Computing the Component Costs of Capital - Financial Management

This section develops and applies methods a firm can use to compute the cost of its major component sources of capital: debt, preferred stock, retained earnings, and new common equity. These are the component costs used in the calculation of the weighted cost of capital as shown in Equation

Marginal Costs

Firms calculate their cost of capital in order to determine a discount rate to use for evaluating proposed capital expenditure projects. Recall that the purpose of capital expenditure analysis is to determine which proposed projects the firm should actually undertake. Therefore, it is logical that the capital whose cost is measured and compared with the expected benefits from the proposed projects should be the next or marginal capital the firm raises.

The capital budgeting process involves an extension of the marginal analysis principle from economics. The marginal revenue (internal rate of return) from a project is compared with the marginal cost of funds needed to finance the project. The marginal cost of funds is the cost of the next increments of capital raised by the firm. Hence, the costs of the various capital funding components (debt, preferred stock, and common equity) must be their marginal costs. Historic average capital costs are not relevant for making new (marginal) resource allocation decisions.

When computing the marginal cost of the various component capital sources, companies typically estimate the component costs they anticipate encountering (paying) during the coming year. If capital costs change significantly during the year, it may be necessary to recompute the new capital costs and use the new estimates when evaluating projects from that time forward. Under most circumstances, a semiannual or annual computation of marginal capital costs is sufficient.

Cost of Debt

The cost of debt capital to the firm is the rate of return required by a firm’s creditors. For a debt issue, this rate of return, kd, equates the present value of all expected future receipts —interest, I, and principal repayment, M—with the net proceeds, Pnet, of the debt security

Cost of Debt

Pnet = I(PVIFAkd,n) + M(PVIFkd,n)

The pretax cost of debt, kd, is calculated in the same way as the yield -to-maturity.The only difference in the calculation is that when making yield -to-maturity calculations, the price of the bond is the current market price.When computing the pretax cost of debt to a company, the price of the bond is the net proceeds the company receives after considering all issuance costs.

Interest payments made to investors are deductible from the firm’s taxable income. Therefore, the after-tax cost of debt, ki, is computed by multiplying the pretax cost of debt, kd, by 1 minus the firm’s marginal tax rate, T:5

ki = kd(1 – T)

To illustrate the cost-of-debt calculation for KMI, assume that the firm sells $100 million of 20-year 7.8 percent coupon rate bonds. The net proceeds to KMI after issuance costs are $980 for each $1,000 bond. To compute the pretax cost, kd, of this debt offering, the relationship in Equation can be used as follows:

Net proceeds = Pnet = $78(PVIFAkd,20)+ $1,000(PVIFkd,20)

The calculation of kd can be done either by trial and error using Tables at the end of the book or with the aid of a financial calculator.
By trial and error, try 8 percent:

$980 = $78(9.818) + $1000(0.215)≈ $980

Therefore, the pretax cost of debt is 8 percent.

Assuming a 40 percent marginal tax rate, the after -tax cost of debt is computed using Equation

ki = kd(1 – T) = 8%(1 – 0.4) = 4.80%

The tax benefits of interest deductibility are available only to firms that are making profits. For a firm losing money, the tax rate in Equation is zero, and the after-tax cost, ki, is the same as the pretax cost, kd.

This procedure works well when a firm is in the process of selling, or has just sold, bonds at the time the cost of capital is being computed. However, in most instances, trips to the capital markets are sporadic. How can the marginal cost of debt be computed in these cases? That is, how can one determine what it would cost a firm to sell debt today (at the time of the cost -of-capital calculation)? This problem has two solutions:

  1. If a firm has bonds that are currently outstanding and are being traded in the marketplace, the firm can observe the current market price for those bonds. Given a current price, the maturity of the bonds, and the coupon rate of interest, the yield -to -maturity on the bond can be computed. This yield -to -maturity may be used as an estimate of the marginal pretax cost of debt, kd, for the firm.
  2. If a firm’s outstanding bonds are not traded frequently or are privately held, then the best estimate of the marginal pretax cost of debt can be derived by looking at the pretax cost of debt recently sold by other firms having risk similar to the firm under consideration. For these purposes, having similar risk is normally interpreted to mean that firms have equivalent bond ratings (according to Moody’s or Standard & Poor’s).

Cost of Preferred Stock

The cost of preferred stock to the firm is the rate of return required by investors on preferred stock issued by the company. Because many preferred stocks are perpetuities, it is possible to use the simplified preferred stock valuation model developed in this chapter

P0 = Dp/kp

where P0 is the preferred stock price; Dp, the annual preferred dividend; and kp, the investors’ required rate of return. The cost of preferred stock, kp, is given by the following equation:

kp = Dp/Pnet

In calculating preferred stock cost, the price that should be used, Pnet, is the net proceeds to the firm, that is, the proceeds from the sale of the stock after subtracting issuance costs.

To illustrate, KMI has just issued 3 million shares of a preferred stock that pay an annual dividend of $4.05. The preferred stock was sold to the public at a price of $52 per share.With issuance costs of $2 per share, the marginal cost of preferred stock is calculated as follows:

kp = $4.05/$52 – $2 = 0.081 or 8.1%

Because payments by the firm to preferred stockholders are in the form of dividends, they are not tax deductible; therefore, the after -tax cost of preferred stock is equal to the pretax rate.

