Case study
11
Cost of Capital
LEARNING OBJECTIVES
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LO 11-1 |
The cost of capital represents the weighted average cost of the source of financing to the firm. |
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LO 11-2 |
The cost of capital is normally the discount rate to use in analyzing an investment. |
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LO 11-3 |
The cost of capital is based on the valuation techniques from the previous chapter and is applied to bonds, preferred stock, and common stock. |
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LO 11-4 |
A firm attempts to find a minimum cost of capital through varying the mix of its sources of financing. |
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LO 11-5 |
The cost of capital may eventually increase as larger amounts of financing are utilized. |
Throughout the previous two chapters, a number of references were made to discounting future cash flows in solving for the present value. How do you determine the appropriate interest rate or discount rate in a real situation? Suppose that a young doctor is rendered incapable of practicing medicine due to an auto accident in the last year of his residency. The court determines that he could have made $100,000 a year for the next 30 years. What is the present value of these inflows? We must know the appropriate discount rate. If 10 percent is used, the value is $942,700; with 5 percent, the answer is $1,537,300—over half a million dollars is at stake.
In the corporate finance setting, the more likely circumstance is that an investment will be made today—promising a set of inflows in the future—and we need to know the appropriate discount rate. This chapter describes the methods and procedures for making such a determination.
First, you should observe that if we invest money today to receive benefits in the future, we must be absolutely certain we are earning at least as much as it costs us to acquire the funds for investment—that, in essence, is the minimum acceptable return. If funds cost the firm 10 percent, then all projects must be tested to make sure they earn at least 10 percent. By using this as the discount rate, we can ascertain whether we have earned the financial cost of doing business.
The Overall Concept
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How does the firm determine the cost of its funds or, more properly stated, the cost of capital? Suppose the plant superintendent wishes to borrow money at 6 percent to purchase a conveyor system, while a division manager suggests stock be sold at an effective cost of 12 percent to develop a new product. Not only would it be foolish for each investment to be judged against the specific means of financing used to implement it, but this would also make investment selection decisions inconsistent. For example, imagine financing a conveyor system having an 8 percent return with 6 percent debt and also evaluating a new product having an 11 percent return but financed with 12 percent common stock. If projects and financing are matched in this way, the project with the lower return would be accepted and the project with the higher return would be rejected. In reality, if stock and debt are sold in equal proportions, the average cost of financing would be 9 percent (one-half debt at 6 percent and one-half stock at 12 percent). With a 9 percent average cost of financing, we would now reject the 8 percent conveyor system and accept the 11 percent new product. This would be a rational and consistent decision. Though an investment financed by low-cost debt might appear acceptable at first glance, the use of debt might increase the overall risk of the firm and eventually make all forms of financing more expensive. Each project must be measured against the overall cost of funds to the firm. We now consider cost of capital in a broader context.
We can best understand how to determine the cost of capital by examining the capital structure of a hypothetical firm, the Baker Corporation, in Table 11-1 . Note that the aftertax costs of the individual sources of financing are shown, then weights are assigned to each, and finally a weighted average cost is determined. (The costs under consideration are those related to new funds that can be used for future financing, rather than historical costs.) In the remainder of the chapter, each of these procedural steps is examined.
Table 11-1 Cost of capital—Baker Corporation
Each element in the capital structure has an explicit, or opportunity, cost associated with it, herein referred to by the symbol K. These costs are directly related to the valuation concepts developed in the previous chapter. If we understand how a security is valued, then there is little problem in determining its cost. The mathematics involved in the cost of capital are not difficult. We begin our analysis with a consideration of the cost of debt.
Cost of Debt
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The cost of debt is measured by the interest rate at which a company can raise new capital. For companies that do not issue bonds but simply borrow from a bank, this rate will be the rate at which they can borrow from the bank. The more interesting case arises when the cost of debt is measured by the interest rate, or yield, paid to bondholders. The simplest case would be a $1,000 bond paying $100 annual interest, thus providing a 10 percent yield. The computation may be more difficult if the bond is priced at a discount or premium from par value. Techniques for computing such bond yields were presented in Chapter 10 .
Assume the firm is preparing to issue new debt. To determine the likely cost of the new debt in the marketplace, the firm will compute the yield on its currently outstanding debt. This is not the rate at which the old debt was issued, but the rate that investors are demanding today. Assume the debt issue pays $100 per year in interest, has a 15-year life (at which time the principal amount of $1,000 will be paid), and is currently selling for $939. The yield to maturity is the interest rate that the market uses to price the bond. In Table 10-3 , we saw how the yield to maturity can be obtained using Excel’s Goal Seek function or Excel’s RATE function. Using the RATE function, as shown in Table 11-2 , we find that the yield to maturity for this bond is 10.84 percent. Calculator keystrokes shown in the margin produce the same result.
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FINANCIAL CALCULATOR |
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Bond YTM |
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Value |
Function |
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15 |
N |
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−939 |
PV |
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100 |
PMT |
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1000 |
FV |
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Function |
Solution |
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CPT |
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I/Y |
10.84 |
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Table 11-2 Yield to maturity
In many cases, you will not have to compute the yield to maturity. It will simply be given to you. The practicing corporate financial manager also can normally consult a source such as S&P Capital IQ Net Advantage to determine the yield to maturity on the firm’s outstanding debt. An excerpt from this bond guide is presented in Table 11-3 . If the firm involved is Keyspan Corp., for example, the financial manager could observe that debt maturing in 2030 would have a yield to maturity of 4.99 percent as highlighted in Table 11-3 .
Once the bond yield is determined through the formula, a calculator, or the tables (or is given to you), you must adjust the yield for tax considerations. Yield to maturity indicates how much the corporation has to pay on a before-tax basis. But keep in mind the interest payment on debt is a tax-deductible expense. Since interest is tax-deductible, its true cost is less than its stated cost because the government is picking up part of the tab by allowing the firm to pay less tax. The aftertax cost of debt is actually the yield to maturity times 1 minus the tax rate. 1 This is presented as Formula 11-1 .
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Table 11-3 Excerpt from S&P Capital IQ Net Advantage
The term Y (yield) in the formula is interchangeable with yield to maturity. Earlier in this section, we determined that the existing yield on the debt was 10.84 percent. We shall assume new debt can be issued at the same going market rate, 2 and that the firm is paying a 35 percent tax (a nice, easy rate with which to work). Applying the tax adjustment factor, the aftertax cost of debt would be 7.05 percent.
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Kd (Cost of debt) |
= Y(1 − T) |
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= 10.84%(1 − 0.35) |
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= 10.84%(0.65) |
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= 7.05% |
Please refer back to Table 11-1 and observe in column (1) that the aftertax cost of debt is the 7.05 percent that we have just computed.
Cost of Preferred Stock
The cost of preferred stock is similar to the cost of debt in that a constant annual payment is made, but dissimilar in that there is no maturity date on which a principal payment must be made. Determining the yield on preferred stock is simpler than determining the yield on debt. All you have to do is divide the annual dividend by the current price (this process was discussed in Chapter 10 ). This represents the rate of return to preferred stockholders as well as the annual cost to the corporation for the preferred stock issue.
We need to make one slight alteration to this process by dividing the dividend payment by the net price or proceeds received by the firm. Since a new share of preferred stock has a selling cost (flotation cost), the proceeds to the firm are equal to the selling price in the market minus the flotation cost. The cost of preferred stock is presented as Formula 11-2 . 3
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where
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Kp = |
Cost of preferred stock |
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Dp = |
The annual dividend on preferred stock |
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Pp = |
The price of preferred stock |
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F = |
Flotation, or selling cost |
In the case of the Baker Corporation, we shall assume the annual dividend is $10.50, the preferred stock price is $100, and the flotation, or selling cost, is $4. The effective cost is:
Because a preferred stock dividend is not a tax-deductible expense, there is no downward tax adjustment.
Please refer back to Table 11-1 and observe in column (1) that 10.94 percent is the value we used for the cost of preferred stock.
Cost of Common Equity
Determining the cost of common stock in the capital structure is a more involved task. The out-of-pocket cost is the cash dividend, but is it prudent to assume the percentage cost of common stock is simply the current year’s dividend divided by the market price?
If such an approach were followed, the common stock costs for selected U.S. corporations in February 2015 would be as follows: Target (2.7 percent), Microsoft (2.8 percent), Walmart (2.2 percent), and PepsiCo (2.6 percent). Ridiculous, you say! If new common stock costs were assumed to be so low, the firms would have no need to issue other securities and could profitably finance projects that earned only 2 or 3 percent. How then do we find the correct theoretical cost of common stock to the firm?
Valuation Approach
In determining the cost of common stock, the firm must be sensitive to the pricing and performance demands of current and future stockholders. An appropriate approach is to develop a model for valuing common stock and to extract from this model a formula for the required return on common stock.
