edition 2

FFOUNDATIONSOUNDATIONS OF OF CCORPORATEORPORATE FFINANCEINANCE

Kent A. Hickman Gonzaga University Hugh O. Hunter San Diego State University John W. Byrd Fort Lewis College chapter 8

CostCost ofof CapitalCapital

“You tell the governor that if he doesn’t come up with some subsidized financing, 258 free land, a tax deferment, a new highway and airport, it’s no deal!” Chapter 8 • 259

CHAPTER 8 IN FOCUS

THE FINANCIAL BALANCE SHEET

Capital supplied Investments for Bonds made by the firm corporate Preferred investments Common stock

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.

hapter 7 described the various capital budgeting techniques employed by corporate managers. Among the techniques, (NPV) Cemerges 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 project is accepted if the pres- ent value exceeds the initial investment. Calculation of NPV requires the analyst to estimate cash flows and an appropriate discount rate. Techniques for estimat- ing cash flows were covered in Chapter 7. 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 (IRR) analysis. Used in IRR, the discount rate becomes a hurdle rate against which to compare the project’s IRR. Estimating the Discount Rate

To illustrate the calculation and use of the discount rate, we continue with the Chapter 7 example of Pacific Offshore Ltd. (POL). The NPV of POL’s harness project is $9,110, which was found by discounting the project’s net cash flows by 12.5%. 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. We have referred to the 12.5% as the harness project’s required rate of re- The required return on an investment turn. To be more specific, 12.5% is the weighted average return demanded by is the weighted average of the returns the company’s investors. The weightings reflect the proportional values of their demanded by the company’s investors. investments. From Chapter 7, the cost of the harness project is $64,384, mean- ing 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 current proportional mix of debt and preferred and common stock. POL’s current capital mix is 28% debt, 7.8% , 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 260 Chapter 8 • Cost of Capital

FIGURE 8.1 FINANCING MIX AND CASH FLOWS FOR THE POGO HARNESS PROJECT

$64,384

$18,028 Pogo Harness Project Bondholders tools, equipment, working capital, plant $5,022 Preferred stockholders Harnesses Consumers $41,334 Common stockholders Cash Flows

shareholders.1 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 stockholders. Figure 8.1 illustrates the flow of capital and cash flows, assuming that the harness project produces its expected cash flows. Visit Ibbotson Associates at POL raises capital by selling these securities to investors, who expect to re- http://www.ibbotson.com ceive a return on their investment. Any investor purchasing POL’s securities must to see how they estimate the cost of expect that the returns will be at least equal to, and preferably greater than, the re- capital. To learn more about how to se- lect the appropriate discount rate, click quired return on an investment having the same risk as the harness project. If ex- on Managing Your Business Finances, pected returns were lower than required, investors would look elsewhere, or they Major Purchases and Projects, and Dis- may be persuaded to buy POL’s securities at a discount, which would increase their count Rate. 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. The basic discount rate for capital investments is the company’s cost This discount rate is known as the cost of capital for the project because the re- of capital. turns investors require are the cost, like rent, that is paid for the use of the capital. The Weighted Average Cost of Capital Calculating the Weighted Average Cost of Capital

The weighted average cost of capital The cost of capital is a weighted average of the required returns for each capital (WACC) is the weighted average of the source. For the harness project, the weighted average cost of capital (WACC) is required returns for each capital the after-tax2 required returns on POL’s bonds, preferred stock, and common eq- source. Weightings are the proportional contributions from each capital source. 1Accountants refer to these as retained earnings, but we prefer cash flows, since earnings, as far as we know, are not legal tender. 2Interest on bonds or any other debt is tax deductible, thus lowering the cost of debt to the firm. Chapter 8 • Cost of Capital 261 uity, weighted by their proportional contribution to the project. As you can see in Exhibit 8.1, of the $64,384 being raised, the bondholders contribute $18,028 (28%), the preferred stockholders contribute $5,022 (7.8%), and the common stockholders 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 . First, though, we present her worksheet for computing POL’s cost of capital. Exhibit 8.1 shows that she multiplied the proportion of each capital source by its after-tax required return. She then summed these re- sults to arrive at the 12.5% cost of capital. Paula’s worksheet may be summarized by a formula for the weighted aver- age cost of capital.

WACC 5 (Wd)(after-tax cost of debt) (8.1)

1 (Wpfd)(cost of preferred stock)

1 (We)(cost of common equity) where

Wd 5 the desired proportion of financing provided by debt

Wpfd 5 the desired proportion of financing provided by preferred stock

We 5 the desired proportion of financing provided by common equity This formula is adaptable to any combination of financing sources. For ex- ample, if preferred stock were not used, then Wpfd 5 0 and preferred stock would drop out of the formula. Some companies borrow from many sources. They may have several issues and perhaps long-term loans from banks or insurance companies. The only source of capital that is common to all companies is com- mon equity. The WACC formula for a company with no preferred stock, but with two types of debt, would be

WACC 5 (WB)(after-tax cost of bonds) (8.2)

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

1 (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 harness project. If the NPV 5 0, then the project should provide all investors

