Chapter 11
Alternative Cost of Capital Analysis and Estimation
1. a) The current earning yield method, as shown by Lintner, is equal to the marginal cost of capital under uncertainty. It is described as r ≥ ye, where r is the marginal internal rate of return, ye = yo/po is the current earnings yield and yo and po are the current EPS and PPS. This equation implies that an investment should not be accepted unless r is larger than ye. Although this method is suggested for use by Lintner over the average earnings yield method, it is not very popular in practical applications.
b) The discounted cash flow method (DCF) determines the cost of capital for a firm’s retained earnings. Using Gordon’s growth equation, po = D1/(Ke – g), we can rearrange to solve for the cost of equity capital, , using both average DPS and PPS. These are readily ascertainable, but the estimation of a proper growth rate can be considerable problem.
c) In order to estimate the weighted average cost of capital (WACC), we (1) determine the relative proportions of the various financial instruments in a firm’s capital structure, and (2) calculate the proper cost of each of the components. Thus we estimate the cost of debt, cost of retained earnings, cost of preferred stock, and the cost of new equity. To determine the appropriate weights of each capital component, we use the market value outstanding of each component/total assets to determine the weight for each financing instrument. Then, WACC equals the sum of these weighted components.
WACC is a more popular method in applications, although it is subject to much criticism for its simplicity, ease of calculation, and lack of completeness. However, Henderson and others have shown that WACC is equivalent theoretically and empirically with other methods.
d) CAPM expresses the required rate of return for a risky asset or investment; therefore it can be used to determine the cost of capital for an investment project undertaken by a firm. CAPM’s advantages over WACC are that (1) the concept of systematic risk is directly incorporated into the CAPM framework, and (2) it does not implicitly assume (as WACC does), that the project is to the same risk class as the firm. However, the simple CAPM does not explicitly consider the effects of leverage and taxes on a firm’s cost of capital. To overcome this potential bias the practitioner should use alternative CAPM’s as derived by Brennan (Chapter 7, 230) and, Litzenberger and Ramaswamy (Chapter 13, 468-471).
e) Under the M & M cross-sectional method, we assume (1) a perpetual stream of earnings from real assets, and (2) a constant capitalization rate (p) at which the market discounts the unlevered equity stream of earnings for some risk classes and perfect markets: the value of a levered firm is
where V = sum of market value of all securities issued,
p = cost of unlevered equity capital/risk class,
D = market value of a firm’s debt,
= expected level of average annual earnings generated by current assets,
and
T = corporate tax rate.
A finite supernormal growth model can be applied to an all-equity firm by partitioning the value of the firm into
V = (S)stock + (D)debt + (P)preferred stock.
Thus it is possible to obtain ,
where k = investment as a percentage of tax adjusted earnings; ρ* = IRR.
By then performing a cross-sectional regression, we can estimate the market capitalization rate and thus the cost of capital.
2. The Chase cost-of-capital method is a useful blend of the CAPM method and M & M’s firm value relationship. This three-step process (1) estimates the equity cost of capital of a firm, (2) adjusts this cost of capital figure for financial risk to arrive at an estimate of the unlevered equity cost of capital, and (3) estimates the total cost of capital using the unlevered cost of capital and an estimate of the future long-term ratio. The main advantage of this method is to more explicitly take account of the effects of leverage in estimating the firm’s cost of capital. In addition, the Chase method is structurally proficient enough to consider both time series and cross-sectional effects on cost of capital estimation.
3. Three methods of growth rate estimation are:
a) Simple growth rate－the average total change in earning over a period of a year:
b) Arithmetic average－growth estimates for short periods are again averaged to arrive at one growth estimate for the total period:
c) Ordinary least squares regression－using EPS and/or DPS information,
Loge EPSt = ao + a1T1 + ε1t and/or Loge DPSt = bo + b1T1 + ε2t.
The regression method takes more information into account. Also, a null hypothesis test can be made to determine if the growth rate obtained is statistically significant from zero.
4. Yes, WACC can be theoretically justified. As Henderson derived in his paper, the WACC can be transformed into a generalized form of WACC:
which proves to be theoretically and conceptually consistent with the equity cost of capital expressions that emerge from the M & M theory as well as from CAPM.
5. The information needed to use CAPM in cost-of-equity capital estimation include:
a) the risk-free rate, which can be calculated or estimated using 90-day T-bills;
b) the risk premium (Rm – Rf), which can be approximated by the long-term market risk premium of a market index such as the Dow Jones 30 or S & P 500 index;
c) each asset’s or investment’s beta, which represents the systematic risk associated with undertaking the project or buying the asset.
6.
The discount rate for the project is equal to the expected return for the security, RS, since the project has the same risk as the firm as a whole. Apply the CAPM to express the firm’s required return, RS, in terms of the firm’s beta, b, the risk-free rate, RF, and the expected market return, M.
RS = RF + b ´ (M – RF)
= 0.06 + 0.8 (0.10)
= 0.14
Subtract the initial investment at year 0. To calculate the PV of the cash inflows, apply the annuity formula, discounted at 0.14.
NPV = C0 + C1 ATr
= -$1,000,000 + $340,000 A50.14
= -$201440
Do not undertake the project since the NPV is negative.
7.