In Chapter 10 , we discussed the constant growth dividend valuation model and said the current price of common stock could be stated to equal:
where
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P0 = |
Price of the stock today |
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D1 = |
Dividend at the end of the first year (or period) |
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Ke = |
Required rate of return |
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g = |
Constant growth rate in dividends |
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We then stated we could arrange the terms in the formula to solve for Ke instead of P0. This was presented in Formula 10-9. We present the formula once again and relabel it Formula 11-3 .
The required rate of return (Ke) is equal to the dividend at the end of the first year (D1), divided by the price of the stock today (P0), plus a constant growth rate (g). Although the growth rate basically applies to dividends, it is also assumed to apply to earnings and stock price over the long term.
If D1 = $2, P0 = $40, and g = 7%, we would say Ke equals 12 percent.
This means stockholders expect to receive a 5 percent dividend yield on the stock price plus a 7 percent growth in their investment, making a total return of 12 percent.
Required Return on Common Stock Using the Capital Asset Pricing Model
The required return on common stock can also be calculated by an alternate approach called the capital asset pricing model. This topic is covered in Appendix 11A , so only brief mention will be made at this point. Some accept the capital asset pricing model as an important approach to common stock valuation, while others suggest it is not a valid description of how the real world operates.
Under the capital asset pricing model (CAPM), the required return for common stock (or other investments) can be described by the following formula:
where
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Kj = |
Required return on common stock |
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Rf = |
Risk-free rate of return; usually the current rate on Treasury bill securities |
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β = |
Beta coefficient. The beta measures the historical volatility of an individual stock’s return relative to a stock market index. A beta greater than 1 indicates greater volatility (price movements) than the market, while the reverse would be true for a beta less than 1. |
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Km = |
Return expected in the market as measured by an appropriate index |
For the Baker Corporation example, we might assume the following values:
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Rf = |
5.5% |
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Km = |
12% |
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β = |
1.0 |
Kj, based on Formula 11-4 , would then equal:
Kj = 5.5% + 1.0(12% − 5.5%) = 5.5% + 1.0(6.5%)
= 5.5% + 6.5% = 12%
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In this calculation, we have assumed that Kj (the required return under the capital asset pricing model) would equal Ke (the required return under the dividend valuation model). They are both computed to equal 12 percent. Under this equilibrium circumstance, the dividend valuation model and the capital asset pricing model would produce the same answer.
For now we shall use the dividend valuation model exclusively; that is, we shall use Ke = (D1/P0) + g in preference to Kj = Rf + β(Km − Rf).
Those who wish to study the capital asset pricing model further are referred to Appendix 11A . This appendix is optional and not required for further reading in the text.
Cost of Retained Earnings
Up to this point, we have discussed the cost (required return) of common stock in a general sense. We have not really specified who is supplying the funds. One obvious supplier of common stock equity capital is the purchaser of new shares of common stock. But this is not the only source. For many corporations the most important source of ownership or equity capital is in the form of retained earnings, an internal source of funds.
Accumulated retained earnings represent the past and present earnings of the firm minus previously distributed dividends. Retained earnings, by law, belong to the current stockholders. They can be either paid out to the current stockholders in the form of dividends or reinvested in the firm. As current funds are retained in the firm for reinvestment, they represent a source of equity capital that is being supplied by the current stockholders. However, they should not be considered free. An opportunity cost is involved. As previously indicated, the funds could be paid out to the current stockholders in the form of dividends, and then redeployed by the stockholders in other stocks, bonds, real estate, and so on. What is the expected rate of return on these alternative investments? That is, what is the opportunity cost? We assume stockholders could at least earn an equivalent return to that provided by their present investment in the firm (on an equal risk basis). This represents D1/P0 + g. In the security markets, there are thousands of investments from which to choose, so it is not implausible to assume the stockholder could take dividend payments and reinvest them for a comparable yield.
Thus when we compute the cost of retained earnings, this takes us back to the point at which we began our discussion of the cost of common stock. The cost of retained earnings is equivalent to the rate of return on the firm’s common stock. 4 This is the opportunity cost. Thus we say the cost of common equity in the form of retained earnings is equal to the required rate of return on the firm’s stock as follows:
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Thus Ke not only represents the required return on common stock as previously defined, but it also represents the cost of equity in the form of retained earnings. It is a symbol that has double significance.
For ease of reference, the terms in Formula 11-5 are reproduced in the box that follows. They are based on prior values presented in this section on the cost of common equity.
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Ke = |
Cost of common equity in the form of retained earnings |
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D1 = |
Dividend at the end of the first year, $2 |
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P0 = |
Price of the stock today, $40 |
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g = |
Constant growth rate in dividends, 7% |
We arrive at the value of 12%.
The cost of common equity in the form of retained earnings is equal to 12 percent. Please refer back to Table 11-1 and observe in column (1) that 12 percent is the value we have used for common equity.
Cost of New Common Stock
Let’s now consider the other source of equity capital, new common stock. If we are issuing new common stock, we must earn a slightly higher return than Ke, which represents the required rate of return of present stockholders. The higher return is needed to cover the distribution costs of the new securities. Assume the required return for present stockholders is 12 percent and shares are quoted to the public at $40. A new distribution of securities must earn slightly more than 12 percent to compensate the corporation for not receiving the full $40 because of sales commissions and other expenses. The formula for Ke is restated as Kn (the cost of new common stock) to reflect this requirement.
The only new term is F (flotation, or selling costs).
Assume the following:
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D1 = |
$2 |
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P0 = |
$40 |
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F = |
$4 |
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g = |
7% |
then
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The cost of new common stock to the Baker Corporation is 12.6 percent. This value will be used more extensively later in the chapter. New common stock is not assumed to be in the original capital structure for the Baker Corporation presented in Table 11-1 .
Overview of Common Stock Costs
For our purposes, there are only two common stock formulas that you will be using in the rest of the chapter and in the problems at the end of the chapter.
The primary emphasis will be on Ke for now, but later in the chapter we will also use Kn when we discuss the marginal cost of capital.
Optimum Capital Structure—Weighting Costs
Having established the techniques for computing the cost of the various elements in the capital structure, we must now discuss methods of assigning weights to these costs. We will attempt to weight capital components in accordance with our desire to achieve a minimum overall cost of capital. This represents an optimum capital structure. For the purpose of this discussion, Table 11-1 (Cost of capital for the Baker Corporation) is reproduced.
How does the firm decide on the appropriate weights for debt, preferred stock, and common stock financing? Though debt is the cheapest form of financing, it should be used only within reasonable limits. In the Baker Corporation example, debt carried an aftertax cost of 7.05 percent, while other sources of financing cost at least 10.94 percent. Why not use more debt? The answer is that the use of debt beyond a reasonable point may greatly increase the firm’s financial risk and thereby drive up the costs of all sources of financing.
Assume you are going to start your own company and are considering three different capital structures. For ease of presentation, only debt and equity (common stock) are being considered. The costs of the components in the capital structure change each time we vary the debt-assets mix (weights).
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The firm is able to initially reduce the weighted average cost of capital with debt financing, but beyond Plan B the continued use of debt becomes unattractive and greatly increases the costs of the sources of financing. Traditional financial theory maintains that there is a U-shaped cost-of-capital curve relative to debt utilization by the firm, as illustrated in Figure 11-1 . In this example, the optimum capital structure occurs at a 40 percent debt-to-assets ratio.
Figure 11-1 Cost of capital curve
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Most firms are able to use 30 to 50 percent debt in their capital structure without exceeding norms acceptable to creditors and investors. Distinctions should be made, however, between firms that carry high or low business risks. As discussed in Chapter 5 , “Operating and Financial Leverage,” a growth firm in a reasonably stable industry can afford to absorb more debt than its counterparts in cyclical industries. Examples of debt use by companies in various industries are presented in Table 11-4 . 5
Table 11-4 2015 long-term debt as a percentage of debt + equity (MV)
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Selected Companies with Industry Designations |
Percent |
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Microsoft (computers) |
9% |
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Intel (semiconductors) |
11 |
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Home Depot (home repair products) |
11 |
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Merck & Co. (pharmaceuticals) |
16 |
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PepsiCo (soft drinks and snacks) |
19 |
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ExxonMobil (integrated oil) |
22 |
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Hyatt Hotels (lodging) |
22 |
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Pfizer (pharmaceuticals) |
25 |
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Delta Air Lines (air travel) |
42 |
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Gannett (newspapers and publishing) |
43 |
In determining the appropriate capital mix, the firm generally begins with its present capital structure and ascertains whether its current position is optimal. 6 If not, subsequent financing should carry the firm toward a mix that is deemed more desirable. Only the costs of new or incremental financing should be considered.
Capital Acquisition and Investment Decision Making
So far the various costs of financial capital and the optimum capital structure have been discussed. Financial capital, as you may have figured out, consists of bonds, preferred stock, and common equity. These forms of financial capital appear on the corporate balance sheet under liabilities and equity. The money raised by selling these securities and retaining earnings is invested in the real capital of the firm, the long-term productive assets of plant and equipment.