EXHIBIT 8.1 WORKSHEET FOR COMPUTING POL’S COST OF CAPITAL (A) (D) TARGETED (B) (A) 3 (B) AFTER TAX (A) 3 (D) CAPITAL PROPORTION PROJECT DOLLARS REQUIRED WEIGHTED COMPONENT OR WEIGHT COST RAISED RETURNS AVERAGE Debt (bonds) 28.0% $64,384 $18,028 6.93% 1.94% Preferred stock 7.8% 64,384 5,022 11.96% 0.93% Common equity 64.2% 64,384 41,334 15.00% 9.63% 100.0% $64,384 12.50% 262 Chapter 8 • Cost of Capital

with their required returns but with nothing more. This is the minimally accept- able outcome. The harness project is expected to do better than that, meaning Discounting project cash flows by the that it should add value because its NPV is $9,110. WACC means that projects will be ac- To summarize, discounting project cash flows at the WACC ensures that the cepted only if they are expected to pro- minimal needs of each class of investor are met. We may rewrite the NPV and vide at least the required returns to all investors. IRR equations from Chapter 7 to include WACC. n OCFt TCFn NPV 52II 1 a t 1 n (7.1) t51 s1 1 Rsrdd s1 1 Rsrdd 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 (in years) of the project r 5 project required rate of return Equation (7.1) may be simplified to

n CFt NPV 5 a t 2 II (8.3) t51 s1 1 rd By substituting WACC for r, the equation becomes

n CFt NPV 5 a t 2 II (8.4) t51 s1 1 WACCd

where CFt 5 total net cash flow for period t. The company should accept proj- ects with NPV > 0. The equation for IRR is

n CFt a t 2 II 5 0 (8.5) t51 s1 1 IRRd The company should accept projects with IRR > WACC. In the following section, we explain how Paula estimated the cost of each capital component. The Cost of Debt

The cost of debt is the yield-to- The cost of debt is the current yield-to-maturity (YTM) on the company’s bonds maturity (YTM) on the company’s or other long-term debt securities. YTM reflects current credit market conditions bonds or other long-term debt and investors’ expectation, and therefore it is the best indicator of returns in- securities. vestors require on the sale of new bonds. Recall from Chapter 5 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.

Kd 5 YTM The current market price of POL’s bonds is $1,003. The bonds mature in 6 years, bear a 9.5% coupon rate, and make coupon payments semiannually. Their par value is $1,000.

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 (IRR) of a bond. Chapter 8 • Cost of Capital 263

$47.50 $47.50 $47.50 $1,003 5 1 1 . . . 1 s1 1 YTMd1 s1 1 YTMd2 s1 1 YTMd12 $1,000 1 s1 1 YTMd12 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. The yield to maturity on these bonds equals 4.72% semiannually, or 9.44% on an annual basis.3 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 2 t), where t is the firm’s marginal tax rate. Substituting Kd for YTM gives us

after-tax cost of debt 5 Kd (1 2 t) (8.6) POL’s marginal tax rate is 30%. Therefore

Kd (1 2 t) 5 9.44% (1 2 0.30) 5 9.44% (0.7) 5 6.61% The Cost of Preferred Stock Preferred stock combines features of debt and equity. Preferred dividends are fixed, like bond interest, but also have an infinite life like common stock dividends. From Chapter 4, we recognize this as a perpetuity—a perpetual annuity—which greatly simplifies the calculation. The cost of preferred stock equals its required rate of re- The cost of preferred stock is its turn, which is its annual dividend divided by its current market price. annual dividend divided by its current The dividend on POL’s preferred stock is $2.50 and its current market price market price. is $21.50 per share. Therefore, the required return on the stock is 11.63%. dividend $2.50 Kpfd 5 5 5 0.1163 5 11.63% (8.7) share price $21.50 No tax adjustment is necessary for preferred stock. The Cost of Common Equity

The cost of common equity is the most difficult of the component costs to esti- The cost of common equity may be es- mate. Chapter 6 presented the capital asset pricing model (CAPM) as one means timated using the CAPM, a discounted of estimating investors’ required return for risky assets. Although this risk-return cash flow (dividend growth) model, or an equity-debt risk premium. model is the most frequently used method for estimating returns to common stock, other models may also be used, most notably the model introduced in Chapter 5. As a general 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. In this sec- tion, we cover three approaches: CAPM, the discounted cash flow model, and the equity-debt risk premium.

K is the cost of common equity. Chap- The CAPM Approach to Ke e ter 6 built on portfolio theory to show the relationship between required returns

3YTM, like IRR, must be solved with the aid of a financial calculator or computer. 264 Chapter 8 • Cost of Capital

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 and the market risk premium. The CAPM is

R(r)i 5 rf 1bi(market risk premium) or

R(r)i 5 ri 1bi[E(rm) 2 rf] (8.8) where

R(r)i 5 the required return for asset i rf 5 the risk-free rate of return bi 5 asset i’s beta market risk premium 5 market’s expected return minus the risk-free return Let’s look at the information needed to solve the CAPM. First is the risk-free return. Although no asset is totally free of risk, U.S. government t-bills are consid- ered nearly riskless. Thus, t-bills are a widely used proxy for the true risk-free rate.4 T-bill returns are widely available in print and on the Web. Next, we need an esti- mate of the equity beta. Brokerage and other investment service firms estimate be- tas for many publicly traded . Betas may be obtained on the Web and in print Value Line can be accessed at from Value Line, Standard & Poor’s, and Bloomberg.5 As we saw in Chapter 6, we http://www.valueline.com. may also estimate beta ourselves using data on past returns. The expected market return is difficult to forecast directly. Therefore, we must rely on historical market returns and the historical market risk premium as our best guide to the future. Stock market indexes, especially the S&P 500, are generally used as market proxies. Since 1926, the average annual return on the S&P 500 is about 13%. This number, or one close to it, is often used in the CAPM as the market’s expected return. The current t-bill rate is subtracted from the market return to derive the market risk premium. Other practitioners prefer to avoid estimating the market return and choose, instead, to use the historical equity market risk premium. The historical market risk premium is found by calculating the average amount by which the market return has exceeded t-bill returns. For example, the difference between the S&P 500 return and the t-bill return for each of the last 70 years could be averaged and used as the historical market risk premium. From the Ibbotson data in Chap- ter 6, we see that over the past 70 years the market risk premium has averaged about 9.4% per year. For POL, Paula gathered the following estimates for the risk-free return, POL’s beta, the market return, and the market risk premium. Notice that she used two different forms for the CAPM, one using the historical S&P return and one using the historical market risk premium. The result is two estimates of POL’s cost of equity, both using the CAPM.

