Bus650 week 4 assignment

Chapter 8

Cost of Capital

Associated Press

Learning Objectives

A�er studying this chapter, you should be able to:

Show how the discount rate is calculated and used. Explain how the weighted average cost of capital is calculated, and outline the significance of its components. Describe how to es�mate the discount rate for individual projects and how risk factors into the process.

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Ch. 8 Introduction

Chapter 6 described the various capital budge�ng techniques employed by corporate managers. Among the techniques, net present value (NPV) emerges as the best measure of a project's contribu�on to shareholder wealth. In NPV analysis, the present value of a project's expected future cash flows is compared to the ini�al investment, and the project is accepted if the present value exceeds the ini�al investment. Calcula�on of NPV requires the analyst to es�mate cash flows and an appropriate discount rate. Techniques for es�ma�ng cash flows were covered in Chapter 6. In this chapter, you will learn how to es�mate the discount rate. The same es�mates 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.

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Financing mix and cash flows for the Pogo harness project.

8.1 Estimating the Discount Rate

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

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

Data Category Value

Project cost $64,384

Required rate of return 12.5%

Internal rate of return 17.2%

Net present value $9,110

We have referred to the 12.5% as the harness project's required rate of return. To be more specific, 12.5% is the weighted average return demanded by the company's investors. The weigh�ngs reflect the propor�onal values of their investments. From Chapter 6, the cost of the harness project is $64,384, meaning that Paula Bauer must raise that amount from her investors to fund tools, equipment, and working capital and to pay the cost of reconfiguring the plant. Paula has decided to fund future projects using the firm's current propor�onal mix of debt and preferred and common stock. POL's current capital mix is 28% debt, 7.8% preferred stock, and 64.2% common stock. POL, therefore, will raise about $18,000 in debt and about $5,000 in preferred stock. The balance of the funding will come from residual cash flows that belong to the firm's shareholders. Table 8.2 shows how POL's capital mix will fund the Pogo harness project. Later, in Sec�on 8.2, we will show you how Paula came up with these numbers.

Table 8.2: POL's capital mix

Capital component Propor�on Cash Value

Debt 28% $18,028

Preferred stock 7.8% $5,022

Common stock 64.2% $41,334

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

Figure 8.1: Pogo harness project

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

Industrial Policy Processing math: 0%

Dr. Bruce Sco� argues that the U.S. has a higher cost of capital than any other country, which influences our economic system. Many companies are harves�ng their businesses, allowing their market share to decline. Do you agree with Dr. Sco�? If so, how would this impact your decision-making as a financial manager?

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

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8.2 The Weighted Average Cost of Capital

The cost of capital is a weighted average of the required returns for each capital source. In this sec�on, we will show you how to calculate the weighted average cost of capital and its components.

Calculating the Weighted Average Cost of Capital

For the Pogo harness project, the weighted average cost of capital (WACC) is the a�er-tax required returns (interest on bonds or other types of debt is tax deduc�ble; thus, it lowers the effec�ve cost of debt to the firm) on POL's bonds, preferred stock, and common equity, weighted by their propor�onal contribu�on to the project. As you can see in Table 8.3, of the $64,384 being raised, the bondholders contribute $18,028 (28%), the preferred stockholders contribute $5,022 (7.8%), and the common stockholders contribute the remaining $41,334 (64.2%) in residual cash flows.

Later we will explain how Paula es�mated the costs of debt, preferred stock, and common equity. First, though, we present her worksheet for compu�ng POL's cost of capital. Table 8.3 shows that she mul�plied the propor�on of each capital source by its a�er-tax required return. She then summed these results to arrive at the 12.5% cost of capital (or the project's required rate of return).

