Week 4 Assignment
Learning Objectives
Upon completion of Chapter 10, you will be able to:
• Understand the meaning of the weighted average cost of capital (WACC).
• Be able to estimate the weights in the WACC.
• Be able to estimate the cost of debt and how it is affected by taxes.
• Be able to estimate the cost of preferred stock.
• Know three approaches for estimating the cost of equity.
• Understand flotation costs and how they affect the WACC.
• Know when the WACC is the appropriate approach for estimating the required return for a project.
• Know an alternative approach for estimating a project’s required return when the WACC is not the appropriate measure.
Cost of Capital
10
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CHAPTER 10Section 10.1 Estimating the Discount Rate
Corporate managers use various capital budgeting techniques. Among these tech-niques, net present value (NPV) emerges as the best measure of a project’s con-tribution 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 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 dis- count 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.
10.1 Estimating the Discount Rate
To illustrate the calculation and use of the discount rate, we introduce a case study of Pacific Offshore Ltd. (POL). POL is considering the manufacture and sale of har-nesses to be used by sailors who must be tethered to their boats in the high seas. The harnesses can save the lives of sailors who are washed overboard in rough water and storms. 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 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. The cost of the harness project is $64,384, meaning that the owners must raise that amount from their investors to fund tools, equipment, and working capital and to pay the cost of reconfiguring the plant. The owners 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% 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.
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 10.1 illustrates the flow of capital and cash flows, assuming that the har- ness project produces its expected cash flows.
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 therefore 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
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CHAPTER 10Section 10.2 The Weighted Average Cost of Capital
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, the owners must be confident that the discount rate they use 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 because the returns investors require are the cost, like rent, that is paid for the use of the capital.
Figure 10.1: Financing mix and cash flows for the POL harness project
10.2 The Weighted Average Cost of Capital
The cost of capital is a weighted average of the required returns for each capital source. For any project, the weighted average cost of capital (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 the firm’s bonds, preferred stock, and com- mon equity, weighted by their proportional contribution to the project.
Later we will explain how the costs of debt, preferred stock, and common equity are cal- culated. First, though, we will present a worksheet for computing POL’s cost of capital. Table 10.1 shows that the owners multiplied the proportion of each capital source by its after-tax required return. They then summed these results to arrive at the 12.5% cost of capital.
Preferred stockholders
Common stockholders
$64,384
$18,028
$5,022
$41,334 Consumers
Bondholders POL Harness Project
tools, equipment, working capital, plant
Harnesses
Cash Flows
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CHAPTER 10Section 10.2 The Weighted Average Cost of Capital
Table 10.1: 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) 28.0% $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%
The owners’ worksheet may be summarized by a formula for the weighted average cost of capital:
(10.1) WACC 5 (W d )(after-tax cost of debt)
1 (W pfd
)(cost of preferred stock)
1 (W e )(cost of common equity)
where
W d 5 the desired proportion of financing provided by debt
W pfd
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 example, if preferred stock were not used, then W
pfd 5 0, and preferred stock would drop out of the
formula. Some companies borrow from many sources. They may have several bond issues and perhaps long-term loans from banks or insurance companies. The only source of capi- tal 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, could be
(10.2) WACC 5 (W B )(after-tax cost of bonds)
1 (W L )(after-tax cost of loan)
1 (W e )(cost of equity)
No matter how many sources of capital there are, the weights always sum to 1 (W
B 1 W
L 1 W
e 5 1). This ensures that all capital sources have been included in the calcu-
lation of WACC.
Discounting expected cash flows by the weighted average cost of capital gives the owners the information they need to make their investment decision on the 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.