POL’S COST OF EQUITY ESTIMATES USING THE CAPM

Risk free return: T-bills (from the Wall Street Journal) rf 5 4% BetaPOL (from POL’s investment banker) bPOL 5 1.2 Market return: historical S&P 500 return (from Ibbotson) E(rm) 5 13% Market risk premium: historical equity market risk premium 9.4% (from Ibbotson)

4For a discussion of the appropriate proxy for the risk-free rate, see the chapter appendix. 5One such site is Yahoo Finance, http://quote.yahoo.com. Chapter 8 • Cost of Capital 265

Paula’s first CAPM estimate was:

R(r)POL 5 rf 1bPOL 1 [E(rm) 2 rf] 5 4% 1 1.2(13% 2 4%) 5 14.8% Her second CAPM estimate was:

R(r)POL 5 rf 1bPOL(market risk premium) 5 4% 1 1.2(9.4%) 5 15.28% These two estimates are similar because the same model was used for both. In fact, the difference in the estimates boils down to the risk-free rate. In the second estimate the market risk premium is based on a historical rf and the first estimate uses a current rf . We now turn to a second model for estimating the cost of equity.

The Discounted Cash Flow Approach to Ke In Chapter 5 the constant dividend growth model for valuing common stock was introduced.

D1 P0 5 (8.9) Ke 2 gn 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 solved for Ke the cost of equity.

D1 Ke 5 1 gn (8.10) P0 The dividend growth model for estimating the required return on common stock reflects the discounted cash flow approach to , 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 com- panies. 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 calcu- late 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, given in Chapter 4.

n FVn 5 PV0 (1 1 r) 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 is the most re- cent dividend, D0. PV0 is the beginning historical dividend, D2n. The rate of re- turn, r, is the compound growth rate, gn. n D0 5 D2n (1 1 gn) (8.11) 266 Chapter 8 • Cost of Capital

Fortunately, POL has paid a dividend for 5 years, so we are able to calculate a

growth rate. The dividend 5 years ago (D25,) was $0.60 and the most recent divi- dend (D0) was $0.84. 5 D0 5 D25(1 1 gn) 5 0.84 5 0.60(1 1 gn) 1/5 (1.4) 5 1 1 gn

1.07 5 1 1 gn

0.07 5 gn, gn 5 7% The current market price of POL’s common stock is about $11.25.6 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.

P0 5 $11.25

gn 5 7% 5 0.07

D1 5 $0.90 $0.90 K 5 1 0.07 5 0.15 5 15% e 11.25

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 unsustain- able. Cyclical firms, such as lumber companies, often have earnings that fluctu- ate dramatically with the business cycle. Exceptionally high initial growth rates of startup companies will eventually fall to more sustainable levels as the indus- try matures. For these types of firms the constant growth assumption is quite dif- ficult to apply. In practice, companies appear to favor the CAPM approach to the discounted cash flow approach for determining their cost of equity.7

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 The difference between returns to between Ke and Kd is the equity-debt-risk premium. equity and returns to debt is the equity-debt-risk premium. 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 needed data are easily obtained.

Estimates 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.

(Kd 1 3%) < Ke < (Kd 1 6%)

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

12.4% < Ke < 15.4%

6We used the word about on purpose because POL is a small company whose stock is infrequently traded in the over-the-counter market. 7See Robert Bruner, Kenneth Eades, Robert Harris, and Robert Higgins, “Best Practices in Estimating the Cost of Capital: Survey and Synthesis,” Financial Practice and Education, Spring/Summer 1998. Chapter 8 • Cost of Capital 267

Paula’s estimates of Ke using the CAPM were 14.8% and 15.28%. Her dis- counted cash flow method produced a 15% cost of equity. All three of these esti- mates are within the range prescribed by the equity-debt premium, which more or less confirms Paula’s estimates. All three estimates of Ke clustered about 15%, so Paula elected 15% as POL’s cost of equity. As with preferred stock, no tax ad- justment is necessary. The Cost of Selling Securities Each component cost 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 Investment banks assist companies in for marketing and the issue. A securities issue is underwritten when marketing new securities offerings. the investment bank buys securities from the company and resells them to in- vestors 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 When an investment bank buys secu- approximate the ’s market value. For example, POL is selling bonds to rities from the issuing company and pay for the harness project. Investors will buy the bonds for approximately resells them to investors, it is under- writing the securities offering. The dif- $1,003, their current market price. However, the underwriting spread reduces ference between the price paid to the POL’s proceeds from the bond sale and raises POL’s effective cost of debt above company and sale price to investors is the 9.44% YTM. the underwriting spread. Costs associated with selling securities are called flotation costs. In the lingo Flotation costs are the costs associ- of Wall Street, firms are said to be floating an issue. Aside from the underwriting ated with selling securities. spread, flotation costs include fees paid to the investment banker for consulta- tion, document preparation, and so on. They also include costs of filing with reg- ulators such as the Securities and Exchange Commission, legal fees, and account- ing fees. Flotation costs as a percentage of the value of the securities issue are greater for equity than for debt, reflecting the increased risk of underwriting stocks. Flotation costs are also 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, transportation, and telecommunications have spurred a virtual renaissance in entrepreneurial activity in the United States, creating new investment opportunities. Venture capital firms have sprung up by Venture capital firms supply high-risk the hundreds to supply early financing to promising companies. Not wishing to capital to small firms prior to an ini- miss out on these opportunities, large investment banks and other companies, tial of stock. such as General Electric, have gotten into the venture capital business. This capi- tal market specializes in high-risk investments, but the returns can be astonish- ing. Venture capitalists generally expect rates of return of 40% to 50%! Through the 1990s, we were entertained by stories of billions of dollars of instant wealth created in initial public offerings (IPOs) of heretofore unknown companies. Ven- ture capitalists and other early investors who take a share of the company’s eq- uity are beneficiaries of successful IPOs. Venture capital firms generally take a 25% or larger stake in a company. 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 268 Chapter 8 • Cost of Capital

the investor. This means that the cost of each component must be adjusted to re- flect flotation costs. Net proceeds to the company equal the sale price to the in- vestors minus flotation costs.