Table 8.3: Worksheet for compu�ng POL's cost of capital

Capital component A Targeted propor�on or weight

B Project cost

A × B Dollars raised

D A�er-tax required returns

A × D Weighted Average

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

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

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

Total 100% $64,384 12.5%

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

(8.1) WACC = (Wd)(a�er-tax cost of debt) + (Wpfd)(cost of preferred stock) + (We)(cost of common equity)

where

Wd = the desired propor�on of financing provided by debt

Wpfd = the desired propor�on of financing provided by preferred stock

We = the desired propor�on of financing provided by common equity

This formula is adaptable to any combina�on of financing sources. For example, if preferred stock were not used, then Wpfd = 0, and preferred stock would drop out of the

formula. Some companies borrow from many sources, and they may have several bond issues and perhaps long-term loans from banks or insurance companies. The only source of capital that is common to all companies is common equity. The WACC formula for a company with no preferred stock, but with two types of debt, might look like this:

(8.2) WACC = (WB)(a�er-tax cost of bonds) + (WL)(a�er-tax cost of loan) + (We)(cost of equity)

No ma�er how many sources of capital there are, the weights always sum to 1 (WB + WL + We = 1). This ensures that all capital sources have been included in the

calcula�on of WACC.

Discoun�ng expected cash flows by the weighted average cost of capital gives Paula the informa�on she needs to make her investment decision on the Pogo harness project. If the NPV = 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 be�er than that, meaning that it should add value because its NPV is $9,110.

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

We may rewrite the NPV and IRR equa�ons from Chapter 6 to include WACC.

Recall Equa�on (6.1), the NPV equa�on, from Chapter 6:

where Processing math: 0%

II = ini�al investment

OCFt = opera�ng cash flows in year t

TCF = terminal cash flows

t = year

n = life span of the project (in years)

r = required rate of return

Rewri�en to include WACC, the NPV equa�on becomes

where

CFt = total net cash flow for period t

The company should accept projects with NPV > 0.

Rewri�en to accommodate WACC, the IRR equa�on becomes

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

Next, we explain how Paula es�mated the cost of each capital component.

The Cost of Debt

The cost of debt, or Kd, is the current yield to maturity on the company's bonds or other long-term debt securi�es.

Cost of debt = Yield to maturity

or

Kd = YTM

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

Let's assume the current market price of POL's bonds is $1,003. The bonds mature in 6 years, bear a 9.5% coupon rate, make coupon payments semiannually, and their par value is $1,000. Given this informa�on, Kd is found by solving for YTM in the following equa�on, which sets the price of the bonds equal to the present value of future cash

flows. We may think of the YTM as the internal rate of return of a bond.

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

Because interest on debt is tax deduc�ble, the YTM must be adjusted for the tax effect. The tax deduc�on lowers the effec�ve cost of debt to the company. We adjust YTM for taxes by mul�plying YTM by (1 – t), where t is the firm's marginal tax rate. Subs�tu�ng Kd for YTM gives us Equa�on (8.6):

The Cost of Preferred Stock

As you recall from Chapter 4, 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 calcula�on. The cost of preferred stock, or Kpfd, equals its

required rate of return, which is its annual dividend divided by its current market price.

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

Again, let's assume the dividend on POL's preferred stock is $2.50 and its current market price is $21.50 per share. As Equa�on (8.7) shows, the required return on the stock is 11.63%.

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

The Cost of Common Equity, Ke

The cost of common equity, or Ke, is the most difficult of the component costs to es�mate. Chapter 7 presented the capital asset pricing model (CAPM) as one means of

es�ma�ng investors' required return for risky assets. Although this risk-return model is the most frequently used method for es�ma�ng returns to common stock, other models may also be used, most notably the discounted cash flow model introduced in Chapter 4. As a general rule, the analyst should approach the problem of es�ma�ngProcessing math: 0%

Websites like Yahoo! are useful for obtaining beta informa�on. What benefit is there to obtaining the informa�on this way versus calcula�ng it yourself?

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common stock returns from several direc�ons and hope to generate a consensus es�mate from these varying approaches. Here, we will cover three approaches: CAPM, the discounted cash flow model, and the equity-debt risk premium.

The CAPM Approach to Ke

Chapter 7 built on por�olio theory to show the rela�onship between required returns on investments and their market risk. The CAPM states that the required return on a risky investment equals the risk-free rate plus the product of the asset's beta and the market risk premium.

