The aftertax cost of debt

COST OF CAPITAL

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 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.

The determination of cost of capital can best be understood by examining the capital structure of a hypothetical firm, the Baker Corporation. 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.)

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 previously. 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 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.

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. 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 simpler process would be to use which gives us the approximate yield to maturity. We reproduce the formula below:

Approximate yield to maturity (Y') =

{Annual interest payment + (Principal payment − Price of the bond/Number of years to maturity)}/{0.6(Price of the bond) + 0.4(Principal payment)}

For the bond under discussion, the approximate yield to maturity (Y’) would be:

Y’={$101.50 + [($1,000−$940)/20]}/{0.6($940)+0.4($1.000)}

Y’=[$101.50+(60/20)]/($564+$400)]

Y’=[($101.50+3)/$964

Y’=$104.50/$964=10.84%

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 Standard & Poor’s Bond Guide to determine the yield to maturity on the firm’s outstanding debt. An excerpt from this bond guide is presented in Table 11–2 on page 334. If the firm involved is MBNA Capital, for example, the financial manager could observe that debt maturing in 2026 would have a yield to maturity of 7.86 percent as shown in the last column of the table.

Excerpt from Standard & Poor’s Bond Guide

Once the bond yield is determined through the formula 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 taxes. The aftertax cost of debt is actually the yield to maturity times one minus the tax rate.

Kd (Cost of debt) = Y (Yield) (1 – T)

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.

Kd(Cost of debt)=Y(Yield)(1−T)

=10.84%(1−.35)=10.84%(.65)=7.05%

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.

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 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 presented as Formula is:

Kp(Cost of preferred stock)=DpPp−F