Long-term funds are usually invested in long-term assets, with several asset-financing mixes possible over the business cycle. Obviously a firm wants to provide all of the necessary financing at the lowest possible cost. This means selling common stock when prices are relatively high to minimize the cost of equity. The financial manager also wants to sell debt at low interest rates. Since there is short-term and long-term debt, the manager needs to know how interest rates move over the business cycle and when to use short-term versus long-term debt.
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A firm has to find a balance between debt and equity to achieve its minimum cost of capital. Although we discussed minimizing the overall cost of capital (Ka) at a single debt-to-equity ratio, in reality a firm operates within a relevant range of debt to equity before it becomes penalized with a higher overall cost because of increased risk.
Figure 11-2 shows a theoretical cost-of-capital curve at three different points. As we move from time period t to time period t + 2, falling interest rates and rising stock prices cause a downward shift in Ka. This graph illuminates two basic points: (1) The firm wants to keep its debt-to-assets ratio between x and y along the bottom axis at all times because this is the lowest area on each of the three curves; and (2) the firm would like to finance its long-term needs at time period t + 2 rather than the other two time periods because overall costs are lowest during this time frame.
Figure 11-2 Cost of capital over time
Corporations are allowed some leeway in the money and capital markets, and it is not uncommon for the debt-to-equity ratio to fluctuate between x and y over a business cycle. The firm that is at point y has lost the flexibility of increasing its debt-to-assets ratio without incurring the penalty of higher capital costs.
Cost of Capital in the Capital Budgeting Decision
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The current cost of capital for each source of funds is important when making a capital budgeting decision. Historical costs for past fundings may have very little to do with current costs against which present returns must be measured. When raising new financial capital, a company will tap the various sources of financing over a reasonable time. Regardless of the particular source of funds the company is using for the purchase of an asset, the required rate of return, or discount rate, will be the weighted average cost of capital. As long as the company earns its cost of capital, the common stock value of the firm will be maintained or will increase, since stockholder expectations are being met. For example, assume the Baker Corporation was considering making an investment in eight projects with the returns and costs shown in Table 11-5 .
Table 11-5 Investment projects available to the Baker Corporation
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Projects |
Expected Returns |
Cost ($ millions) |
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A |
16.00% |
$10 |
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B |
14.00 |
5 |
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C |
13.50 |
4 |
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D |
11.80 |
20 |
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E |
10.65 |
11 |
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F |
9.50 |
20 |
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G |
8.60 |
15 |
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H |
7.00 |
10 |
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$95 million |
These projects in Table 11-5 could be viewed graphically and merged with the weighted average cost of capital to make a capital budgeting decision, as indicated in Figure 11-3 .
Figure 11-3 Cost of capital and investment projects for the Baker Corporation
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Notice in Figure 11-3 that the Baker Corporation is considering $95 million in potential projects, but given the weighted average cost of capital of 10.41 percent, it will choose only projects A through E, or $50 million in new investments. Selecting assets F, G, and H would probably reduce the market value of the common stock because these projects do not provide a return equal to the overall costs of raising funds. The use of the weighted average cost of capital assumes the Baker Corporation is in its optimum capital structure range.
The Marginal Cost of Capital
Nothing guarantees the Baker Corporation that its cost of capital will stay constant for as much money as it wants to raise even if a given capital structure is maintained. If a large amount of financing is desired, the market may demand a higher cost of capital for each amount of funds desired. The point is analogous to the fact that you may be able to go to your relatives and best friends and raise funds for an investment at 10 percent. After you have exhausted the lending or investing power of those closest to you, you will have to look to other sources and the marginal cost of your capital will go up.
As a background for this discussion, the cost of capital table for the Baker Corporation is reproduced again as follows:
We need to review the nature of the firm’s capital structure to explain the concept of marginal cost of capital as it applies to the firm. Note the firm has 60 percent of the capital structure in the form of equity capital. The equity (ownership) capital is represented by retained earnings. It is assumed that 60 percent is the amount of equity capital the firm must maintain to keep a balance between fixed income securities and ownership interest. But equity capital in the form of retained earnings cannot grow indefinitely as the firm’s capital needs expand. Retained earnings are limited to the amount of past and present earnings that can be redeployed into the investment projects of the firm. Let’s assume the Baker Corporation has $23.40 million of retained earnings available for investment. Since retained earnings are to represent 60 percent of the capital structure, there are adequate retained earnings to support a capital structure of up to $39 million. More formally, we say:
(Where X represents the size of the capital structure that retained earnings will support.)
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Big Bonds Are “Liquid” Bonds Finance in ACTION Managerial
Corporate bond buyers have found that there can be safety in bigger bond deals amid a pullback in bond trading by big Wall Street banks. The Dodd–Frank law’s “Volcker Rule” bans U.S. banks from some proprietary trading. This ban makes it harder for the big banks to hold inventory for “making markets” in illiquid corporate bonds.
The difficulty in trading junk bonds has long been a factor in the high yield-to-maturity paid on these debt instruments. Certainly, junk bonds require high interest rates because they have credit risk, but they also often have liquidity risk. Credit risk is the risk that the bond’s issuer will go bankrupt before the bond matures. Liquidity risk is the risk that if a bondholder wants to sell the bond prior to maturity, no one else will be eager to buy it.
Researchers Amihud and Mendelson (1986) showed that the most illiquid stocks have yielded monthly returns that are over 0.5 percent higher than the most liquid stocks. That is over 6 percent per year! Similarly, buyers of illiquid bonds require a higher return than liquid bonds. Simply put, many investors don’t want to buy a bond if selling it later will be difficult.
The Wall Street Journal has reported that “investors are flocking to investment-grade bonds issued in amounts of $500 million or more, which are called benchmark deals. Bonds sold in big batches are performing better than smaller debt issued as part of smaller deals, data show. Some companies have taken note and are boosting offerings in order to pass the $500 million threshold.” * One such company is Ventas, a publicly traded real estate investment trust.
In August 2012, Ventas issued $275 million in senior debt due in August of 2022. Because of the low interest rate environment at the time, the yield on these 10-year bonds was only 3.25 percent. Then Ventas realized that issuing more of the same bonds might not cost them much more. In December 2012, Ventas issued another $225 million of the same bonds, taking the total to the $500 million benchmark. Ventas has acknowledged that it is “clearly wanting to create liquidity for our investors” by increasing the total size of its individual bond issuances.
* “For Bonds, Bigger Is Better,” The Wall Street Journal, February 12, 2012, p. C4.
After the first $39 million of capital is raised, retained earnings will no longer be available to provide the 60 percent equity position in the capital structure. Nevertheless, lenders and investors will still require that 60 percent of the capital structure be in the form of common equity (ownership) capital. Because of this, new common stock will replace retained earnings to provide the 60 percent common equity component for the firm. That is, after $39 million, common equity capital will be in the form of new common stock rather than retained earnings.
In the left portion of Table 11-6 on the next page, we see the original cost of capital that we have been discussing throughout the chapter. This applies up to $39 million. After $39 million, the concept of marginal cost of capital becomes important. The cost of capital then goes up as shown on the right portion of the table.
Kmc in the bottom right portion of the table represents the marginal cost of capital, and it is 10.77 percent after $39 million. The meaning of Kmc is basically the same as Ka; they both represent the cost of capital, but the mc subscript after K indicates the (marginal) cost of capital is going up.
The marginal cost of capital has increased after $39 million because common equity is now in the form of new common stock rather than retained earnings. The aftertax (A/T) cost of new common stock is slightly more expensive than retained earnings because of flotation costs (F). The equation for the cost of new common stock was shown earlier in the chapter as Formula 11-6 and now we are using it:
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Table 11-6 Costs of capital for different amounts of financing
The flotation cost (F) is $4 and the cost of new common stock is 12.60 percent. This is higher than the 12 percent cost of retained earnings that we have been using and causes the increase in the marginal cost of capital.
To carry the example a bit further, we will assume the cost of debt of 7.05 percent applies to the first $15 million of debt the firm raises. After that the aftertax cost of debt will rise to 8.60 percent. Since debt represents 30 percent of the capital structure for the Baker Corporation, the cheaper form of debt can be used to support the capital structure up to $50 million. We derive the $50 million by using Formula 11-8 .
(Here Z represents the size of the capital structure in which lower-cost debt can be utilized.)
After the first $50 million of capital is raised, lower-cost debt will no longer be available to provide 30 percent of the capital structure. After $50 million in total financing, the aftertax cost of debt will go up to the previously specified 8.60 percent. The marginal cost of capital for over $50 million in financing is shown in Table 11-7 .
The change in the cost of debt gives way to a new marginal cost of capital (Kmc) of 11.23 percent after $50 million of financing. You should observe that the capital structure with over $50 million of financing reflects not only the change in the cost of debt, but also the continued exclusive use of new common stock to represent common equity capital. This change occurred at $39 million, but must be carried on indefinitely as the capital structure expands.