Required return on risky investment = Risk-free rate + Asset's beta (Market risk premium)

Represented as an equa�on, the CAPM is

where

R(r)i = required return for asset i

Rf = risk-free rate of return

βi = beta of asset i

Now, let's look at the individual components of the equa�on to find the informa�on needed to solve the CAPM.

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

Next, we need an es�mate of the equity beta. Brokerage and other investment service firms es�mate betas for many publicly traded stocks. Betas may be obtained on the Web and in print from Value Line, Standard & Poor's, Yahoo!, and Bloomberg. As we saw in Chapter 7, we may also es�mate beta ourselves using data on past returns.

In place of market risk premium, we use the historical market risk premium. This is found by calcula�ng the average amount by which the market return has exceeded T-bond returns. For example, the difference between the S&P 500 return and the T-bond return for years 1931 through 2011 could be averaged and used as the historical market risk premium. In that 80-year period, the market risk premium has averaged about 7.6% per year (Damodaran, 2011). There are many other es�mates of the markets risk premium (or equity risk premium). For more informa�on, please see the Web Resources sec�on at the end of the chapter.

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

Table 8.4: POL's cost of equity es�mates using the CAPM

CAPM component Value

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

BetaPOL (from POL's investment banker) βPOL = 1.2

Market risk premium (historical equity market risk premium) 7.6%

If we plug these numbers into Equa�on (8.8), Paula's CAPM es�mate is

R(r)POL = rf + βPOL[market risk premium]

= 5% + 1.2(7.6%)

= 14.12%

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

The Discounted Cash Flow Approach to Ke

In Chapter 4, the constant dividend growth model for valuing common stock was introduced. To find the cost of equity, we use a form of that constant growth formula.

where

P0 = today's price of the stock

Ke = the required return on equity, also known as the cost of equityProcessing math: 0%

gn = the normal, constant growth rate of dividends

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

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

This equa�on may also be adapted to allow us to solve for Ke:

The dividend growth model for es�ma�ng the required return on common stock reflects the discounted cash flow approach to valua�on, as do the YTM for debt and the preferred stock perpetuity model.

This approach requires a current market price, an es�mate of next year's dividend per share, and an es�mate 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 ac�vely 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 applica�on of the future value of a single cash flow formula, as given in Chapter 3.

FVn = PV0 (1 + r) n

where

FVn = the future value at the end of n �me periods

PV0 = the present value of the cash flow

r = the periodic interest rate

The difference is that rather than looking forward, we are looking back. To use the model, we must change the defini�on of its components. FVn becomes the most recent

dividend, D0. PV0 becomes the beginning historical dividend, D–n ("–n" refers to n periods in the past). Finally, the rate of return, r, becomes the compound growth rate, gn.

Equa�on (8.11) shows us what the new formula looks like:

where

D0 = the most recent dividend

D–n = the beginning historical dividend

gn = the compound growth rate

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

was $0.84. Now, let's solve for gn.

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

Having es�mated Ke using the constant growth formula, we must remember that this formula assumes a constant growth rate into perpetuity. Therefore, this method may

not be appropriate for firms whose growth is unstable or unsustainable. Cyclical firms, such as lumber companies, o�en have earnings that fluctuate drama�cally with the business cycle. Excep�onally high ini�al growth rates of start-up companies will eventually fall to more sustainable levels as the industry matures. For these types of firms, the constant growth assump�on is quite difficult to apply. In prac�ce, 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 es�ma�ng 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.

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

equity-debt risk premium approach yields the following range for Ke.

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

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

12.4% < Ke < 15.4%Processing math: 0%

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

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Recall that Paula's es�mates of Ke using the CAPM were 14.12%, and her discounted cash flow method produced a 15% cost of equity. Those es�mates are within the range

prescribed by the equity-debt risk premium, which more or less confirms Paula's es�mates. Weighing the results of the three approaches to es�ma�ng Ke, Paula elected 15%

as POL's cost of equity. As with preferred stock, no tax adjustment is necessary because dividends are not a tax-deductable expense.