Pnet 5 P 2 (flotation costs) (8.12) 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. POL is selling bonds and preferred stock to finance the har- ness project. Common equity financing comes from retained earnings. POL’s in- vestment 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. For bonds:

new Kd 5 YTM (YTM was calculated using Pnet for bonds) (8.13)

Pnet for bonds 5 $1,003 2 $20 5 $983

Based on the Pnet of $983, we recalculate YTM: YTM* 5 4.94% semiannually

new Kd 5 9.9% annually new Kd (1 2 t) 5 (9.9%)(0.7) 5 6.93% We now have calculated four numbers masquerading as the cost of debt. We have costs before and after the tax adjustment, and with and without flotation costs.

BEFORE TAX AFTER TAX

Without flotation costs 9.44% 6.61% Including flotation costs 9.88% 6.93%

The actual YTM of the bonds is 9.44%, but after adjusting for taxes and flota- tion, 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. For preferred stock:

Pnet 5 $21.50 2 $0.60 5 $20.90

new D $2.50 Kpdf 5 5 5 11.96% Pnet $20.90 Because there are no flotation costs associated with retained earnings, POL’s cost of common equity remains at 15%.

Kret earn 5 15% 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 adjust- ment, we reduce the stock price by the amount of the flotation costs, which raises the cost of equity to the company. Chapter 8 • Cost of Capital 269

D1 Knew stock 5 1 gn (8.14) Pnet where

Pnet 5 P 2 (flotation costs) 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, Exhibit 8.1. Using Equation (8.1), she multiplied these com- ponent costs by their desired proportions to derive the WACC. We have not described in detail how Paula decided on the mix of common equity, preferred stock, and bonds to finance the harness project. In the next section, we show how she determined her financing mix. The financing mix is called . Capital structure is the mix of debt, Capital refers to long-term financing, such as that used to fund the harness pro- preferred equity, and common equity. ject. Determining the best capital structure for a company raises some rather com- Short-term financing is excluded. plicated issues, which we leave for Chapter 10. The Financing Mix and Weights in the WACC 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. Generally, firms that are satisfied with their current capital mix will at- tempt to maintain those proportions. The existing mix of capital can be determined by examining the right-hand side (RHS) 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. Public companies tend to use market rather than book values.8 When possible, the proportions of each Paula determined the current financing mix by estimating the market values component in the capital structure for each of POL’s capital sources. She first obtained the current prices for the should be calculated using market rather than book weights. company’s bonds, preferred 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 to- tal market value of POL’s capital. The calculations are shown in Exhibit 8.2.

Finance in the Firm

EXPLAINING A CHANGING COST OF CAPITAL As mentioned in Chapter 7, project analysis in- changing discount rates make planning nearly volves virtually every unit within a company and impossible. They are especially upset when the cuts across many disciplines. By necessity, cost of discount rate increases, placing some of their capital calculations are performed centrally, often planned investments in jeopardy. It is therefore in the office of the corporate treasurer, and are important that cost of capital calculations be provided to the various company units. Man- fully explained and changes justified by changing agers and analysts in these units may protest that capital market rates of return.

8Bruner, et al., p. 17. 270 Chapter 8 • Cost of Capital

EXHIBIT 8.2 CALCULATING THE MARKET WEIGHTINGS OF EACH CAPITAL SOURCE

CAPITAL PRICE PER NUMBER TOTAL MARKET COMPONENT BOND OR SHARE OUTSTANDING VALUE OF COMPONENT PROPORTION Debt (bonds) $1,003.00 1,537 $1,541,611 28.0% Preferred stock $21.50 20,068 $ 431,462 7.8% Equity (retained cash) $11.25 313,867 $3,531,004 64.2% $5,504,077 100.0%

Paula calculated the proportion for each component by dividing its market value by the total market value of capital, $5,504,077. 3,531,004 proportion of common equity financing 5 5 64.2% 5,504,077 431,462 proportion of preferred stock financing 5 5 7.8% 5,504,077 1,541,611 proportion of debt financing 5 5 28.0% 5,504,077 Paula intends to finance the harness project using capital from these three sources in these proportions. As we saw in Exhibit 8.1, the WACC for the har- ness project is 12.5%. We may confirm this with the WACC formula.

new new WACC 5 (Wd)(Kd )(1 2 t) 1 (Wpfd)(Kpfd ) 1 (Wret earn)(Kret earn) (8.15) 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 8.15, you may wonder why Paula doesn’t finance the en- tire project with debt and discount it at the after tax cost of debt. The after-tax cost of debt is only (9.9%) (1 2 0.30) 5 6.93%. Discounting at 6.93% rather than 12.5% would certainly raise the harness project’s NPV. The problem with

Finance in the Firm

ACCOUNTING VS. FINANCE The widespread use of market rather than book capital markets. This provides ample opportu- weights is a rather recent phenomenon. Book nity for mistrustful accountants and others to weights have the advantages of being relatively believe that the calculation is performed more stable over time and being observable by anyone with smoke and mirrors than with solid num- with access to company financial statements. bers. Of course, their suspicions are confirmed if Market weights change continually, and, for they discover that, in a year when no new capi- many not schooled in finance, the calculations tal was raised, their debt weighting fell from are opaque because they require monitoring of 30% to 20% of capital. Chapter 8 • Cost of Capital 271 this scheme is that POL must maintain some balance between debt and equity.9 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 con- sistent, it would discount that project at the 15% cost of equity. Consider two A project should be discounted at the projects, perhaps quite similar in most respects, one accepted and the other re- WACC, rather than at the costs of in- jected just because POL is seeking some balance to its capital structure and not dividual capital components, regard- less of how the project is financed. because one project is better or worse than the other. This illustrates why it is im- portant 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. WACC reflects the firm’s long-term capital mix. A firm that finances a pro- ject 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 un- balance 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 prohibi- tive. This project would probably be funded entirely from retained earnings, meaning that POL would temporarily unbalance its capital structure. Estimating the Discount Rate for Individual Projects

