Foundations of Financial Management: An Analysis (part 39)

“The stock market is filled with individuals who know the price of everything, but the value of nothing.” 

– Philip Fisher

Cost of Capital

by

Charles Lamson

Throughout the previous several posts, a number of references were made to discounting future cash flows and 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 it 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. The next few posts set down the methods and procedures for making such a determination.

First, the reader 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

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 and 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 that 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.

The determination of cost of capital can best be understood by examining the capital structure of a hypothetical firm, the Lamson Corporation, in Table 1. Note that the after-tax 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 cost. In the next few posts, each of these procedural steps is examined.

Table 1 Cost of capital---Lamson 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 posts. If a reader understands 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

The cost of debt is measured by the interest rate, or yield, paid to the 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 Part 34 of this analysis.

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 $101.50 per year in interest, has a 20-year life, and is currently selling for $940. To find the current yield to maturity on the debt, we could use the trial-and-error process described in part 33 of this analysis. That is, we would experiment with discount rates until we found the rate that would equate the current bond price of $940 with interest payments of $101.50 for 20 years and a maturity payment of $1,000. A simple process would be to use Formula 1, which gives us the approximate yield to maturity.

In many cases you will not have to compute the yield to maturity. With just a quick web search, it will simply be given to you. Anyone can go to any search engine to determine the yield to maturity on the firm's outstanding debt. For example, I just went to Google, and in the search field I typed "yield to maturity for Meade Corporation (paper company) bond," and right away just by looking at the search results we observe that the Meade corporation has 6-year, $1,000 par value bonds that have a yield to maturity of 8.5 percent.

Once the bond yield is determined through the formula (or is given to you via the Internet), 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, it's 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 taxes. The after-tax cost of debt is actually the yield-to-maturity times one minus the tax rate. This is represented in Formula 2.

The term yield in the formula is interchangeable with yield to maturity or approximate yield to maturity. In using the approximate yield to maturity formula 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, 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. 

Please refer back to Table 1 and observe in column (1) that the aftertax cost of debt is the 7.05 percent that we have just computed. 

*MAIN SOURCE: BLOCK & HIRT, 2005, FOUNDATIONS OF FINANCIAL MANAGEMENT, 11TH ED., PP. 312-316*

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