The Cost of Selling Securities

The cost of capital reflects returns required by investors who are supplying capital to the firm. These returns reflect the amount the investors paid for their respec�ve securi�es. However, when a company raises funds by selling securi�es, it usually employs a company to assist it in marke�ng its securi�es. Companies that specialize in selling new securi�es issues, called investment banks, take a cut for marke�ng and underwri�ng the issue. A securi�es issue is underwri�en when the investment bank buys securi�es 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 underwri�ng spread. Of course, the sale price must approximate the security's market value. For example, let's assume that POL is selling bonds to pay for the harness project. Investors will buy the bonds for their current market price, $1,003. However, the underwri�ng spread reduces POL's proceeds from the bond sale and raises POL's effec�ve cost of debt above the 9.44% YTM.

Costs associated with selling securi�es are called flota�on costs. Aside from the underwri�ng spread, flota�on costs include fees paid to the investment banker for consulta�on, document prepara�on, and so on. They also include costs of filing with regulators such as the Securi�es and Exchange Commission, as well as legal and accoun�ng fees. Here is a list of common features of flota�on costs:

They make up a greater percentage of the value of the securi�es issues for equity than those for debt, reflec�ng the increased risk of underwri�ng stocks. They are propor�onally greater for issues of small dollar value. There are significant scale economies to securi�es issues. Some fees and other costs are rela�vely fixed.

With the high cost of issuing securi�es for smaller companies, it would seem that small firms might have a tough �me 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 dissemina�on of technology, and the deregula�on of financial services, of transporta�on, and of telecommunica�ons have bolstered entrepreneurial ac�vity in the United States, crea�ng new investment opportuni�es. As evidence, venture capital firms have sprung up by the hundreds to supply early financing to promising companies. One such company was Facebook, which went public in May of 2012. Unfortunately, the IPO was something of a flop for investors, though the investment bankers reportedly made over $170 million of fees plus possibly another $100 million trading the shares the first weeks a�er the IPO (venturebeat.com, 2012)!

Flota�on costs siphon money from the securi�es issue, raising the effec�ve 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 flota�on costs. Net proceeds to the company equal the sale price to the investors minus flota�on costs.

Net proceeds to company = Sale price – Flota�on costs

or

Virtually all financing with bonds and preferred stock represents new issues and therefore includes flota�on costs. Common equity financing may be done through stock sales, but more o�en it comes from retained earnings, which carry no flota�on costs. In the case of POL, the company is selling bonds and preferred stock to finance the harness project. Common equity financing comes from retained earnings. POL's investment banker es�mates that flota�on 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 flota�on costs. Let's look at each of these in turn.

Adjus�ng cost of POL's debt (bonds) to reflect flota�on costs:

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

Now we have calculated four numbers masquerading as the cost of debt for POL. Table 8.5 shows costs before and a�er the tax adjustment, and with and without flota�on costs.

Table 8.5: POL's cost of debt es�mates before and a�er flota�on costs

Floata�on costs Before tax A�er tax

Excluded 9.44% 6.61%

Included 9.88% 6.93%

As Table 8.5 shows, the actual YTM of the bonds is 9.44%, but a�er adjus�ng for taxes and flota�on, the cost of debt to POL is 6.93%. The tax savings reduces the cost of debt, but flota�on costs take back some of that savings. Now, let's look at preferred stock.

Adjus�ng cost of POL's preferred stock to reflect flota�on costs:

Because there are no flota�on costs associated with retained earnings, POL's cost of common equity remains at 15%. Processing math: 0%

Kre tearn = 15%

For the record, the following equa�on shows how flota�on costs would affect the cost of a new stock issue. The effect of flota�on 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 flota�on costs, which raises the cost of equity to the company.

where

Pnet = P – (flota�on costs)

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

The Financing Mix and Weights in the WACC

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

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

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

Paula determined the current financing mix by es�ma�ng the market values for each of POL's capital sources. First, she obtained the current prices for the company's bonds, preferred stock, and common stock. Next, she mul�plied these prices by the number of bonds or shares of stock outstanding to compute the market value of each component. Summing these market values gave her the total market value of POL's capital. These calcula�ons are shown in Table 8.6.