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Table 11-7 Cost of capital for increasing amounts of financing
We could continue this process by next indicating a change in the cost of preferred stock, or by continually increasing the cost of debt or new common stock as more capital is used. For now it is sufficient that you merely observe the basic process. To summarize, we have said the Baker Corporation has a basic weighted average cost of capital of 10.41 percent. This value was developed throughout the chapter and was originally presented in Table 11-1 . However, as the firm began to substantially expand its capital structure, the weighted average cost of capital increased. This gave way to the term, marginal cost of capital. The first increase or break point was at $39 million in which the marginal cost of capital went up to 10.77 percent as a result of replacing retained earnings with new common stock. The second increase or break point was at $50 million in which the marginal cost of capital increased to 11.23 percent as a result of the utilization of more expensive debt. The changes are summarized in Figure 11-4 .
|
|
|
|
Amount of Financing |
Marginal Cost of Capital |
|
0–$39 million |
10.41% |
|
$39–50 million |
10.77 |
|
Over $50 million |
11.23 |
|
|
In previously presented Figure 11-3 , we showed returns from investments A through H. In Figure 11-4 , we reproduce the returns originally shown in Figure 11-3 but include the concept of marginal cost of capital. Observe the increasing cost of capital (dotted lines) in relationship to the decreasing returns (straight lines).
In Figure 11-3 , the Baker Corporation was justified in choosing projects A through E for a capital expenditure of $50 million. This is no longer the case in Figure 11-4 . Because of the increasing marginal cost of capital, the returns exceed the cost of capital only up to $39 million and now only projects A through D are acceptable.
Although the concept of marginal cost of capital is very important, for most of our capital budgeting decisions in the next chapter, we will assume we are operating on the initial flat part of the marginal cost of capital curve in Figure 11-4 , and most of our decisions can be made based on the initial weighted average cost of capital.
Page 358
Figure 11-4 Marginal cost of capital and Baker Corporation projects
SUMMARY
The cost of capital for the firm is determined by computing the costs of various sources of financing and weighting them in proportion to their representation in the capital structure. The cost of each component in the capital structure is closely associated with the valuation of that source, which we studied in the prior chapter. For debt and preferred stock, the cost is directly related to the current yield, with debt adjusted downward to reflect the tax-deductible nature of interest.
For common stock, the cost of retained earnings (Ke) is the current dividend yield on the security plus an anticipated rate of growth for the future. Minor adjustments are made to the formula to determine the cost of new common stock. A summary of Baker Corporation’s capital costs is presented in Table 11-8 .
We weight the elements in the capital structure in accordance with our desire to achieve a minimum overall cost. While debt is usually the “cheapest” form of financing, excessive debt use may increase the financial risk of the firm and drive up the costs of all sources of financing. The wise financial manager attempts to ascertain what debt component will result in the lowest overall cost of capital. Once this has been determined, the weighted average cost of capital is the discount rate we use in present-valuing future flows to ensure we are earning at least the cost of financing.
Page 359
Table 11-8 Cost of components in the capital structure
The marginal cost of capital is also introduced to explain what happens to a company’s cost of capital as it tries to finance a large amount of funds. First the company will use up retained earnings, and the cost of financing will rise as higher-cost new common stock is substituted for retained earnings in order to maintain the optimum capital structure with the appropriate debt-to-equity ratio. Larger amounts of financial capital can also cause the individual means of financing to rise by raising interest rates or by depressing the price of the stock because more is sold than the market wants to absorb.
REVIEW OF FORMULAS
1. Kd (cost of debt) = Y(1 − T) (11-1)
Y is yield
T is corporate tax rate
2.
Dp is the annual dividend on preferred stock
Pp is the price of preferred stock
F is flotation, or selling, cost
3.
D1 is dividend at the end of the first year (or period)
P0 is the price of the stock today
g is growth rate in dividends
4. Kj (required return on common stock) = Rf + β(Km − Rf) (11-4)
Rf is risk-free rate of return
β is beta coefficient
Km is return in the market as measured by the appropriate index
5.
D1 is dividend at the end of the first year (or period)
P0 is price of the stock today
g is growth rate in dividends
Page 360
6.
Same as above with:
F as flotation, or selling, cost
7.
8.
LIST OF TERMS
cost of capital 341
flotation cost 344
dividend valuation model 345
capital asset pricing model (CAPM) 346
common stock equity 347
optimum capital structure 349
weighted average cost of capital 350
financial capital 351
marginal cost of capital 354
DISCUSSION QUESTIONS
1. Why do we use the overall cost of capital for investment decisions even when only one source of capital will be used (e.g., debt)? (LO11-1)
2. How does the cost of a source of capital relate to the valuation concepts presented previously in Chapter 10 ? (LO11-3)
3. In computing the cost of capital, do we use the historical costs of existing debt and equity or the current costs as determined in the market? Why? (LO11-3)
4. Why is the cost of debt less than the cost of preferred stock if both securities are priced to yield 10 percent in the market? (LO11-3)
5. What are the two sources of equity (ownership) capital for the firm? (LO11-3)
6. Explain why retained earnings have an associated opportunity cost. (LO11-3)
7. Why is the cost of retained earnings the equivalent of the firm’s own required rate of return on common stock (Ke)? (LO11-3)
8. Why is the cost of issuing new common stock (Kn) higher than the cost of retained earnings (Ke)? (LO11-3)
9. How are the weights determined to arrive at the optimal weighted average cost of capital? (LO11-4)
10. Explain the traditional, U-shaped approach to the cost of capital. (LO11-4)
11. It has often been said that if the company can’t earn a rate of return greater than the cost of capital it should not make investments. Explain. (LO11-2)
12. What effect would inflation have on a company’s cost of capital? (Hint: Think about how inflation influences interest rates, stock prices, corporate profits, and growth.) (LO11-3)
13. What is the concept of marginal cost of capital? (LO11-5)
Page 361
PRACTICE PROBLEMS AND SOLUTIONS
Yield to maturity and cost of debt
(LO11-3)
1. a. A $1,000 par value bond issued by Conseco Electronics has 16 years to maturity. The bond pays $78 a year in interest and is selling for $884. What is the yield to maturity?
b. If the firm is in a 30 percent tax bracket, what is the aftertax cost of the debt?
Weighted average cost of capital
(LO11-1)
2. a. Assume the following capital structure for the Morgan Corp.
|
|
|
|
Debt |
35% |
|
Preferred stock |
15% |
|
Common equity |
50% |
|
|
The following facts are also provided:
|
|
|
|
Bond yield to maturity |
9% |
|
Corporate tax rate |
35% |
|
Dividend, preferred stock |
$ 8.50 |
|
Price, preferred stock |
$ 100 |
|
Flotation cost, preferred stock |
$ 2 |
|
Dividend, common stock |
$ 1.20 |
|
Price, common stock |
$ 30 |
|
Growth rate, common stock |
9% |
|
|
Compute the weighted average cost of capital.
b. If there are $30 million in retained earnings, at what dollar value will the marginal cost of capital go up? If the flotation cost on common stock is $1.50, what will be the cost of new common stock?
Solutions
1. a. Yield to maturity (YTM)
The yield to maturity is 9.21 percent.
b.
|
Kd (aftertax cost of debt) |
= Y (yield)(1 − T) |
|
|
= 9.21% (1 − 0.30) |
|
|
= 9.21% (0.70) |
|
|
= 6.45% |
|
|
|
|
FINANCIAL CALCULATOR |
|
|
Bond YTM |
|
|
Value |
Function |
|
16 |
N |
|
−884 |
PV |
|
78 |
PMT |
|
1000 |
FV |
|
Function |
Solution |
|
CPT |
|
|
I/Y |
9.21 |
|
|
Page 362
2. a. First compute the cost of the components in the capital structure.
|
Dp = |
Dividend, preferred stock = $8.50 |
|
Pp = |
Price, preferred stock = $100 |
|
F = |
Flotation cost, preferred stock = $2 |
|
D1 = |
Dividend, common stock = $1.20 |
|
P0 = |
Price, common stock = $30 |
|
g = |
Growth rate, common stock = 9% |
Now combine these with the weights in the capital structure to compute the weighted average cost of capital.
b. The marginal cost of capital will go up when there are no longer enough retained earnings to support the capital structure. This is point X.
Solve for X:
At this point, new common stock will be used instead of retained earnings in the capital structure. The cost of the new common stock is:
Kn = Cost of new common stock
The only new term is F:
D1 = $1.20
Page 363
|
P0 = |
$30 |
|
F = |
Flotation cost, new common stock $1.50 |
|
g = |
9% |
|
|
PROBLEMS
Selected problems are available with Connect. Please see the preface for more information.
Basic Problems
Cost of capital
(LO11-2)
1. In March 2010, Hertz Pain Relievers bought a massage machine that provided a return of 8 percent. It was financed by debt costing 7 percent. In August, Mr. Hertz came up with a heating compound that would have a return of 14 percent. The chief financial officer, Mr. Smith, told him it was impractical because it would require the issuance of common stock at a cost of 16 percent to finance the purchase. Is the company following a logical approach to using its cost of capital?