In summary, discounting project cash flows at the WACC ensures that the minimal needs of each class of investor are met. We may rewrite the NPV and IRR equations to include WACC as follows:
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CHAPTER 10Section 10.2 The Weighted Average Cost of Capital
(10.3a) NPV 5 2II 1 a n
t 5 1
OCFt 11 1 R1r2 2 t 1
TCFn 11 1 R1r2 2 n
Where
II 5 initial investment OCF
t 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 (10.3a) may be simplified to
(10.3b) NPV 5 a n
t 5 1
CFt 11 1 r2 t 2 II
By substituting WACC for r, the equation becomes
(10.4) NPV 5 a n
t 5 1
CFt 11 1 WACC2 t 2 II
The equation for IRR is
(10.5) a n
t 5 1
CFt 11 1 IRR2 t 2 II 5 0
The company should accept projects with IRR . WACC. If the company has multiple projects and limited capital, then they normally invest first in the projects with the largest positive difference between the IRR and WACC.
In the following section, we explain how the owners estimated the cost of each capital component.
The Cost of Debt
The cost of debt (K d ) is the current yield to maturity on the company’s bonds or other
long-term debt securities. 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 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:
K d 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.
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CHAPTER 10Section 10.2 The Weighted Average Cost of Capital
K d is found by solving for YTM in the following equation:
$1,003 5 $47.50
11 1 YTM2 1 1 $47.50
11 1 YTM2 2 1 c1
$47.50 11 1 YTM2 12
1 $1,000
11 1 YTM2 12
That is, we set 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.
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)/25] ($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.
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 K
d for
YTM gives us
(10.6) After-Tax Cost of Debt 5 K d (1 2 t)
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. We recognize this as a perpetuity—a perpetual annuity—which greatly simplifies the calculation. The cost of preferred stock equals its required rate of return, which is its annual dividend, divided by its current market price.
The dividend on POL’s preferred stock is $2.50, and its current market price is $21.50 per share. Therefore,
(10.7) Kpfd 5 dividend
share price 5
$2.50 $21.50
5 0.1163 5 11.63%
and so the required return on the stock is 11.63%. No tax adjustment is necessary for preferred stock because dividends are paid with after-tax cash flows.
The Cost of Common Equity
The cost of common equity (K e ) is the most difficult of the component costs to estimate.
The Capital Asset Pricing Model (CAPM) is 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
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CHAPTER 10Section 10.2 The Weighted Average Cost of Capital
notably the discounted cash flow model. As a general rule, the analyst should approach the problem of estimating common stock returns from several directions and hope to gen- erate a consensus estimate from these varying approaches. In this section, we cover three approaches: CAPM, the discounted cash flow model, and the equity–debt–risk premium.
The CAPM Approach to K e
Chapter 9 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. The CAPM is
(10.8) R(r) i 5 r
f 1 b
i (market risk premium)
or
R(r) i 5 r
f 1 b
i [E(r
m ) 2 r
f ]
where
R(r) i 5 Required Return for Asset i
b i 5 Asset i’s Beta
E(r m
) 5 Expected Return of the Overall Market R
f 5 Risk-Free Rate of 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. Treasury bonds are considered nearly risk- less. Thus, Treasury bonds are a widely used proxy for the true risk-free rate.
Treasury bond returns are widely available in print and on the Internet. Next, we need an estimate of the equity beta. Brokerage and other investment service firms estimate betas for many publicly traded stocks. Betas may be obtained on the Internet and in print from Value Line, Standard & Poor’s, Yahoo!, and Bloomberg. As we saw in Chapter 9, we may also estimate beta ourselves using data on past returns.
The historical market risk premium is found by calculating the average amount by which the market return has exceeded Treasury bond returns. For example, the difference between the S&P 500 return and the Treasury bond return for each of the last 80 years could be averaged and used as the historical market risk premium. There are many esti- mates of the market risk premium (or equity risk premium). Over the past 80 years, we will assume that the market risk premium has averaged about 7.6% per year.
For POL, the owners gathered the following estimates for the risk-free return, POL’s beta, and the market risk premium:
Risk-Free Return 5 5% b 5 1.2
Market Risk Premium 5 7.6%
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CHAPTER 10Section 10.2 The Weighted Average Cost of Capital
Using Equation (10.8) the owners’ CAPM estimate is
R(r) POL
5 r f 1 b
POL [market risk premium]
5 5% 1 1.2(7.6%) 5 14.12%
This 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.