Table 8.6: Calcula�ng market weigh�ngs of each capital source

Capital component Price/unit Number outstanding Total market value of component

Propor�on

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

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

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

Total $5,504,077 100%

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

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

Glancing at Equa�on (8.16), you may wonder why Paula doesn't finance the en�re project with debt and discount it at the a�er tax cost of debt. The a�er-tax cost of debt is only (9.9%) (1 – 0.30) = 6.93%. Discoun�ng 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 consistently evaluated. This illustrates why it is important to discount all projects at the cost of capital and not at the cost of debt one �me and the cost of equity the next �me, regardless of how a par�cular project is financed. We separate the investment decision from the financing decision; that is, we evaluate investment decisions like the Pogo harness project using the long-term mix of debt and equity that we expect over the project's life, not the specific type of securi�es (debt, preferred stock, or common stock) that were most recently issued.

WACC reflects the firm's long-term capital mix. A firm that finances a project with either debt or equity will temporarily unbalance its capital structure and, we can assume, will a�empt to rebalance it the next �me around. Firms o�en unbalance their capital structure temporarily to take advantage of scale economies of large securi�es issues. In reality, POL would never fund such a small project by selling both preferred stock and bonds because flota�on costs would be prohibi�ve. This project would probably be funded en�rely from retained earnings, meaning that POL would temporarily unbalance its capital structure.

Field Trip: Cost of Capital Data

Ibbotson provides financial data for commercial and academic use.

Visit the Ibbotson Cost of Capital Resources Center: h�p://corporate.morningstar.com/ib/asp/subject.aspx?xmlfile=5532.xml (h�p://corporate.morningstar.com/ib/asp/subject.aspx?xmlfile=5532.xml)Processing math: 0%

and the Ibbotson Cost of Capital Yearbook: h�p://corporate.morningstar.com/ib/asp/subject.aspx?xmlfile=1420.xml (h�p://corporate.morningstar.com/ib/asp/subject.aspx?xmlfile=1420.xml)

Reflec�on Ques�ons

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

Processing math: 0%

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

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8.3 Estimating the Discount Rate for Individual Projects

For many projects, the appropriate discount rate to use in the NPV calcula�on is the firm's WACC, as outlined in the previous sec�on. However, there are circumstances in which WACC is not the appropriate discount rate. Every company is risky, and this risk is reflected in its WACC. Investors in a par�cularly risky company demand higher returns on their securi�es, which increases the company's WACC. In project analysis, we are actually interested in the risk of the par�cular 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 iden�cal. 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 inves�ng in high-risk projects, investors expect a higher return; therefore, these risky projects should carry a higher discount rate.

In POL's case, Paula believes that the Pogo harness project has the same risk as the company's exis�ng business. Paula reasons that the harness is simply another product to add to POL's exis�ng line of hardware and sailing gear. Therefore, the business risk of the Pogo harness project is essen�ally iden�cal to that of the company's exis�ng products. Of course, she understands that there are uncertain�es in producing a new product, but no more than in the normal course of extending and upgrading an exis�ng line of products. Paula also realizes that the relevant risk for es�ma�ng required returns is the market-wide or nondiversifiable risks of the business (as discussed in Chapter 7). The new harness is probably about as sensi�ve to market-wide forces as are POL's current products. All are sensi�ve to economic recession (in which case sales of discre�onary products will decline), changing tastes, changes in tax codes, and so on.

Why a Project's Risk May Differ From the Company's Overall Risk

While the harness fits neatly into POL's exis�ng product line, there are many occasions when this is not the case. In such instances, we must es�mate a discount rate that reflects the project's risk. Here, we explain why differences in risk might arise and how discount rates for individual projects might be es�mated. Consider Campbell Soup. The company has a dominant posi�on 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 hypothe�cal projects. The first is a tomato soup with a spicy Mexican taste. The second proposal is to start a chain of small soup cafes—tenta�vely called "17 Flavors Soup Cafes." The cafes would feature 17 flavors (hence the name) of Campbell's soups ready for immediate serving.