For many, perhaps most, projects, the appropriate discount rate to use in the WACC is the appropriate discount rate NPV calculation is the firm’s weighted average cost of capital (WACC), as out- for projects whose risk is about equal lined in the previous section. However, there are circumstances in which WACC to the risk of the company as a whole. is not the appropriate discount rate. Every company, of course, 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 proj- ect 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 im- plicitly 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 ex- ample, 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 dis- count rate. Paula believes that the harness project has the same risk as POL’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 harness project is essentially identical to that of the company’s existing prod- ucts. She understands that there are uncertainties, to be sure, 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 are the marketwide or nondiversifiable risks of the business. (She apparently read Chapter 6.) The new harness is probably about as sensitive to marketwide 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.

9If you don’t believe that the company must maintain some balance in its capital structure, read Chapter 10. 272 Chapter 8 • Cost of Capital

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 oc- casions when this is not the case. In such instances we must estimate a discount rate that reflects the project’s risk. This section describes why differences in risk might arise and how discount rates for individual projects might be estimated. Consider Campbell Soup. The company has a dominant 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 projects. The first is a tomato soup with a spicy Mexican taste. This soup follows the successful intro- duction of a spicy Italian tomato soup in 1992. 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 imme- diate serving. Do these two proposals have the same risk? Probably they do not. The spicy Mexican soup is a standard Campbell’s product. Campbell Soup has enormous experience evaluating, producing, marketing, and distributing such products. It also has recent experience with a similar soup—the spicy Italian tomato soup. By contrast, a chain of fast-food restaurants differs markedly from any of Camp- bell’s other businesses. The fast-food industry is very competitive, with several dominant chains vying for market share. Campbell’s managers have little experi- ence in this industry. Also, the two projects will probably respond differently to economywide 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 analo- gous to POL’s harness project. Campbell’s managers would judge that the soup cafes add risk to company, and therefore should take a higher discount rate. Estimating a Risk-Adjusted Discount Rate for NPV Analysis Chapter 6 introduced the capital asset pricing model (CAPM) 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 con- tain mostly market risk; therefore, we may use the CAPM to determine a proj- ect’s discount rate. required return on a project 5 risk-free rate (8.16) 1 (project beta) (market return 2 risk-free rate)

An asset beta is a measure of market The project beta, commonly called an asset beta, is not the same as the common risk for a project. stock beta from Chapter 6; it is actually a measure of a project’s market risk. In the next section we discuss how to estimate a project’s beta. Estimating a Project’s Beta Recall from Chapter 6 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. Of course, there is no convenient market index for soup cafes, so we Chapter 8 • Cost of Capital 273

Finance in the Firm

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

cannot directly calculate the beta for Campbell’s project. Therefore, the analyst must look for clues regarding the project’s risk. One widely used technique for estimating a project’s cost of capital is the pure-play method. A pure-play is a A pure-play is a publicly traded firm publicly traded firm that engages primarily in the same line of business as the that engages primarily in the same project being considered. The beta of this pure-play’s equity may then be found line of business as the project being considered. and used as a proxy for the project’s beta.10 The pure-play’s beta may be fed into the CAPM to estimate the appropriate risk-adjusted discount rate (RADR) The risk-adjusted discount rate for the project. (RADR) applies to projects whose risk Identifying a publicly traded pure-play firm is seldom easy. For the soup is substantially different from com- pany risk. cafes, Campbell’s managers may begin with small chains of specialized fast-food restaurants. Another chain of soup cafes would be ideal, but none probably ex- ists. 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. Ide- ally, 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. The best choice is an all equity-financed firm. 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 re- quired return could then be used as the discount rate for NPV or as the hurdle rate for IRR. Suppose, for example, there exists a chain of soup cafes that is all equity financed. The beta for this company is 1.3. This beta may then be trans- ferred to Campbell’s cafe project and a RADR could then be estimated.

We will assume rf 5 4% and E(Rm) 5 13%.

RADR 5 required Returnsoup cafes 5 rf 1basset[E(Rm) 2 rf)] 5 4% 1 1.3(13% 2 4%) 5 15.7% If the capital structure of the pure-play firm includes debt, we may estimate the asset beta using the Hamada equation.11 The Hamada equation may be used to convert the equity beta of a pure-play bequity firm into an asset beta. b 5 (8.17) asset 1 1 sD Eds1 2 td >

10Here we are assuming that the pure-play engages in the same business and uses the same mix of debt and equity in its financing. 11See Robert Hamada, “The Effect of the Firm’s Capital Structure on the Systematic Risk of Common Stock,” Journal of Finance, May 1972, 435–452. 274 Chapter 8 • Cost of Capital

Here bequity is the beta of the pure-play’s common stock. The pure-play’s tax rate is t and D/E is the 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. 1.5 bassets 5 1 5 1.11 1 1 s1 2 0.3d2 This beta could then be used to estimate the project’s appropriate discount rate. RADR 5 4% 1 1.11(13% 2 4%) 5 13.99, or 14% Of course, for many projects a pure-play cannot be found. The methods for estimat- ing the RADR under such circumstances range from ad hoc techniques (like adding or subtracting 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 cur- rent 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 en- countered using this method are obvious, but at times there is no choice. Account- ing betas are found by measuring the comovement 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. Ideally, each project will have its own discount rate reflecting its risk. In prac- tice, 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. Summary

