The cost of capital
Cost of Capital
LEARNING OBJECTIVES
| LO 11-1 | The cost of capital represents the weighted average cost of the source of financing to the firm. |
| LO 11-2 | The cost of capital is normally the discount rate to use in analyzing an investment. |
| 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. |
| LO 11-4 | A firm attempts to find a minimum cost of capital through varying the mix of its sources of financing. |
| 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.
| FINANCIAL CALCULATOR | |
| Bond YTM | |
| Value | Function |
| 15 | N |
| −939 | PV |
| 100 | PMT |
| 1000 | FV |
| Function | Solution |
| CPT | |
| I/Y | 10.84 |
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.
| Kd (Cost of debt) | = Y(1 − T) |
| = 10.84%(1 − 0.35) | |
| = 10.84%(0.65) | |
| = 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
| Kp = | Cost of preferred stock |
| Dp = | The annual dividend on preferred stock |
| Pp = | The price of preferred stock |
| 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
| P0 = | Price of the stock today |
| D1 = | Dividend at the end of the first year (or period) |
| Ke = | Required rate of return |
| 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
| Kj = | Required return on common stock |
| Rf = | Risk-free rate of return; usually the current rate on Treasury bill securities |
| 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. |
| Km = | Return expected in the market as measured by an appropriate index |
For the Baker Corporation example, we might assume the following values:
| Rf = | 5.5% |
| Km = | 12% |
| 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.
| Ke = | Cost of common equity in the form of retained earnings |
| D1 = | Dividend at the end of the first year, $2 |
| P0 = | Price of the stock today, $40 |
| 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:
| D1 = | $2 |
| P0 = | $40 |
| F = | $4 |
| 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.