Cost of capital
(LO11-2)
2. Speedy Delivery Systems can buy a piece of equipment that is anticipated to provide an 11 percent return and can be financed at 6 percent with debt. Later in the year, the firm turns down an opportunity to buy a new machine that would yield a 9 percent return but would cost 15 percent to finance through common equity. Assume debt and common equity each represent 50 percent of the firm’s capital structure.
a. Compute the weighted average cost of capital.
b. Which project(s) should be accepted?
Effect of discount rate
(LO11-2)
3. A brilliant young scientist is killed in a plane crash. It is anticipated that he could have earned $240,000 a year for the next 50 years. The attorney for the plaintiff’s estate argues that the lost income should be discounted back to the present at 4 percent. The lawyer for the defendant’s insurance company argues for a discount rate of 8 percent. What is the difference between the present value of the settlement at 4 percent and 8 percent? Compute each one separately.
Aftertax cost of debt
(LO11-3)
4. Telecom Systems can issue debt yielding 9 percent. The company is in a 30 percent bracket. What is its aftertax cost of debt?
Aftertax cost of debt
(LO11-3)
5. Calculate the aftertax cost of debt under each of the following conditions:
|
|
||
|
|
Yield |
Corporate Tax Rate |
|
a. |
8.0% |
18% |
|
b. |
12.0 |
34 |
|
c. |
10.6 |
15 |
|
|
Aftertax cost of debt
(LO11-3)
6. Calculate the aftertax cost of debt under each of the following conditions:
|
|
||
|
|
Yield |
Corporate Tax Rate |
|
a. |
8.0% |
26% |
|
b. |
9.0 |
35 |
|
c. |
8.0 |
0 |
|
|
Aftertax cost of debt
(LO11-3)
Page 364
7. The Goodsmith Charitable Foundation, which is tax-exempt, issued debt last year at 9 percent to help finance a new playground facility in Los Angeles. This year the cost of debt is 25 percent higher; that is, firms that paid 11 percent for debt last year will be paying 13.75 percent this year.
a. If the Goodsmith Charitable Foundation borrowed money this year, what would the aftertax cost of debt be, based on their cost last year and the 25 percent increase?
b. If the receipts of the foundation were found to be taxable by the IRS (at a rate of 34 percent because of involvement in political activities), what would the aftertax cost of debt be?
Aftertax cost of debt
(LO11-3)
8. Royal Jewelers Inc. has an aftertax cost of debt of 7 percent. With a tax rate of 35 percent, what can you assume the yield on the debt is?
Yield to maturity and cost of debt
(LO11-3)
9. Airborne Airlines Inc. has a $1,000 par value bond outstanding with 25 years to maturity. The bond carries an annual interest payment of $88 and is currently selling for $950. Airborne is in a 40 percent tax bracket. The firm wishes to know what the aftertax cost of a new bond issue is likely to be. The yield to maturity on the new issue will be the same as the yield to maturity on the old issue because the risk and maturity date will be similar.
a. Compute the yield to maturity on the old issue and use this as the yield for the new issue.
b. Make the appropriate tax adjustment to determine the aftertax cost of debt.
Yield to maturity and cost of debt
(LO11-3)
10. Russell Container Corporation has a $1,000 par value bond outstanding with 30 years to maturity. The bond carries an annual interest payment of $105 and is currently selling for $880 per bond. Russell Corp. is in a 40 percent tax bracket. The firm wishes to know what the aftertax cost of a new bond issue is likely to be. The yield to maturity on the new issue will be the same as the yield to maturity on the old issue because the risk and maturity date will be similar.
a. Compute the yield to maturity on the old issue and use this as the yield for the new issue.
b. Make the appropriate tax adjustment to determine the aftertax cost of debt.
Changing rates and cost of debt
(LO11-3)
11. Terrier Company is in a 40 percent tax bracket and has a bond outstanding that yields 10 percent to maturity.
a. What is Terrier’s aftertax cost of debt?
b. Assume that the yield on the bond goes down by 1 percentage point, and due to tax reform, the corporate tax rate falls to 25 percent. What is Terrier’s new aftertax cost of debt?
c. Has the aftertax cost of debt gone up or down from part a to part b? Explain why.
Real-world example and cost of debt
(LO11-3)
12. KeySpan Corp. is planning to issue debt that will mature in 2035. In many respects, the issue is similar to currently outstanding debt of the corporation.
a. Using Table 11-3 , identify the yield to maturity on similarly outstanding debt for the firm in terms of maturity.
Page 365
b. Assume that because the new debt will be issued at par, the required yield to maturity will be 0.15 percent higher than the value determined in part a. Add this factor to the answer in a. (New issues sold at par sometimes require a slightly higher yield than older seasoned issues because there are fewer tax advantages and more financial leverage that increase company risk.)
c. If the firm is in a 30 percent tax bracket, what is the aftertax cost of debt?
Cost of preferred stock
(LO11-3)
13. Medco Corporation can sell preferred stock for $90 with an estimated flotation cost of $2. It is anticipated the preferred stock will pay $8 per share in dividends.
a. Compute the cost of preferred stock for Medco Corp.
b. Do we need to make a tax adjustment for the issuing firm?
Cost of preferred stock
(LO11-3)
14. Wallace Container Company issued $100 par value preferred stock 12 years ago. The stock provided a 9 percent yield at the time of issue. The preferred stock is now selling for $72. What is the current yield or cost of the preferred stock? (Disregard flotation costs.)
Comparison of the costs of debt and preferred stock
(LO11-3)
15. The treasurer of Riley Coal Co. is asked to compute the cost of fixed income securities for her corporation. Even before making the calculations, she assumes the aftertax cost of debt is at least 3 percent less than that for preferred stock. Based on the following facts, is she correct?
Debt can be issued at a yield of 11.0 percent, and the corporate tax rate is 20 percent. Preferred stock will be priced at $60 and pay a dividend of $6.40. The flotation cost on the preferred stock is $6.
Costs of retained earnings and new common stock
(LO11-3)
16. Murray Motor Company wants you to calculate its cost of common stock. During the next 12 months, the company expects to pay dividends (D1) of $2.50 per share, and the current price of its common stock is $50 per share. The expected growth rate is 8 percent.
a. Compute the cost of retained earnings (Ke). Use Formula 11-5 .
b. If a $3 flotation cost is involved, compute the cost of new common stock (Kn). Use Formula 11-6 .
Costs of retained earnings and new common stock
(LO11-3)
17. Compute Ke and Kn under the following circumstances:
a. D1 = $5.00, P0 = $70, g = 8%, F = $7.00.
b. D1 = $0.22, P0 = $28, g = 7%, F = $2.50.
c. E1 (earnings at the end of period one) = $7, payout ratio equals 40 percent, P0 = $30, g = 6.0%, F = $2.20.
d. D0 (dividend at the beginning of the first period) = $6, growth rate for dividends and earnings (g) = 7%, P0 = $60, F = $3.
Intermediate Problems
Growth rates and common stock valuation
(LO11-3)
18. Business has been good for Keystone Control Systems, as indicated by the four-year growth in earnings per share. The earnings have grown from $1.00 to $1.63.
a. Determine the compound annual rate of growth in earnings (n = 4).
b. Based on the growth rate determined in part a, project earnings for next year (E1). Round to two places to the right of the decimal point.
c. Assume the dividend payout ratio is 40 percent. Compute D1. Round to two places to the right of the decimal point.
d. The current price of the stock is $50. Using the growth rate (g) from part a and (D1) from part c, compute Ke.
e. If the flotation cost is $3.75, compute the cost of new common stock (Kn).
Weighted average cost of capital
(LO11-1)
Page 366
19. Global Technology’s capital structure is as follows:
|
|
|
|
Debt |
35% |
|
Preferred stock |
15 |
|
Common equity |
50 |
|
|
The aftertax cost of debt is 6.5 percent; the cost of preferred stock is 10 percent; and the cost of common equity (in the form of retained earnings) is 13.5 percent. Calculate Global Technology’s weighted average cost of capital in a manner similar to Table 11-1 .
Weighted average cost of capital
(LO11-1)
20. Evans Technology has the following capital structure:
|
|
|
|
Debt |
40% |
|
Common equity |
60 |
|
|
The aftertax cost of debt is 6 percent, and the cost of common equity (in the form of retained earnings) is 13 percent.
a. What is the firm’s weighted average cost of capital?
b. An outside consultant has suggested that because debt is cheaper than equity, the firm should switch to a capital structure that is 50 percent debt and 50 percent equity. Under this new and more debt-oriented arrangement, the aftertax cost of debt is 7 percent, and the cost of common equity (in the form of retained earnings) is 15 percent. Recalculate the firm’s weighted average cost of capital.
c. Which plan is optimal in terms of minimizing the weighted average cost of capital?