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 re- quired 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 individ- ual 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, therefore, 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). Key Terms

cost of capital cost of debt weighted average cost of capital cost of preferred stock (WACC) cost of common equity Chapter 8 • Cost of Capital 275 equity-debt-risk premium venture capital firms investment banks capital structure underwriting asset beta underwriting spread pure-play method flotation costs risk-adjusted discount rate (RADR) Key Formulas

Cost of Debt

Kd 5 Yield to Maturity

the after-tax cost of debt 5 Kd (1 2 t) new Kd 5 YTM YTM calculated using Pnet for Bonds Cost of Preferred Stock dividend K 5 pfd share price

PNet 5 P 2 (flotation costs) Cost of Common Equity CAPM

Ke 5 rf 1bi[E(rm) 2 rf]

Dividend Growth

D1 Ke 5 1 gn P0 Equity-Debt Risk Premium

Ke 5 Kd 1 RP

D1 Knew stock 5 1 gn Pnet Weighted Average Cost of Capital

new new WACC 5 (Wd) (Kd ) (1 2 t) 1 (Wpfd) (Kpfd ) 1 (Wret earn) (Kret earn) Calculating the Asset Beta

bequity b 5 assets 1 1 sD Eds1 2 td > 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 ar- gue 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.) 276 Chapter 8 • Cost of Capital

2. Accounting balance sheets reflect the book values of claims, based on the historical 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 pre- mium, 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, com- pares to the 50–50 mix reflected on the accounting balance sheet? 3. Explain why (1 2 t) does not appear in the cost of preferred and the cost of common equity formulas. 4. Suppose a firm uses all equity financing, but half that financing is internal eq- uity 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. Which of the following hypothetical projects would appropriately use the firm’s current WACC as the discount rate in capital budgeting, and which do you feel require some risk adjustment? a. Boeing is considering producing a new version of the 777 aircraft, altered for use as a cargo plane. It will be called the 777C. b. Pogo Offshore Ltd., discussed in this chapter, is analyzing the market for producing windsurfing equipment. c. AT&T is considering the production of fax machines. d. McDonald’s is analyzing the addition of a new menu item, onion rings. 6. A project with an NPV 5 0 provides all corporate investors with their re- quired return; therefore all investors are satisfied. Do you agree or disagree with this statement? 7. Consider a project for which NPV 5 $18,000. Which investors have a claim on this net present value amount? 8. There are three methods of estimating the cost of corporate equity. Name or briefly describe two of these methods. 9. Flotation costs ______(raise/lower) the corporate cost of capital. 10. (True/False.) A project beta provides a way to estimate the required return to reflect project risk. 11. The corporate weighted average cost of capital is the appropriate required rate of return for which of the following? a. All corporate projects b. Projects whose risk is about equal to overall corporate risk c. Projects whose risk is generally less than overall corporate risk d. Projects whose risk is generally greater than overall corporate risk e. None of the above Chapter 8 • Cost of Capital 277

Demonstration Problem Stan & Ollie’s WACC Stan and Ollie’s Popcorn is considering a new, fat-free product for distribution in movie theaters. The firm’s management believes that the new product has about the same risk as the firm’s current product line. Management therefore believes the firm’s current WACC is the appropriate discount rate for finding the project’s NPV. The RHS of the firm’s financial balance sheet, shown here, reflects the mar- ket value of each capital component.

CAPITAL SOURCE MARKET VALUE

Bonds, 100,000 outstanding; 8% annual coupon rate; $ 64,636,183 payable semiannually; mature in 15 years Preferred stock, $5 annual dividend, 2,000,000 shares outstanding $ 71,420,000 Common stock, 13,000,000 shares outstanding $312,000,000 Total $448,056,183

The common stock just paid a dividend of $2.25 per share. Dividends are ex- pected to grow at 6% annually. Find Stan and Ollie’s WACC if the tax rate is 34%. solution

WACC 5 Wd Kd (1 2 t) 1 WpfdKpfd 1 WeKe step 1 Find the weights of each capital source. value debt W 5 d total value $64,636,183 5 $448,056,183 5 0.1443 value preferred W 5 pfd total value $71,420,000 550.1594 $448,056,183 value equity W 5 e total value $312,000,000 550.6963 $448,056,183 Check:

Wd 1 Wpfd 1 We 5 1.0000 0.1443 1 0.1594 1 0.6963 5 1.0000 1.0000 5 1.0000 278 Chapter 8 • Cost of Capital

Now, we know:

WACC 5 (0.1443) Kd (1 2 t) 1 (0.1594) Kpfd 1 (0.6963) Ke step 2 Find the costs.

a. Kd 5 YTM on bonds. The price of each bond is $64,636,183 divided by the total number of bonds outstanding, 100,000: $64,636,1834100,000 5 $646. $40 $40 $40 $646 5 1 1 . . . 1 s1 1 YTMd1 s1 1 YTMd2 s1 1 YTMd30 $1,000 1 s1 1 YTMd30 Because the annual coupon rate is 8%, the annual coupon payment is $80, but payments are made semiannually and therefore equal $40 each. Because there are 15 years to maturity, there will be 30 semiannual periods until the bond matures. In absence of a stated maturity or par value, $1,000 is assumed. Solving for YTM results in a solution of YTM 5 6.79% semiannually or YTM 5 13.58% per year

Kd 5 13.58% b. The price per share of the preferred can be found by dividing the total mar- ket value by the number of preferred shares outstanding, $71,420,000 price per share 5 5 $35.71 2,000,000 $5 K 5 5 14% pfd $35.71 c.