The Discounted Cash Flow Approach to K e
The constant dividend growth model can be used for valuing common stock. Note that K
e , the cost of equity for the firm, is the same as the required return of investors
who purchase the equity, so the current price (P 0 ) equals next year ’s dividend (D
1 )
divided by the difference between equity’s required return (r) and the long-run divi- dend growth rate (g
n ):
(10.9) P0 5 D1
Ke 2 gn
This equation may also be solved for the cost of equity, giving
(10.10) 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 (FV) of a single cash flow formula:
FV 5 PV 0 (1 1 r)n
where PV 0 is the present value of the cash flow, r is the rate of return, and n is the number
of periods. The difference is that rather than looking forward, we are looking back. To use the model, we must change the definition of its components. FV is the most recent divi- dend, D
0 . PV
0 is the beginning historical dividend, D
2n (where 2n refers to nth period in
the past). The rate of return, r, is the compound growth rate, g n , so
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CHAPTER 10Section 10.2 The Weighted Average Cost of Capital
(10.11) D 0 5 D
2n (1 1 g
n )n
Fortunately, POL has paid a dividend for 5 years, so we are able to calculate a growth rate. The dividend 5 years ago (D
25 ), was $0.60 and the most recent dividend (D
0 ) was $0.84.
Therefore
D 0 5 D
25 (1 1 g
n )5
so
a D0 D25
b 1 5
5 11 1 gn2
Solving for g n gives
gn 5 a D0
D25 b
1 5
2 1
5 a0.84 0.60
b 1 5
2 1
5 1.07 2 1 5 0.07
Therefore g n 5 7%.
The current market price of POL’s common stock is $11.25. Next year’s dividend, D 1 ,
should equal D 0 (1 1 g
n ). So D
1 5 $0.84(1.07) 5 $0.90. Now, we may solve for K
e to get
Ke 5 D1 P0
5 $0.90 11.25
1 0.07 5 0.15 5 15%
Having estimated K e using the constant growth formula, we must remember that in this
formula a constant growth rate into perpetuity has been assumed. 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 startup companies will eventu- ally 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 K e
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 K
e exceed K
d . The difference between K
e and K
d
is the equity–debt –risk premium:
(10.12) K e 5 K
d 1 RP
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CHAPTER 10Section 10.2 The Weighted Average Cost of Capital
The risk premium, RP, is generally in the range of 3% to 6%, based on a variety of factors including the bond rating of the company. The method is ad hoc but works fairly well as a benchmark because the necessary data are easily obtained. Estimates of K
e , using CAPM
and discounted cash flow models, that fall outside the range [K d 5 (3% to 6%)] should
prompt any analyst to revisit his or her estimates. For POL, the equity–debt–risk premium approach yields the following range for K
e :
(K d 1 3%) , K
e , (K
d 1 6%)
(9.4% 1 3%) , K e , (9.4% 1 6%)
12.4% , K e , 15.4%
The owners’ estimates of K e using the CAPM was 14.12%. Their discounted cash flow
method produced a 15% cost of equity. All three of these estimates are within the range prescribed by the equity—debt premium, which more or less confirms the owners’ esti- mates. The owners elected 15% as POL’s cost of equity. As with preferred stock, no tax adjustment is necessary because dividends are not a tax-deductible expense.
A Closer Look: Explaining a Changing Cost of Capital
Project analysis involves virtually every unit within a company and cuts across many disciplines. By necessity, cost of capital calculations are performed centrally, often in the office of the corporate treasurer, and are provided to the various company units. Managers and analysts in these units may protest that changing discount rates make planning nearly impossible. They are especially upset when the discount rate increases, placing some of their planned investments in jeopardy. It is there- fore important that cost of capital calculations be fully explained and changes justified by changing capital market rates of return.