Weighted average cost of capital
(LO11-1)
21. Sauer Milk Inc. wants to determine the minimum cost of capital point for the firm. Assume it is considering the following financial plans:
|
|
||
|
|
Cost (Aftertax) |
Weights |
|
Plan A |
|
|
|
Debt |
4.0% |
30% |
|
Preferred stock |
8.0 |
15 |
|
Common equity |
12.0 |
55 |
|
Plan B |
|
|
|
Debt |
4.5% |
40% |
|
Preferred stock |
8.5 |
15 |
|
Common equity |
13.0 |
45 |
|
Plan C |
|
|
|
Debt |
5.0% |
45% |
|
Preferred stock |
18.7 |
15 |
|
Common equity |
12.8 |
40 |
|
Plan D |
|
|
|
Debt |
12.0% |
50% |
|
Preferred stock |
19.2 |
15 |
|
Common equity |
14.5 |
35 |
|
|
Page 367
a. Which of the four plans has the lowest weighted average cost of capital? (Round to two places to the right of the decimal point.)
b. Briefly discuss the results from Plan C and Plan D, and why one is better than the other.
Weighted average cost of capital
(LO11-1)
22. Given the following information, calculate the weighted average cost of capital for Hamilton Corp. Line up the calculations in the order shown in Table 11-1 .
Percent of capital structure:
|
|
|
|
Debt |
35% |
|
Preferred stock |
20 |
|
Common equity |
45 |
|
|
Additional information:
|
|
|
|
Bond coupon rate |
11% |
|
Bond yield to maturity |
9% |
|
Dividend, expected common |
$ 5.00 |
|
Dividend, preferred |
$ 12.00 |
|
Price, common |
$ 60.00 |
|
Price, preferred |
$106.00 |
|
Flotation cost, preferred |
$ 4.50 |
|
Growth rate |
6% |
|
Corporate tax rate |
35% |
|
|
Weighted average cost of capital
(LO11-1)
23. Given the following information, calculate the weighted average cost of capital for Digital Processing Inc. Line up the calculations in the order shown in Table 11-1 .
Percent of capital structure:
|
|
|
|
Preferred stock |
20% |
|
Common equity |
40 |
|
Debt |
40 |
|
|
Additional information:
|
|
|
|
Corporate tax rate |
34% |
|
Dividend, preferred |
$ 8.50 |
|
Dividend, expected common |
$ 2.50 |
|
Price, preferred |
$105.00 |
|
Growth rate |
7% |
|
Bond yield |
9.5 |
|
Flotation cost, preferred |
$ 3.60 |
|
Price, common |
$ 75.00 |
|
|
Advanced Problems
Changes in costs and weighted average cost of capital
(LO11-1)
24. Brook’s Window Shields Inc. is trying to calculate its cost of capital f or use in a capital budgeting decision. Mr. Glass, the vice president of finance, has given you the following information and has asked you to compute the weighted average cost of capital.Page 368
The company currently has outstanding a bond with a 12.2 percent coupon rate and another bond with a 9.5 percent coupon rate. The firm has been informed by its investment banker that bonds of equal risk and credit rating are now selling to yield 13.4 percent.
The common stock has a price of $58 and an expected dividend (D1) of $5.30 per share. The firm’s historical growth rate of earnings and dividends per share has been 9.5 percent, but security analysts on Wall Street expect this growth to slow to 7 percent in future years.
The preferred stock is selling at $54 per share and carries a dividend of $6.75 per share. The corporate tax rate is 35 percent. The flotation cost is 2.1 percent of the selling price for preferred stock. The optimum capital structure is 40 percent debt, 25 percent preferred stock, and 35 percent common equity in the form of retained earnings.
Compute the cost of capital for the individual components in the capital structure, and then calculate the weighted average cost of capital (similar to Table 11-1 ).
Changes in cost and weighted average cost of capital
(LO11-1)
25. A-Rod Manufacturing Company is trying to calculate its cost of capital for use in making a capital budgeting decision. Mr. Jeter, the vice president of finance, has given you the following information and has asked you to compute the weighted average cost of capital.
The company currently has outstanding a bond with a 10.6 percent coupon rate and another bond with an 8.2 percent rate. The firm has been informed by its investment banker that bonds of equal risk and credit rating are now selling to yield 11.5 percent. The common stock has a price of $65 and an expected dividend (D1) of $1.50 per share. The historical growth pattern (g) for dividends is as follows:
|
$1.40 |
|
1.54 |
|
1.69 |
|
1.85 |
Compute the historical growth rate, round it to the nearest whole number, and use it for g.
The preferred stock is selling at $85 per share and pays a dividend of $8.50 per share. The corporate tax rate is 40 percent. The flotation cost is 2.6 percent of the selling price for preferred stock. The optimum capital structure for the firm is 35 percent debt, 5 percent preferred stock, and 60 percent common equity in the form of retained earnings.
Compute the cost of capital for the individual components in the capital structure, and then calculate the weighted average cost of capital (similar to Table 11-1 ).
Impact of credit ratings on cost of capital
(LO11-3)
26. Northwest Utility Company faces increasing needs for capital. Fortunately, it has an Aa3 credit rating. The corporate tax rate is 40 percent. Northwest’s treasurer is trying to determine the corporation’s current weighted average cost of capital in order to assess the profitability of capital budgeting projects.Page 369
Historically, the corporation’s earnings and dividends per share have increased about 8.2 percent annually and this should continue in the future. Northwest’s common stock is selling at $64 per share, and the company will pay a $6.50 per share dividend (D1).
The company’s $96 preferred stock has been yielding 8 percent in the current market. Flotation costs for the company have been estimated by its investment banker to be $6.00 for preferred stock.
The company’s optimum capital structure is 55 percent debt, 20 percent preferred stock, and 25 percent common equity in the form of retained earnings. Refer to the following table on bond issues for comparative yields on bonds of equal risk to Northwest:
Compute the answers to the following questions from the information given:
a. Cost of debt, Kd. (Use the accompanying table—relate to the utility bond credit rating for yield.)
b. Cost of preferred stock, Kp.
c. Cost of common equity in the form of retained earnings, Ke.
d. Weighted average cost of capital.
Marginal cost of capital
(LO11-5)
27. Delta Corporation has the following cap ital structure:
a. If the firm has $18 million in retained earnings, at what size capital structure will the firm run out of retained earnings?
b. The 8.1 percent cost of debt referred to earlier applies only to the first $14 million of debt. After that the cost of debt will go up. At what size capital structure will there be a change in the cost of debt?
Marginal cost of capital
(LO11-5)
Page 370
28. The Nolan Corporation finds it is necessary to determine its margina l cost of capital. Nolan’s current capital structure calls for 50 percent debt, 30 percent preferred stock, and 20 percent common equity. Initially, common equity will be in the form of retained earnings (Ke) and then new common stock (Kn). The costs of the various sources of financing are as follows: debt, 9.6 percent; preferred stock, 9 percent; retained earnings, 10 percent; and new common stock, 11.2 percent.
a. What is the initial weighted average cost of capital? (Include debt, preferred stock, and common equity in the form of retained earnings, Ke.)
b. If the firm has $18 million in retained earnings, at what size capital structure will the firm run out of retained earnings?
c. What will the marginal cost of capital be immediately after that point? (Equity will remain at 20 percent of the capital structure, but will all be in the form of new common stock, Kn.)
d. The 9.6 percent cost of debt previously referred to applies only to the first $29 million of debt. After that, the cost of debt will be 11.2 percent. At what size capital structure will there be a change in the cost of debt?
e. What will the marginal cost of capital be immediately after that point? (Consider the facts in both parts c and d.)
Marginal cost of capital
(LO11-5)
29. The McGee Corporation finds it is necessary to determine its marginal cost of capital. McGee’s current capital structure calls for 40 percent debt, 30 percent preferred stock, and 30 percent common equity. Initially, common equity will be in the form of retained earnings (Ke) and then new common stock (Kn). The costs of the various sources of financing are as follows: debt, 9.6 percent; preferred stock, 9.0 percent; retained earnings, 10.0 percent; and new common stock, 11.4 percent.
a. What is the initial weighted average cost of capital? (Include debt, preferred stock, and common equity in the form of retained earnings, Ke.)
b. If the firm has $28.5 million in retained earnings, at what size capital structure will the firm run out of retained earnings?
c. What will the marginal cost of capital be immediately after that point? (Equity will remain at 30 percent of the capital structure, but will all be in the form of new common stock, Kn.)
d. The 9.6 percent cost of debt referred to earlier applies only to the first $30 million of debt. After that, the cost of debt will be 11.2 percent. At what size capital structure will there be a change in the cost of debt?
e. What will the marginal cost of capital be immediately after that point? (Consider the facts in both parts c and d.)
Capital asset pricing model and dividend valuation model
(LO11-3)
30. Eaton Electronic Company’s treasurer uses both the capital asset pricing model and the dividend valuation model to compute the cost of common equity (also referred to as the required rate of return for common equity).