Do these two proposals have the same risk? Let's consider them both individually. The spicy Mexican soup is a standard Campbell's product. Campbell Soup has enormous experience evalua�ng, producing, marke�ng, and distribu�ng such products. By contrast, a chain of fast-food restaurants differs markedly from any of Campbell's other businesses. The fast-food industry is very compe��ve, with several dominant chains vying for market share. Campbell's managers have li�le experience in this industry. Also, the two projects will probably respond differently to economy-wide risk factors. For example, in a recession individuals tend to eat out less but may consume more canned soup at home.

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

Estimating a Risk-Adjusted Discount Rate for NPV Analysis

Chapter 7 introduced the capital asset pricing model and the idea that the capital markets price only market risk. This follows from the no�on that unique risk is generally absent from well-diversified por�olios. Projects also contain mostly market risk; therefore, we may use the CAPM to determine a project's discount rate.

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

The project beta, commonly called an asset beta, is not the same as the common stock beta. As introduced in Chapter 7, asset beta measures the project's market risk. Next, we discuss how to es�mate a beta that is appropriate for evalua�ng the Campbell Soup "17 Flavors Soup Cafes" ini�a�ve.

Estimating a Project's Beta

Recall from Chapter 7 that beta is a measure of the extent to which the returns on a stock move with changes in the returns of a market por�olio, such as the S&P 500. One widely used technique for es�ma�ng 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 es�mate the appropriate risk-adjusted discount rate (RADR) for the project.

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

Aside from iden�fying appropriate business lines for the pure-play firms, Campbell's managers must also consider their capital mix. We said that to use the pure-play company's beta directly, the pure-play's risk and financing must be close to that of the project. Financing is an issue because the equity betas of companies with the same business risk (same asset beta) will differ according to how much debt each company has. The more debt a company has, the higher the equity beta will be. The intui�on behind this result (more debt, higher beta, all else being equal) is that the risk of the assets is fixed, so as low-risk debt replaces equity in a company's financing mix that

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asset risk has to go somewhere. If the debt is safe because of priority payments and contractual obliga�ons, 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 iden�cal to its asset beta. If a pure-play can be found with no debt, the project's required return may be es�mated 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, and the beta for this company is 1.3. This beta may then be transferred to Campbell's cafe project, and a RADR could then be es�mated.

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

If the capital structure of the pure-play firm includes debt, we may es�mate the asset beta using the Hamada (1972) equa�on:

where

βequity = beta of the pure-play's common stock

t = the pure-play's tax rate

D/E = ra�o 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 βequity equal to 1.5, we can es�mate its asset beta as follows:

This beta could then be plugged into Equa�on (8.18) and used to es�mate the project's appropriate discount rate.

RADR = 4% + 1.11(9%) = 13.99% or 14%

Of course, for many projects a pure-play cannot be found. The methods for es�ma�ng the RADR under such circumstances range from ad hoc techniques (like adding or subtrac�ng a few percentage points to the firm's exis�ng WACC) to developing betas based on accoun�ng informa�on. Ad hoc es�mates require careful judgment on the part of the analyst. Should Campbell Soup, for example, add 2% to its current WACC to reflect the added risk of the cafes, or should it add 5%? Other new projects may be perceived as being less risky than exis�ng lines of business, so a few percentage points would be subtracted from the current WACC. The difficul�es encountered using this method are obvious, but at �mes there is no choice. Accoun�ng betas are found by measuring the co-movement of an accoun�ng-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 reflec�ng its risk. In prac�ce, large companies use divisional hurdle rates, so that, for example, projects in a home appliances division carry a different RADR than do projects in broadcas�ng division.

Use and Misuse of Risk-Adjusted Discount Rates

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

Cri�cal Thinking Ques�ons

1. Why do you think managers con�nue to use RADR, despite its flaws? 2. What kind of informa�on would you include in your defense of a high RADR?