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 securi- ties. 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 company 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, POL is sell- ing bonds to pay for the harness project. Investors will buy the bonds for approximately $1,003, their current market price. However, the underwriting spread reduces POL’s pro- ceeds 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. In the lingo of Wall Street, firms are said to be floating an issue. Aside from the underwriting spread, flotation costs include fees paid to the investment banker for consultation, document preparation, and so on. They also include costs of filing with regulators such as the Securities and Exchange Commission, legal fees, and accounting fees. Flotation costs as a percentage of the value
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CHAPTER 10Section 10.2 The Weighted Average Cost of Capital
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 dol- lar 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 entrepre- neurial activity in the United States, creating new investment opportunities. Venture capital firms have sprung up by the hundreds to supply early financing to promising companies. For example, in May 2012 Facebook went public. 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!
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:
(10.13) P net
5 P 2 (flotation costs)
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 harness project. 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. The owners adjust the cost of debt and preferred stock to reflect these flotation costs.
For bonds,
(10.14) K d new 5 YTM (calculated using P
net for bonds)
Then
P net
for Bonds 5 $1,003 2 $20 5 $983
Based on a P net
of $983, we recalculate YTM as
YTM* 5 4.94% semiannually
and so
K d new 5 9.9% annually
giving us a result of
K d new (1 2 t) 5 9.9% (0.7) 5 6.93%
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CHAPTER 10Section 10.2 The Weighted Average Cost of Capital
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. These are sum- marized in Table 10.2.
Table 10.2: POL’s cost of equity
Risk free return: T-bills (from the Wall Street Journal) r f 5 5%
Beta POL
(from POL’s investment banker) b POL
5 1.2
Market risk premium: historical equity market risk premium (from Ibbotson) 9.4%
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.
For preferred stock,
P net
5 $21.50 2 $0.60 2 $20.90
and so
Knewd 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 common equity remains at 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 adjustment, we reduce the stock price by the amount of the flotation costs, which raises the cost of equity to the company.
(10.15) 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 stock (11.96%), and the cost of equity (15%) are the component costs that the owners used in their WACC worksheet, Table 10.1. Using Equation (10.1), they multiplied these component costs by their desired proportions to derive the WACC. We have not described in detail how the owners decided on the mix of common equity, preferred stock, and bonds to finance the harness project. In the next section, we show how the owners determined their financing mix—the capital structure referred to in Chapter 9. Capital refers to long-term financing, such as that used to fund the harness project.
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CHAPTER 10Section 10.2 The Weighted Average Cost of Capital
The Financing Mix and Weights in the WACC
The weights in the WACC formula could reflect any target or desired financing mix. The owners have chosen to finance the harness project using POL’s current mix of capital. 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 (equity and liabilities) 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.
The owners determined the current financing mix by estimating the market values for each of POL’s capital sources. They first obtained the current prices for the company’s bonds, preferred stock, and common stock. Next, they multiplied these prices by the num- ber of bonds or shares of stock outstanding to compute the market value of each compo- nent. Summing these market values gave them the total market value of POL’s capital. The calculations are shown in Table 10.3.
Table 10.3: Calculating market weightings of each capital source
Capital component
Price per bond or share
Number outstanding
Total market 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%
The owners 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%
The owners intend to finance the harness project using capital from these three sources in these proportions. These are summarized in Table 10.4. As we saw in Table 10.1, the WACC for the harness project is 12.5%. We may confirm this with the WACC formula,
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CHAPTER 10Section 10.3 Estimating the Discount Rate for Individual Projects
(10.16) WACC 5 (W d )(K
d new)(1 2 t) 1 (W
pfd )(K
pfd ) 1 (W
ret earn )(K
ret earn )
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%
Table 10.4: Costs before and after flotation costs
Before tax After tax
Without flotation costs 9.44% 6.61%
Including flotation costs 9.88% 6.93%
Glancing at Equation 10.16, you may wonder why the owners don’t finance the entire project with debt and discount it at the after-tax cost of debt. The after-tax cost of debt is only (9.9%)(1 20.30) 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 projects if all projects were con- sistently 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, regard- less of how a particular project is financed. We separate the investment decision from the financing decision; that is, we evaluate investment decisions like the 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, 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.