Assume the following:
|
Rf = |
7% |
|
Km = |
10% |
|
β = |
1.6 |
|
D1 = |
$.70 |
|
P0 = |
$19 |
|
g = |
8% |
Page 371
a. Compute Ki (required rate of return on common equity based on the capital asset pricing model).
b. Compute Ke (required rate of return on common equity based on the dividend valuation model).
COMPREHENSIVE PROBLEM
Medical Research Corporation
(Marginal cost of capital and investment returns)
(LO11-5)
Medical Research Corporation is expanding its research and production capacity to introduce a new line of products. Current plans call for the expenditure of $100 million on four projects of equal size ($25 million each), but different returns. Project A is in blood clotting proteins and has an expected return of 18 percent. Project B relates to a hepatitis vaccine and carries a potential return of 14 percent. Project C, dealing with a cardiovascular compound, is expected to earn 11.8 percent, and Project D, an investment in orthopedic implants, is expected to show a 10.9 percent return.
The firm has $15 million in retained earnings. After a capital structure with $15 million in retained earnings is reached (in which retained earnings represent 60 percent of the financing), all additional equity financing must come in the form of new common stock.
Common stock is selling for $25 per share and underwriting costs are estimated at $3 if new shares are issued. Dividends for the next year will be $.90 per share (D1), and earnings and dividends have grown consistently at 11 percent per year.
The yield on comparative bonds has been hovering at 11 percent. The investment banker feels that the first $20 million of bonds could be sold to yield 11 percent while additional debt might require a 2 percent premium and be sold to yield 13 percent. The corporate tax rate is 30 percent. Debt represents 40 percent of the capital structure.
a. Based on the two sources of financing, what is the initial weighted average cost of capital? (Use Kd and Ke.)
b. At what size capital structure will the firm run out of retained earnings?
c. What will the marginal cost of capital be immediately after that point?
d. At what size capital structure will there be a change in the cost of debt?
e. What will the marginal cost of capital be immediately after that point?
f. Based on the information about potential returns on investments in the first paragraph and information on marginal cost of capital (in parts a, c, and e), how large a capital investment budget should the firm use?
g. Graph the answer determined in part f.
COMPREHENSIVE PROBLEM
Masco Oil and Gas
(Cost of capital with changing financial needs)
(LO11-1)
Masco Oil and Gas Company is a very large company with common stock listed on the New York Stock Exchange and bonds traded over the counter. As of the current balance sheet, it has three bond issues outstanding:
|
|
|
|
$150 million of 10 percent series |
2026 |
|
$50 million of 7 percent series |
2020 |
|
$75 million of 5 percent series |
2016 |
|
|
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The vice president of finance is planning to sell $75 million of bonds next year to replace the debt due to expire in 2016. Present market yields on similar Baa-rated bonds are 12.1 percent. Masco also has $90 million of 7.5 percent noncallable preferred stock outstanding, and it has no intentions of selling any preferred stock at any time in the future. The preferred stock is currently priced at $80 per share, and its dividend per share is $7.80.
The company has had very volatile earnings, but its dividends per share have had a very stable growth rate of 8 percent and this will continue. The expected dividend (D1) is $1.90 per share, and the common stock is selling for $40 per share. The company’s investment banker has quoted the following flotation costs to Masco: $2.50 per share for preferred stock and $2.20 per share for common stock.
On the advice of its investment banker, Masco has kept its debt at 50 percent of assets and its equity at 50 percent. Masco sees no need to sell either common or preferred stock in the foreseeable future as it has generated enough internal funds for its investment needs when these funds are combined with debt financing. Masco’s corporate tax rate is 40 percent.
Compute the cost of capital for the following:
a. Bond (debt) (Kd).
b. Preferred stock (Kp).
c. Common equity in the form of retained earnings (Ke).
d. New common stock (Kn).
e. Weighted average cost of capital.
WEB EXERCISE
1. In Table 11-4 , Intel was shown to have a low debt ratio. Let’s learn more about this company. Go to its website at www.intel.com , and follow these steps. Click on “Investor Relations” at the bottom of the home page. Click on “Financials and Filings.” Click on “Trended Financial Statements.” Click on “Download (PDF).”
2. Compute the $ change in “Total Assets” over the last two years.
3. Do the same computation for “Stockholders’ Equity.”
4. Do the same computation for “Long-Term Debt.”
5. In a brief paragraph, describe the change in long-term obligations (debt) that has taken place relative to the changes in total assets and stockholders’ equity. Does it appear to be good or bad?
Note: Occasionally a topic we have listed may have been deleted, updated, or moved into a different location on a website. If you click on the site map or site index, you will be introduced to a table of contents that should aid you in finding the topic you are looking for.
APPENDIX | 11A
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Cost of Capital and the Capital Asset Pricing Model
The Capital Asset Pricing Model
The capital asset pricing model (CAPM) relates the risk-return trade-offs of individual assets to market returns. Common stock returns over time have generally been used to test this model since stock prices are widely available and efficiently priced, as are market indexes of stock performance. In theory, the CAPM encompasses all assets, but in practice it is difficult to measure returns on all types of assets or to find an all-encompassing market index. For our purposes, we will use common stock returns to explain the model and occasionally we will generalize about other assets.
The basic form of the CAPM is a linear relationship between returns on individual stocks and stock market returns over time. By using least squares regression analysis, the return on an individual stock, Kj, is expressed in Formula 11A-1 :
where
|
Kj = |
Return on individual common stock of a company |
|
α = |
Alpha, the intercept on the y-axis |
|
β = |
Beta, the coefficient |
|
Km = |
Return on the stock market (an index of stock returns is used, usually the Standard & Poor’s 500 Index) |
|
e = |
Error term of the regression equation |
As indicated in Table 11A-1 and Figure 11A-1 , this equation uses historical data to generate the beta coefficient (β), a measurement of the return performance of a given stock versus the return performance of the market. Assume that we want to calculate a beta for Parts Associates Inc. (PAI), and that we have the performance data for that company and the market shown in Table 11A-1 . The relationship between PAI and the market appears graphically in Figure 11A-1 .
Table 11A-1 Performance of PAI and the market
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|
Rate of Return on Stock |
|
|
Year |
PAI |
Market |
|
1 |
12.0% |
10.0% |
|
2 |
16.0 |
18.0 |
|
3 |
20.0 |
16.0 |
|
4 |
16.0 |
10.0 |
|
5 |
6.0 |
8.0 |
|
Mean return |
14.0% |
12.4% |
|
Standard deviation |
4.73% |
3.87% |
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Figure 11A-1 Linear regression of returns between PAI and the market
The alpha term in Figure 11A-1 of 2.8 percent is the y intercept of the linear regression. It is the expected return on PAI stock if returns on the market are zero. However, if the returns on the market are expected to approximate the historical rate of 11.6 percent, the expected return on PAI would be Kj = 2.8 + 0.9(11.6) = 13.2 percent. This maintains the historical relationship. If the returns on the market are expected to rise to 18 percent next year, expected return on PAI would be Kj = 2.8 + 0.9(18.0) = 19 percent.
Notice that we are talking in terms of expectations. The CAPM is an expectational (ex ante) model, and there is no guarantee historical data will reoccur. One area of empirical testing involves the stability and predictability of the beta coefficient based on historical data. Research has indicated that betas are more useful in a portfolio context (for groupings of stocks) because the betas of individual stocks are less stable from period to period than portfolio betas. In addition, research indicates betas of individual common stocks have the tendency to approach 1.0 over time.
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The Security Market Line The capital asset pricing model evolved from Formula 11A-1 into a market risk premium model where the basic assumption is that for investors to take more risk, they must be compensated by larger expected returns. Investors should also not accept returns that are less than they can get from a riskless asset. For CAPM purposes, it is assumed that short-term U.S. Treasury bills may be considered a riskless asset. 1 When viewed in this context, an investor must achieve an extra return above that obtainable from a Treasury bill in order to induce the assumption of more risk. This brings us to the more common and theoretically useful model:
where
|
Rf = |
Risk-free rate of return |
|
β = |
Beta coefficient from Formula 11A-1 |
|
Km = |
Return on the market index |
|
Km − Rf = |
Premium or excess return of the market versus the risk-free rate (since the market is riskier than Rf, the assumption is that the expected Km will be greater than Rf) |
|
β(Km − Rf) = |
Expected return above the risk-free rate for the stock of Company j, given the level of risk |
The model centers on “beta,” the coefficient of the premium demanded by an investor to invest in an individual stock. For each individual security, beta measures the sensitivity (volatility) of the security’s return to the market. By definition, the market has a beta of 1.0, so that if an individual company’s beta is 1.0, it can expect to have returns as volatile as the market and total returns equal to the market. A company with a beta of 2.0 would be twice as volatile as the market and would be expected to generate more returns, whereas a company with a beta of 0.5 would be half as volatile as the market.