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Ch. 8 Conclusion

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

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Ch. 8 Learning Resources

Key Ideas

The required return on an investment is the weighted average of the returns demanded by the company's investors. The basic discount rate for capital investments is the company's cost of capital. The weighted average cost of capital (WACC) is the weighted average of the required returns for each capital source. Weigh�ngs are the propor�onal contribu�ons from each capital source. Discoun�ng project cash flows by the WACC means that projects will be accepted only if they are expected to provide at least the required returns to all investors. The cost of debt is the yield to maturity (YTM) on the company's bonds or other long-term debt securi�es. The cost of preferred stock is its annual dividend divided by its current market price. The cost of common equity may be es�mated using the CAPM, a discounted cash flow (dividend growth) model, or an equity-debt risk premium. The difference between returns to equity and returns to debt is the equity-debt risk premium. Investment banks assist companies in marke�ng new securi�es offerings. When an investment bank buys securi�es from the issuing company and resells them to investors, it is underwri�ng the securi�es offering. The difference between the price paid to the company and sale price to investors is the underwri�ng spread. Venture capital firms supply high-risk capital to small firms prior to an ini�al public offering of stock. Capital structure is the mix of debt, preferred equity, and common equity. Short-term financing is excluded. When possible, the propor�ons of each component in the capital structure should be calculated using market rather than book weights. A project should be discounted at the WACC, rather than at the costs of individual capital components, regardless of how the project is financed. WACC is the appropriate discount rate for projects whose risk is about equal to the risk of the company as a whole. A pure-play is a publicly traded firm that engages primarily in the same line of business as the project being considered. The Hamada equa�on may be used to convert the equity beta of a pure-play firm into an asset beta. The risk-adjusted discount rate (RADR) applies to projects whose risk is substan�ally different from company risk.

Key Equa�ons

Cri�cal Thinking Ques�ons

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. Accoun�ng balance sheets reflect the book values of claims, based on the historical contribu�ons of capital suppliers. Suppose a firm raised its ini�al capital 10 years ago, and its accoun�ng 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 excep�onally 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 accoun�ng balance sheet?

3. Explain why (1 – 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 equity and half is external equity.

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

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

6. There are three methods of es�ma�ng the cost of corporate equity. Name or briefly describe these methods.

Key Terms

Click on each key term to see the defini�on.

SLIDE 1 OF 13

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asset beta (h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

Refers to the systema�c or market risk of an investment asset.

capital structure (h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

The mix of debt and preferred equity in a company's por�olio.

cost of capital (h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

The rate of return that must be earned in order to sa�sfy investors.

cost of common equity (h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

The investors' required return on common equity.

cost of debt (h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

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 (h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

The investors' required return on preferred stock.

equity-debt risk premium (h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

A representa�on of the difference between returns to equity and returns to debt.

flota�on costs (h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

The transac�on costs incurred when raising capital externally, for example, when selling newly issued stock or bonds.

investment bank (h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

A financial services company that specializes in selling new securi�es issues for client firms.

pure-play (h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

An ac�vely 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 es�mated.

risk-adjusted discount rate (RADR) (h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

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 exis�ng projects.

underwri�ng (h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

A method of selling securi�es in which the investment bank buys the securi�es from the client firm and resells them to investors.

underwri�ng spread (h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

The price at which the investment bank sells securi�es to the public minus the price paid to the client firm.

venture capital firms (h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

Businesses and individuals that finance high-risk start-up ventures, usually before an ini�al public offering of stock.

weighted average cost of capital (WACC) (h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

The discount rate that may be found by incorpora�ng the required returns (costs) for each capital source used to finance the firm.

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For more informa�on on other es�mates of the market's risk premium (or equity risk premium), read Pablo Fernandez's paper "Equity Premium: Historical, Expected, Required and Implied." Available at SSRN: h�p://ssrn.com/abstract=933070 (h�p://ssrn.com/abstract=933070) .

A very simple cost-of-capital calculator is available at the following website. To test your skill, you could make up a simple set of assump�ons and see if you and the online calculator get the same answer for the WACC. h�p://www.wacccalculator.com/ (h�p://www.wacccalculator.com/)

Morningstar is a well-known financial informa�on provider that produces cost-of-capital es�mates that are published in an annual yearbook. These yearbooks are costly; nevertheless, it is instruc�ve to peruse their website to see the scope of issues and informa�on that surrounds es�ma�ng the cost of capital. h�p://corporate.morningstar.com/ib/asp/subject.aspx?xmlfile=5532.xml (h�p://corporate.morningstar.com/US/asp/home2.aspx?xmlfile=7083.xml)

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