10.3 Estimating the Discount Rate for Individual Projects
For many projects, the appropriate discount rate to use in the NPV calculation is the firm’s weighted average cost of capital (WACC), as outlined in the previous section. However, there are circumstances in which WACC 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
new
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CHAPTER 10Section 10.3 Estimating the Discount Rate for Individual Projects
the company’s WACC. In project analysis, we are actually interested in the risk of the par- ticular 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; there- fore, these risky projects should carry a higher discount rate.
The owners believe that the harness project has the same risk as POL’s existing business. They reason 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 products. They understand that there are uncer- tainties, 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. The owners also realize that the relevant risk for estimating required returns is the market-wide or nondiversifiable risks of the business. The new harness 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 project fits neatly into POL’s existing product line, there are many occa- sions 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 The Campbell Soup Company. 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 Camp- bell’s has average or slightly below-average risk. Now suppose that Campbell’s managers propose two hypothetical projects. The first is a tomato soup with a spicy Mexican taste. The second proposal is to start a chain of small soup cafés—tentatively called “17 Flavors Soup Cafés.” The cafés would feature 17 flavors (hence the name) of Campbell’s soups ready for immediate serving.
Do these two proposals have the same risk? Probably not. The spicy Mexican soup is a standard Campbell’s product. Campbell’s has enormous experience evaluating, produc- ing, 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 Campbell’s other businesses. The fast-food industry is very com- petitive, 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 harness proj- ect. Campbell’s managers would likely judge that the soup cafés add risk to company, and therefore they should take a higher discount rate.
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CHAPTER 10Section 10.3 Estimating the Discount Rate for Individual Projects
Estimating a Risk-Adjusted Discount Rate for NPV Analysis
Chapter 9 introduced the Capital Asset Pricing Model (CAPM) and the idea that the capi- tal markets price only market risk. This follows from the notion that unique risk is gen- erally absent from well-diversified portfolios. Projects also contain mostly market risk; therefore, we may use the CAPM to determine a project’s discount rate.
(10.17) 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. The asset beta, introduced in Chapter 9, measures the project’s market risk. In the next section we discuss how to estimate a beta that is appropriate for evaluating Camp- bell’s soup cafe initiative.
Estimating a Project’s Beta
Recall from Chapter 9 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.
A Closer Look: Use and Misuse of Risk-Adjusted Discount Rates
The risk-adjusted discount rate (RADR) 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 that generated 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.
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 none probably exists. 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, has a specialized menu, and their product (ice cream) is some what 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. As we stated earlier, using the pure-play
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CHAPTER 10Section 10.3 Estimating the Discount Rate for Individual Projects
company’s beta directly requires that the risk and financing must be close to those of the project. Financing is an issue because the equity betas of companies with the same busi- ness risk (the same asset beta) will differ according to how much debt each company has. The more debt, the higher the equity beta. The intuition behind this result (more debt, higher beta, all else 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 somewhere. 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, then 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 exists a chain of soup cafes that is all-equity-financed. The beta for this company is 1.3. This beta may then be transferred to Campbell’s cafe project, and a RADR can then be estimated.