The term (Km − Rf) indicates common stock is expected to generate a rate of return higher than the return on a U.S. Treasury bill. This makes sense since common stock has more risk. Research by Roger Ibbotson shows that this risk premium over the last 83 years is close to 6.5 percent on average but exhibits a wide standard deviation. 2 In the actual application of the CAPM to cost of capital, companies often will use this historical risk premium in their calculations. In our example, we use 6.5 percent to represent the expected (Km − Rf).
For example, assuming the risk-free rate is 5.5 percent and the market risk premium (Km − Rf) is 6.5 percent, the following returns would occur with betas of 2.0, 1.0, and 0.5:
K2 = 5.5% + 2.0(6.5%) = 5.5% + 13.0% = 18.5%
K1 = 5.5% + 1.0(6.5%) = 5.5% + 6.5% = 12.0%
K.5 = 5.5% + 0.5(6.5%) = 5.5% + 3.25% = 8.75%
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The beta term measures the riskiness of an investment relative to the market. To outperform the market, one would have to assume more risk by selecting assets with betas greater than 1.0. Another way of looking at the risk-return trade-off would be that if less risk than the market is desired, an investor would choose assets with a beta of less than 1.0. Beta is a good measure of a stock’s risk when the stock is combined into a portfolio, and therefore it has some bearing on the assets that a company acquires for its portfolio of real capital.
In Figure 11A-1 , individual stock returns were compared to market returns and the beta from Formula 11A-1 was shown. From Formula 11A-2 , the risk-premium model, a generalized risk-return graph called the security market line (SML) can be constructed that identifies the risk-return trade-off of any common stock (asset) relative to the company’s beta. This is shown in Figure 11A-2 .
Figure 11A-2 The security market line (SML)
The required return for all securities can be expressed as the risk-free rate plus a premium for risk. Thus we see that a stock with a beta of 1.0 would have a risk premium of 6.5 percent added to the risk-free rate of 5.5 percent to provide a required return of 12 percent. Since a beta of 1.0 implies risk equal to the stock market, the return is also at the overall market rate. If the beta is 2.0, twice the market risk premium of 6.5 percent must be earned, and we add 13 percent to the risk-free rate of 5.5 percent to determine the required return of 18.5 percent. For a beta of 0.5, the required return is 8.75 percent.
Cost of Capital Considerations When calculating the cost of capital for common stock, remember that Ke is equal to the expected total return from the dividend yield and capital gains.
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Ke is the return required by investors based on expectations of future dividends and growth. The SML provides the same information, but in a market-related risk-return model. As required returns rise, prices must fall to adjust to the new equilibrium return level, and as required returns fall, prices rise. Stock markets are generally efficient, and when stock prices are in equilibrium, the Ke derived from the dividend model will be equal to Kj derived from the SML.
The SML helps us to identify several circumstances that can cause the cost of capital to change. Figure 11-2 in Chapter 11 examined required rates of returns over time with changing interest rates and stock prices. Figure 11A-3 does basically the same thing, only through the SML format.
Figure 11A-3 The security market line and changing interest rates
When interest rates increase from the initial period (Rf1 versus Rf0), the security market line in the next period is parallel to SML0, but higher. What this means is that required rates of return have risen for every level of risk, as investors desire to maintain their risk premium over the risk-free rate.
One very important variable influencing interest rates is the rate of inflation. As inflation increases, lenders try to maintain their real dollar purchasing power, so they increase the required interest rates to offset inflation. The risk-free rate can be thought of as
Rf = RR + IP
where
RR is the real rate of return on a riskless government security when inflation is zero.
IP is an inflation premium that compensates lenders (investors) for loss of purchasing power.
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An upward shift in the SML indicates that the prices of all assets will shift downward as interest rates move up. In Chapter 10 , “Valuation and Rates of Return,” this was demonstrated in the discussion that showed that when market interest rates went up, bond prices adjusted downward to make up for the lower coupon rate (interest payment) on the old bonds.
Another factor affecting the cost of capital is a change in risk preferences by investors. As investors become more pessimistic about the economy, they require larger premiums for assuming risks. Even though the historical average market risk premium may be close to 6.5 percent, this is not stable and investors’ changing attitudes can have a big impact on the market risk premium. For example, the 1987 stock market crash on October 19 (a 22.6 percent decline in one day) had to be somewhat influenced by investors’ quick moves to a more risk-averse attitude. This risk aversion shows up in higher required stock returns and lower stock prices. For example, if investors raise their market risk premium to 8 percent, the required rates of return from the original equations will increase as follows:
K2 = 5.5% + 2.0(8.0%) = 5.5% + 16.0% = 21.5%
K1 = 5.5% + 1.0(8.0%) = 5.5% + 8.0% = 13.5%
K.5 = 5.5% + 0.5(8.0%) = 5.5% + 4.0% = 9.5%
The change in the market risk premium will cause the required market return (beta = 1.00) to be 13.5 percent instead of the 12 percent from Figure 11A-2 . Any asset riskier than the market would have a larger increase in the required return. For example, a stock with a beta of 2.0 would need to generate a 21.5 percent return, instead of the 18.5 percent in Figure 11A-2 . The overall shape of the new security market line (SML1) is shown in Figure 11A-4 . Note the higher slope for SML1, in comparison to SML0.
Figure 11A-4 The security market line and changing investor expectations
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In many instances rising interest rates and pessimistic investors go hand-in-hand, so the SML may change its slope and intercept at the same time. This combined effect would cause severe drops in the prices of risky assets and much larger required rates of return for such assets.
The capital asset pricing model and the security market line have been presented to further your understanding of market-related events that impact the firm’s cost of capital, such as market returns and risk, changing interest rates, and changing risk preferences.
While the capital asset pricing model has received criticism because of the difficulties of dealing with the betas of individual securities and because of the problems involved in consistently constructing the appropriate slope of the SML to represent reality, it provides some interesting insights into risk-return measurement.
List of Terms
capital asset pricing model 373
market risk premium 374
beta 375
security market line 376
Discussion Questions
11A-1. How does the capital asset pricing model help explain changing costs of capital? (LO11-1)
11A-2. How does the SML react to changes in the rate of interest, changes in the rate of inflation, and changing investor expectations? (LO11-2)
Problems
Capital asset pricing model
(LO11-3)
11A-1. Assume that Rf = 5 percent and Km = 10.5 percent. Compute Kj for the following betas, using Formula 11A-2 .
a. 0.6
b. 1.3
c. 1.9
Capital asset pricing model
(LO11-3)
11A-2. Assume that Rf = 6 percent and the market risk premium (Km − Rf) is 7.0 percent. Compute Kj for the following betas, using Formula 11A-2 .
a. 0.6
b. 1.3
c. 1.9
1 The yield may also be thought of as representing the interest cost to the firm after considering all selling and distribution costs, though no explicit representation is given above to these costs in relationship to debt. These costs are usually quite small, and they are often bypassed entirely in some types of loans. For those who wish to explicitly include this factor in Formula 11-1 , we would have:
Kd = [Yield/(1 − Distribution costs)] (1 − T)
2 Actually the rate might be slightly lower to reflect that bonds trading at a discount from par ($939 in this case) generally pay a lower yield to maturity than par value bonds because of potential tax advantages and higher leverage potential. This is not really a major issue in this case.
3 Note that in Chapter 10 , Kp was presented without any adjustment for flotation costs. The instructor may wish to indicate that we have altered the definition slightly. Some may wish to formally add an additional subscript to Kp to indicate we are now talking about the cost of new preferred stock. The adjusted symbol would be Kpn.
4 One could logically suggest this is not a perfectly equivalent relationship. For example, if stockholders receive a distribution of retained earnings in the form of dividends, they will have to pay taxes on the dividends before they can reinvest them in equivalent yield investments. Also the stockholder may incur brokerage costs in the process. For these reasons, one might suggest the opportunity cost of retained earnings is less than the rate of return on the firm’s common stock. The authors have generally supported this position in the past. However, the current predominant view is that the appropriate cost for retained earnings is equal to the rate of return on the firm’s common stock. The strongest argument for this equality position is that, in a publicly traded company, a firm always has the option of buying back its stock in the market. Given that this is the case, it is assured a return of Ke. Thus, the firm should not make a physical asset investment that has an expected equity return of less than Ke. Having presented both sides of the argument, the authors have adopted the equality position in recent editions and have used it throughout this chapter. Nevertheless, some instructors may wish to discuss both sides of the issue.
5 This table measures total debt to total assets. Some may choose to measure long-term debt to stockholders’ equity. Either method can be used as long as it is consistently applied.
6 Market value rather than book value should be used—though in practice, book value is sometimes used.
1 A number of studies have also indicated that longer-term government securities may appropriately represent Rf (the risk-free rate).
2 Ibbotson Associates, Stocks, Bonds, Bills and Inflation: 2007 Yearbook (Chicago: Ibbotson Associates and Capital Market Research Center, 2010).