com/ib/asp/subject.aspx?xmlfile55532.xml

byr80601_08_c08_225-252.indd 251 1/24/13 4:00 PM

byr80601_08_c08_225-252.indd 252 1/24/13 4:00 PM