We will assume r f 5 4% and that the market risk premium (MRP) is 9%. Then
RADR 5 required return soup cafes
5 r f 1 b
asset (MRP)
5 4% 1 1.3(9%) 5 15.7%
If the capital structure of the pure-play firm includes debt, then we may estimate the asset beta using the Hamada equation
(10.18) basset 5 bequity
1 1 1D/E2 11 2 t2
Here b equity
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 b
equity equal to
1.5, then 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 used to estimate the project’s appropriate discount rate:
RADR 5 r f 1 b
asset (MRP)
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’s, 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
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CHAPTER 10Section 10.3 Estimating the Discount Rate for Individual Projects
Demonstration Problem 10.1: 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 prod- uct line. Management therefore believes the firm’s current WACC is the appropriate discount rate for finding the project’s NPV. The right-hand (liabilities and equity) side of the firm’s financial balance sheet, shown here, reflects the market value of each capital component:
Capital Source Market Value
Bonds, 100,000 outstanding; 8% annual coupon rate $ 64,636,183
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 expected to grow at 6% annually. Find Stan and Ollie’s WACC if the tax rate is 34%.
Solution
WACC 5 W d K
d (1 2 t) 1 W
pfd K
pfd 1 W
e K
e
Step 1: Find the weights of each capital source:
Wd 5 value debt total value
5 $64,636,183
$448,056,183 5 0.1443
Wpfd 5 value preferred
total value
5 $71,420,000
$448,056,183 5 0.1594
We 5 value equity total value (continued)
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.
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 a broadcasting division.
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CHAPTER 10Section 10.3 Estimating the Discount Rate for Individual Projects
Demonstration Problem 10.1: Stan & Ollie’s WACC (continued)
5 $312,000,000 $448,056,183
5 0.6963
As a check, substitute back to see if the weights add to one:
W d 1 W
pfd 1 W
e 5 1.0000
0.1443 1 0.1594 1 0.6963 5 1.0000 1.0000 5 1.0000
Now, we know
WACC 5 (0.1443) K d (1 2 t) 1 (0.1594) K
pfd 1 (0.6963) K
e
Step 2: Find the costs.
a. K d 5 YTM on bonds. The price of each bond is $64,636,183 divided by the total number of
bonds outstanding (100,000), so $64,636,183/100,000 5 $646. 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 semian- nual periods until the bond matures. In the absence of a stated maturity or par value, $1,000 is assumed. We need to solve for YTM in the following equation:
$646 5 $40
11 1 YTM2 1 1 $40
11 1 YTM2 2 1 c 1
$40 11 1 YTM2 30
1 $1,000
11 1 YTM2 30
The solution is
YTM 5 6.79% semiannually or YTM 5 13.58% per year
K d 5 13.58%
b. The price per share of the preferred can be found by dividing the total market value by the number of preferred shares outstanding:
price per share 5 $71,420,000
2,000,000 5 $35.71
Kpfd 5 $5
$35.71 5 14%
c. Ke 5 D1 P0
1 gn
g n 5 6% 5 0.06
D 1 5 D
0 (1 1 g
n ) 5 $2.25(1.06) 5 $2.385 (continued)
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CHAPTER 10Key Terms
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 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).
Demonstration Problem 10.1: Stan & Ollie’s WACC (continued)
P0 5 $312,000,000
13,000,000 5 $24
Ke 5 $2.385
$24 1 0.06 5 0.1594 5 15.94%
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%
Key Terms
asset beta The systematic or market risk of an investment asset.
cost of capital The rate of return that must be earned in order to satisfy investors.
cost of common equity (K e ) The investors’
required return on common equity.
cost of debt (K d ) The required return of
investors 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.
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CHAPTER 10Web Resources
Web Resources
For more information on equity risk premiums, read Aswath Damodaran’s “Equity Risk Premiums (ERP): Determinants, Estimation and Implications—The 2011 Edition,” updated February 2011 and available at http://people.stern.nyu.edu/adamodar/pdfiles/papers/ERP2011.pdf.
For a discussion on estimates of the market risk premium with examples, see Pablo Fernandez’s, “Equity Premium: Historical, Expected, Required and Implied, ”published February 16, 2007, and available at http://ssrn.com/abstract5933070 or http://dx.doi.org/10.2139/ssrn.933070.