D1 Ke 5 1 gn P0

gn 5 6% 5 0.06

D1 5 D0(1 1 gn) 5 $2.25(1.06) 5 $2.385 $312,000,000 P 5 5 $24 0 13,000,000 $2.385 K 5 1 0.06 5 0.1594 5 15.94% e $24 step 3 Insert the costs and tax rate, and solve. WACC 5 (0.1443)(0.1358)(1 2 0.34) 1 (0.1594)(0.14) 1 (0.6963)(0.1594) 5 0.01293 1 0.02232 1 0.11099 5 0.14624 5 14.624% Chapter 8 • Cost of Capital 279

Problems

1. Cost of Debt Three years ago, Ron’s Rubbish Service issued 30-year bonds at par with a coupon rate of 8%, payable semiannually. Today, these bonds are selling for $875 each. What is Ron’s after-tax cost of debt if the company is in the 28% excel tax bracket? 2. Cost of Equity Dr. Watson’s Frosty Mornin’ Spring Water, Inc., has an equity beta of 1.5. As- suming t-bills are yielding 7% annually and the market risk premium is 5%, what is Watson’s cost of equity? 3. Cost of Equity Telebrations is a rapidly growing business. Its niche is allowing virtual par- ties by providing a closed-circuit video linkup for people all across the coun- try. Thus, grandparents in New Jersey can attend Tommy’s first birthday in Arizona. Telebrations’ dividends have been growing at an 8% rate annually. The last dividend paid was $1.15 and the stock is selling for $9.50 per share. a. What is Telebrations’ cost of retained earnings? b. If flotation costs are 30¢ per share, what is Telebrations’ cost of new stock? 4. Cost of Equity If Telebrations’ (see Problem 3) bonds yield 13%, what would be a reason- able range, in your estimation, for the firm’s cost of equity? 5. Cost of Preferred Stock What is a firm’s cost of preferred stock if it pays an annual dividend of $3 a share and is selling for $18 per share? 6. Calculating Weights A corporation’s capital structure consists of bonds and common stock. There are $8 million in corporate bonds outstanding, selling at par value. Book value of the common equity is $6 million. There are 1 million shares of com- mon stock outstanding. Currently, the market price per share is $18. a. What are the proportions of debt and equity using book values? b. What are the proportions of debt and equity using market values? c. Which is preferred for calculating WACC, book or market values? 7. Calculating Weights A company has a capital structure as reflected on the following balance sheet.

Bonds ($1000 par) 500 outstanding $ 500,000 Preferred stock ($3 coupon) 100,000 shares outstanding $ 300,000 Common stock 100,000 shares outstanding $1,000,000

a. What are the firm’s capital structure proportions based on book values? b. The bonds pay interest semiannually, have an 8% annual coupon rate, and mature in 10 years. Currently, investors require a 6% annual return from these bonds. What is the current price of each bond? What is the to- tal current value of these bonds? c. The required return for the preferred stock is 8%. What is the current price per share of the preferred and what is the preferred stock total value? 280 Chapter 8 • Cost of Capital

d. Common stock is expected to pay a $1.10 dividend next year. Dividends are expected to grow at an 8% rate for the foreseeable future. Investors require a 10% return from their investment in securities that have the same risk as this stock. What is the stock’s current price and total value? e. Construct the RHS of this corporation’s financial balance sheet. Then find the weights, based on market values that would be used in finding this firm’s WACC. 8. Calculating WACC Mainsail Corporation is financed by the following proportions of capital:

Long-term debt 30% Preferred stock 5% Common equity (retained cash) 65% Mainsail’s corporate tax rate is 30%

a. The yield to maturity on long-term debt is 9%. What is the after-tax cost of this debt to Mainsail? b. The preferred stock dividend is $6.50 per share. The price of the pre- ferred stock is $50. What is the cost of preferred stock to Mainsail? c. The risk-free interest rate is 8%. The market risk premium is 5%. The company’s beta is 1.3. What is the cost of common equity to Mainsail? d. Calculate the weighted average cost of capital for Mainsail. e. If the project is financed solely by debt, what is the required rate of return for the project, assuming its risk is the same as that of the overall com- pany and the firm will maintain its current capital structure as its long- term target? 9. Comprehensive WACC Santa Fe Industries manufactures frozen tamales, which are distributed through- out the Southwest. The corporation is considering a geographic expansion excel into New England. The project requires additional processing capacity in the Santa Fe factory. Total initial investment will be $2,000,000. You have been hired by Santa Fe to estimate the cost of capital for the project. The firm wishes to maintain its current capital mix and considers the project to have risk equal to its existing business. Santa Fe’s management has provided the fol- lowing details of its existing capital from its accounting balance sheet.

Long-term debt Bank loan* $ 1,500,000 Bonds (originally sold at par)† $ 6,000,000 Equity Common stock, $1 per share par $ 1,000,000 Additional paid in capital $ 9,000,000 Retained earnings $13,000,000

*The bank loan floats at the prime rate. †Bonds are $1,000 par value, mature 12 years from today, and pay coupons annually at a 9% rate.

You have done some research on your own. The following notes reflect the pertinent information. Chapter 8 • Cost of Capital 281

Bonds: Santa Fe’s bonds are selling for $920. Investment bankers charge $50 per bond to sell a new issue. Bank loan: The bank is willing to extend a long-term loan to Santa Fe at 9% current APR, with interest paid monthly. The bank will waive any loan origi- nation fees. Equity: Santa Fe has no internal cash flow available for investment in the project. Common stock is selling for $24 per share. Dividends were $1.20 last year and were $0.50 per share 10 years ago. Investment bankers will charge $3 per share to market a new issue of stock. a. What are the components of capital for Santa Fe? b. What are the weights of each component? c. Of the $2,000,000, how many dollars must be raised from each capital source? d. For the new bonds to be sold at par value ($1,000 each), what annual coupon rate should they carry? e. How many bonds must Santa Fe sell? (Round up to the next bond if your answer is not a whole number.) f. How many shares of stock must be sold to raise the needed capital? (Round up if you have a fractional answer.) g. What is the cost of bond debt? What is the after tax cost of bond debt if Santa Fe is in the 34% marginal tax bracket? h. What is the cost of bank debt? What is the after tax cost of bank debt? i. What is the cost of equity? j. Does the cost of equity you calculated in part (i) fall within the range found using the equity-debt risk premium? k. What is the WACC? 10. RADR Santa Fe (Problem 9) is also considering starting a new chain of fast-food restaurants, to be called the Santa Fe Cafe. These will be funded using 100% equity, all of it internally generated cash. To calculate the risk-adjusted discount cost of capital for this project, you have found the betas of two pure-plays:

Tijuana Tacos beta 5 1.6 The Big Burrito beta 5 1.4

You note that Tijuana Tacos’ capital mix is 20% debt and 80% equity, while The Big Burrito uses no debt in its capital structure. Tijuana Taco’s tax rate is 33%. a. Estimate Santa Fe Cafe’s beta. b. The market risk premium has historically been close to 6%, and t-bills are yielding 5.7%. What is the cost of equity for the cafe project? c. Will the WACC for the project differ from the cost of equity in this case? 11. Calculating NPV and IRR If the Santa Fe Cafe project (Problem 10) requires an initial investment of $1,500,000 and is expected to generate cash flows of $180,000 in year 1, $250,000 in year 2, and $300,000 in each of the next 8 years, what is the excel project’s NPV? What is its IRR? Would you recommend that the project be pursued? Why or why not? 12. RADR Suppose that Campbell Soup finds a comparable firm with which it can esti- mate the beta of the 17 Flavors Soup Cafes project (see text for a complete 282 Chapter 8 • Cost of Capital

description). The pure-play firm is called Chicago Soup Kitchens. Chicago’s equity beta is 1.30, its tax rate is 35%, and its debt-equity ratio based on 1 market values is 3 . What is your estimate of the 17 Flavors’ asset beta? 13. Calculating WACC Barnstorm Aircraft, Inc. has a target capital structure of 45% debt and 55% equity. Its cost of equity is 19%, its tax rate is 34%, and its cost of debt is 13%. What is Barnstorm’s WACC? 14. Calculating Weights The management of Blue Thumb Tools believes the firm’s current capital structure is optimal and intends to maintain it in the future. Blue Thumb’s bonds are selling for $950 each. Its common stock is selling for $37 a share and its preferred stock is selling for $88 per share. There are 50,000 bonds outstanding, 10,000,000 shares of stock, and 3,000,000 shares of preferred stock outstanding, respectively. What are the current weights of Blue Thumb’s capital sources? 15. Calculating WACC Blue Thumb’s (see Problem 14) stock has a beta of 1.2. The current t-bill yield is 5.5% and the expected return on the market portfolio is 11.5%. The company’s preferred stock pays a $8.50-per-share dividend each year. The yield to maturity of Blue Thumb’s bonds is currently 9.7%. If Blue Thumb is in the 29% tax bracket, what is the company’s WACC? 16. NPV Suppose Blue Thumb Tools (Problem 15) is considering the introduction of a new, heavier hammer to be used for driving spikes. The new hammer is called excel the Black Thumb. Use the WACC you found in Problem 15 to find the NPV of the Black Thumb project. The project’s projected cost and cash flows are given here. cost 5 $459,000

YEAR CASH FLOW

1 $178,000 2 $239,000 3 $225,000 4 $180,000

Internet Exercise

Cost of Capital Data Ibbotson Associates provides financial data for commercial and academic use. Log on to the Ibbotson Web site, http://www.ibbotson.com. View the Cost of Capital Center and Cost of Capital Yearbook pages. a. Summarize the cost of capital information provided by Ibbotson. b. Why do you think that clients would be willing to pay such high prices for this information? What might they use if for? c. From the Cost of Capital Center, click on Research Papers and read the ab- stracts of the papers. Looking at the data provided by Ibbotson and the top- ics of the research papers, is there more focus on cost of debt or cost of eq- uity? Why do you think this is true? appendix 8 TheThe BestBest ProxyProxy forfor thethe Risk-FreeRisk-Free RateRate

raditionally, returns on the 3-month treasury bill have been used as the risk-free rate in calculating a company’s cost of equity. The bill is not only Tfree of default risk, it is also virtually free of interest-rate risk because of its short life span. Today practitioners favor use of a long-term treasury bond, primarily because it more closely matches the long-term character of common stocks. In a widely used practitioner’s guide to valuation, Tom Copeland et al. suggest using the 10-year treasury bond rate.12 In an article summarizing prac- tices in estimating a firm’s cost of capital, Bruner et al. report that only 4% of responding companies used the 3-month treasury bill rate, while 70% used rates on treasury bonds of 10 or more years’ maturity.13 The choice of a risk-free rate can significantly alter the calculated cost of eq- uity. Returns on 10-year treasury bonds have averaged about 1.5% higher than those on treasury bills.14 Reworking the cost of equity calculation, with a beta of 1.2, the cost of equity for Pacific Offshore Ltd., we get the following.

USING THE T-BILL RATE USING THE T-BOND RATE

Risk-free rate 4% 5.5% Market return 13% 13% Market risk premium 9% 7.5%

Using the two estimates of the risk-free rate to calculate POL’s cost of equity gives us

R(r)POL 5 rf 1bPOL 1 [E(rm) 2 rf]

R(r)POL 5 4% 1 1.2(9%) 5 14.8% (t-bill rate)

R(r)POL 5 5.5% 1 1.2(7.5%) 5 14.5% (t-bond rate) The magnitude of the differences in these estimates is dependent on beta. With a beta of 1, it does not matter which risk-free rate is used. In either case, the cost of equity is 13%. For betas below or above 1, the cost of equity estimates will differ, depending on which risk-free rate is used; the greater the distance from 1, the greater the difference. In the POL example, if beta 5 1.8, the cost of equity would be 20.2% using t-bills and 19% using t-bonds.

12Tom Copeland, Tim Koller, and Jack Murrin, Valuation: Measuring and Managing the Value of Companies (New York: John Wiley & Sons, 1996), Chapter 8. 13Bruner, et al., 13–28. 14Bruner, et al., 19. 283