An increasing number of preferred stock issues are callable, have a sinking fund redemption provision, or have a fixed maturity. In these cases, the computation of the cost of preferred stock financing is similar to that for bonds. For example, Progress Energy plans an offering of $50 par value preferred stock that will pay a $5.00 dividend per year. The preferred stock is expected to yield Progress net proceeds of $46.40 per share after all issue costs. The preferred stock must be retired at its par value in 15 years. The cost of this preferred stock issue can be computed by solving for kp in the following valuation model:

Pnet = $46.40 = $5(PVIFAkp,15) + $50(PVIFkp,15)


Therefore, kp equals 11 percent for Progress’s anticipated preferred stock offering.

Cost of Internal Equity Capital

Like the cost of debt and preferred stock, the cost of equity capital to the firm is the equilibrium rate of return required by the firm’s common stock investors.

Firms raise equity capital in two primary ways:

  • Internally, through retained earnings
  • Externally, through the sale of new common stock

Some analysts and managers incorrectly assume that the cost of internal equity is zero. The opportunity cost concept makes it clear that this is an erroneous assumption.When funds are generated through the earnings of the firm, either managers can pay out these funds as dividends to common stockholders, or the funds can be retained and reinvested in the firm.

If the funds were paid out to stockholders, they could reinvest the funds elsewhere to earn an appropriate return, given the risk of the investment. Therefore, if managers decide to retain earnings and reinvest them in the firm, there must be investment opportunities in the firm offering a return equivalent to the returns available to common stockholders, on a risk -adjusted basis, in alternative investments.

The cost of internal equity to the firm is less than the cost of new common stock because the sale of new stock requires the payment of issuance costs. The concept of the cost of internal equity (or simply equity, as it is commonly called) can be developed using several different approaches. The first considered here is based on the dividend valuation model.

Dividend Valuation Model Approach

Briefly reviewing from Chapter, the general dividend valuation model (or the dividend capitalization model, as it is often referred to) for common stock valuation is as follows:

Dividend Valuation Model Approach

where P0 is the stock’s present value or current market price;Dt, the dividend received in period t ; and ke, the return required by investors. This equation shows that in efficient capital markets, ke, the required return and thus the cost of equity capital, equates the present value of all expected future dividends with the current market price of the stock.

In principle, the cost of equity capital can be calculated by solving Equation for ke. In practice, however, the expected future dividends are not known and cannot be estimated with the same degree of confidence as preferred stock dividends and debt interest. As a result, the general form of the dividend valuation model is not directly useful in calculating the cost of equity capital.

As shown in Chapter, if the firm’s future per -share dividends are expected to grow each period perpetually at a constant rate, g, the dividend valuation model can be written as follows:

P0 = D1/ke– g

where D1 = D0(1 + g) and D0 is the current period dividend (t = 0). Note that in Equation, kemust be greater than g, the expected growth rate. The constant growth valuation model assumes that a firm’s earnings, dividends, and stock price will grow at rate g. Thus, g equates to the yearly price appreciation (capital gain).

But the total return to stockholders, ke, is composed of both the price appreciation and the dividend yield. Therefore, g cannot be greater than or equal to ke because it is only one of two components making up ke.

Equation can be rearranged to obtain an expression for calculating the cost of equity, assuming that dividends are expected to grow perpetually at a rate g per year:

ke = D1/P0 + g

To illustrate the use of Equation, suppose KMI’s common stock is currently selling for $56 a share. Its present dividend, D0, is $0.20 a share, and the expected long-term earnings and dividend growth rate is 10.0 percent. The cost of internal equity capital, ke, is calculated as follows:

ke = $0.20(1 + 0.10)/$56 + 0.10 = 0.104 or 10.4%

Nonconstant Dividend Growth and the Cost of Common Equity The dividend valuation model can also be used to compute the cost of equity for common stocks expected to pay dividends that grow at variable rates in the future. An approach similar to the nonconstant growth dividend valuation model illustrated in Chapter can be used.

For example, Avtec Corporation is a rapidly growing producer of microcircuit boards used in the aerospace industry. Its stock is currently selling for $10.95 per share. Current dividends, D0, are $1.00 per share and are expected to grow at a rate of 10 percent per year over the next four years and 6 percent annually thereafter. Avtec’s cost of internal equity, ke, can be found as follows:

$10.95 = $1.10/(1 + ke)1 + $1.21/(1 + ke)2 + $1.33/(1 + ke)3 + $1.46/(1 + 46/(1 + ke)4 + 1/ (1 + ke)4 * $1.55/ke - 0.06
       = $1.10(PVIFke,1) + $1.21(PVIFke,2) + $1. 33(PVIFke,3) + $1.46(PVIFke,4) + (PVIFke,4)$1.55/ke - 0.06
       = $1.10(0.855) + $1.21(0.731) + $1.33(0.624) + $1.46(0.534 * [$1.55/0.17 - 0.06]
       = $10.95#END##


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