For further information on the Hamada equation see Robert Hamada’s “The Effect of the Firm’s Capital Structure on the Systematic Risk of Common Stock,” from the May 1972 edition of the Journal of Finance, (pp. 435–452), which can be found at http://www.psc.state.ky.us/pscscf/2007%20cases/2007-00008/CD_Columbia_042407 /AG%20Set%201%20No.%2098/2007-00008%20AG%20Set%201-098%20%283%29%20 attachment.pdf.
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 exter- nally for example, when selling newly issued stock or bonds.
investment banks 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 project 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 which finance high-risk startup 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.
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CHAPTER 10Critical Thinking and Discussion Questions
Critical Thinking and Discussion 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?
3. Explain why (1 2 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 of 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. 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. Pacific 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 . 0 provides all corporate investors with their required return; therefore, all investors are satisfied. Do you agree or disagree with this statement?
7. Consider a project for which NPV is $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. Do flotation costs raise or lower the corporate cost of capital? 10. Does a project’s beta provide a way to estimate the required return to reflect proj-
ect risk?
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CHAPTER 10Practice Problems
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
Practice Problems
1. Three years ago, Rakesh’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 Rakesh’s after-tax cost of debt if the company is in the 28% tax bracket?
2. Dr. Watson’s Frosty Mornin’ Spring Water Inc. has an equity beta of 1.5. Assum- ing Treasury bonds are yielding 7% annually and the market risk premium is 5%, what is Watson’s cost of equity?
3. Telebrations is a rapidly growing business. Its niche is allowing virtual parties by providing a closed-circuit video linkup for people all across the country. Thus, grandparents in New Jersey can attend My-Lan’s first birthday in Arizona. Tele- brations’s 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’s cost of retained earnings? b. If flotation costs are $0.30 per share, what is Telebrations’s cost of new stock? c. If Telebrations’s bonds yield 13%, what would be a reasonable range, in your
estimation, for the firm’s cost of equity? 4. 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? 5. 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 common stock out- standing. 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?
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CHAPTER 10Practice Problems
6. A company has a capital structure as reflected on the following balance sheet.
Bonds ($1,000 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 total 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?
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 right-hand side 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.
7. 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 preferred 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 com- pany’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 company and the firm will maintain its current capital structure as its long-term target?
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CHAPTER 10Practice Problems
Mini-Case: Comprehensive WACC
Santa Fe Industries manufactures frozen tamales, which are distributed throughout the Southwest. The corporation is considering a geographic expansion into New England. The project requires addi- tional 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 following details of its existing capital from its accounting balance sheet.
Long-term debt Bank loan*
Bonds (originally sold at par)† $ 1,500,000 $ 6,000,000
Equity Common stock, $1 per share Additional paid in capital Retained earnings
$ 1,000,000 $ 9,000,000 $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.
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 origination 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?
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CHAPTER 10Practice Problems
8. Santa Fe (see the Mini-Case above) 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 dis- count 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’s capital mix is 20% debt and 80% equity, while The Big Burrito uses no debt in its capital structure. Tijuana Tacos’s tax rate is 33%. a. Estimate Santa Fe Cafe’s beta. b. The market risk premium has historically been close to 6%, and Treasury
bonds 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?
9. If the Santa Fe Cafe project (see the Mini-Case above) 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 project’s NPV? What is its IRR? Would you recommend that the project be pursued? Why or why not?
10. Suppose that Campbell Soup finds a comparable firm with which it can estimate the beta of the 17 Flavors Soup Cafes project (see Section 10.3 for a complete 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 market values is 1. What is your estimate of 17 Flavors’s asset beta?
11. 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 before-tax cost of debt is 13%. What is Barnstorm’s WACC?
Mini-Case: Calculating Weights, WACC, and NPV
a. 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 com- mon 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?
b. Blue Thumb’s stock has a beta of 1.2. The current Treasury bond yield is 5.5%, and the expected return on the market portfolio is 11.5%. The company’s preferred stock pays an $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?
c. Suppose Blue Thumb is considering the introduction of a new, heavier hammer to be used for driving spikes. The new hammer is called the Black Thumb. Use the WACC you found in part b 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
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