When we adjust the wacc to reflect flotation costs, this approach:

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 (Wd )(after-tax cost of debt) 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 example, 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 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 (WB)(after-tax cost of bonds) 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 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

t51

OCFt 11 1 R 1r 2 2 t 1

TCFn 11 1 R 1r 2 2n

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 (10.3a) may be simplified to

(10.3b) NPV 5 a n

t51

CFt 11 1 r 2 t 2 II

By substituting WACC for r, the equation becomes

(10.4) NPV 5 a n

t51

CFt 11 1 WACC 2 t 2 II

The equation for IRR is

(10.5) a n

t51

CFt 11 1 IRR 2 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 (Kd) 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:

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.

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CHAPTER 10Section 10.2 The Weighted Average Cost of Capital

Kd is found by solving for YTM in the following equation:

$1,003 5 $47.50

11 1 YTM 2 1 1 $47.50

11 1 YTM 2 2 1 c1

$47.50 11 1 YTM 2 12

1 $1,000

11 1 YTM 2 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 Kd for YTM gives us

(10.6) After-Tax Cost of Debt 5 Kd (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 (Ke) 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 Ke 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 rf 1 bi(market risk premium)

or

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

where

R(r)i 5 Required Return for Asset i bi 5 Asset i’s Beta

E(rm ) 5 Expected Return of the Overall Market Rf 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 rf 1 bPOL[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 Ke The constant dividend growth model can be used for valuing common stock. Note that Ke, the cost of equity for the firm, is the same as the required return of investors who purchase the equity, so the current price (P0) equals next year’s dividend (D1) divided by the difference between equity’s required return (r) and the long-run divi- dend growth rate (gn):

(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 PV0(1 1 r) n

where PV0 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, D0. PV0 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, gn, so

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CHAPTER 10Section 10.2 The Weighted Average Cost of Capital

(10.11) D0 5 D2n(1 1 gn) 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 (D0) was $0.84. Therefore

D0 5 D25(1 1 gn ) 5

so

a D0 D25

b 1 5

5 11 1 gn 2

Solving for gn 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 gn 5 7%.

The current market price of POL’s common stock is $11.25. Next year’s dividend, D1, should equal D0(1 1 gn). So D15 $0.84(1.07) 5 $0.90. Now, we may solve for Ke to get

Ke 5 D1 P0

5 $0.90 11.25

1 0.07 5 0.15 5 15%

Having estimated Ke 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 Ke The final method for estimating the cost of equity is to add a risk premium to the cost of debt. Because equity is a residual claim with a lower priority than debt, equity is riskier than debt; therefore investors require that Ke exceed Kd. The difference between Ke and Kd is the equity–debt –risk premium:

(10.12) Ke 5 Kd 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 Ke, using CAPM and discounted cash flow models, that fall outside the range [Kd 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 Ke:

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

12.4% , Ke , 15.4%

The owners’ estimates of Ke 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) Pnet 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) Kd new 5 YTM (calculated using Pnet for bonds)

Then

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

Based on a Pnet of $983, we recalculate YTM as

YTM* 5 4.94% semiannually

and so

Kd new 5 9.9% annually

giving us a result of

Kd 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) rf 5 5%

BetaPOL (from POL’s investment banker) bPOL 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,

Pnet 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 1 flotation costs 2

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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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.