Calculate the square root of the stock’s variance and the market’s variance to find the standard deviation, s, of each.
sC = (s2C)1/2
= (0.003025)1/2
= 0.055
sM = (s2M)1/2
= (0.001764)1/2
= 0.042
Use the formula for beta:
bC = [Corr (RC, RM) ´ sC] / sM
= [(0.75) (0.055)] / (0.042)
= 0.982
The beta of Company BBB is 0.982.
8.
In order to calculate the weighted average cost of capital, one has to determine the proper weights expressing the firm’s proportion of debt in terms of the firm’s proportion of equity. Solve for the equity to value ratio [S / (S+B)] and the debt to value ratio [B / (S+B)].
B / S = 0.45
B = 0.45 S
[S / (S+B)] = [S / (S + 0.45´S)]
= [S / (1.45 ´ S)]
= 1 / 1.45
= 0.69
[B / (S+B] = [0.45 ´ S / (S + 0.45 ´ S)]
= [(0.45 ´ S) / (1.45 ´ S)]
= 1 / 5
= 0.31
Interest on debt is tax deductible at the corporate level, which leads to tax benefits for the firm. Multiply the cost of debt, rB, by (1 - TC), to include the tax benefit created by the interest tax shield. The tax benefit of debt will lower the firm’s overall cost of capital.
rWACC = [S / (S+B)] ´ rS + [B / (S+B)] ´ rB ´ (1 – TC)
= (0.69) (0.15) + (0.31) (0.08) (0.70)
= 0.1209
The weighted average cost of capital is 12.09%.
9.
Apply the CAPM to estimate DDD’s cost of equity, RS. The following equation expresses the firm’s required return, RS, in terms of the firm’s beta, bS, the risk-free rate, RF, and the market return, M.
RS = RF + b ´ (M – RF)
= 0.06+ 1.2 (0.15 – 0.06)
= 0.168
DDD’s cost of equity is 16.8%.
Use the debt-to-equity ratio to determine the weighted average cost of capital. Calculate the equity to value ratio [S / (S+B)] and the debt to value ratio [B / (S+B)] by substitution.
B / S = 1.2
B = S
[S / (S+B)] = [S / (1.2S + S)]
= [S / (2.2 ´ S)]
= 1 / 2.2
= 0.4545
[B / (S+B] = [1.2 ´ S / (S + 1.2 ´ S)]
= [(1.2S) / (2.2 ´ S)]
= 1.2 / 2.2
= 0.5455
Remember that interest on debt is tax deductible at the corporate level, which will lower the firm’s overall cost of capital. Multiply the cost of debt, rB, by (1 - TC) to include the interest tax shield in the weighted average cost of capital.
rWACC = [S / (S+B)] ´ rS + [B / (S+B)] ´ rB ´ (1 – TC)
= (0.4545) (0.168) + (0.5455) (0.09) (1 – 0.35)
= 0.09645
The weighted average cost of capital is 10.83%.
10.
Use the market value of debt to compute the weighted average cost of capital. To calculate the market value of the debt, multiply the book value of EEE’s debt by 120 percent.
B = $50,000,000 ´ 1.3
= $65,000,000
The market value of EEE’s stock is equal to the number of shares outstanding multiplied by the market price per share.
S = 6,000,000 ´ $25
= $150,000,000
The value of the firm is the market value of EEE’s debt plus the market value of EEE’s stock.
V = B + S
= $65,000,000 + $150,000,000
= $215,000,000
Calculate the debt-to-value and equity-to-value ratios. These ratios will be used to compute the weighted average cost of capital.
B / (S + B) = $65,000,000 / $215,000,000
= 0.3023
S / (S + B) = $150,000,000 / $215,000,000
= 0.6977
Use the cost of debt and cost of equity, 10 percent and 16 percent, respectively, and the weights calculated above, to determine the weighted average cost of capital. Remember that interest on debt is tax deductible at the corporate level, which will lower the firm’s overall cost of capital. Multiply the cost of debt, rB, by (1 - TC) to include the interest tax shield in the weighted average cost of capital.
rWACC = [S / (S+B)] ´ rS + [B / (S+B)] ´ rB ´ (1 – TC)
= (0.6977) (0.16) + (0.3023) (0.10) (0.65)
= .1313
The weighted average cost of capital for Company EEE is 13.13%.
11.
a. The average earnings yield is the most basic method of estimating the cost of capital and defines the yield as average expected future earnings () divided by the market value of the firm (V). The current yield is defined as EPS divided by price per share. It is considered superior to the average earnings yield in that the current yield accounts for expected future growth.
b. The cost of retained earnings. KRE, is the rate of return stockholders require on the firm's common stock. It is defined as the dividend yield,, plus the expected growth rate in dividends, g. The cost of new common stock is similar to the cost of retained earnings in that it reflects of rate of return stockholders require; however, flotation costs are incurred when selling new common stock. Thus, the cost of new common stock, K≠, reflects these costs by dividing the cost of retained earnings, KRE by (1 – f) where f represents the percentage flotation cost.
c. The weighted cost of capital (WACC) or therefoe the marginal cost of capital (MCC) is defined as the cost of an additional unit of financing. It is measured as the weighted average of the component sources of financing where the weights are determined by the percentage obtained from each source. The WACC should not be confused with the ACC which the authors refer to as the weighted average of the marginal costs of each interval. (See pp.239-240 for a discussion of WACC, MCC, and ACC.)
d. The marginal cost of capital (MCC) is defined as the cost of an additional unit of financing. See the previous discussion for a comparison to ACC and WACC.
e. The unleveraged cost of capital is that which would exist if the firm were unlevered. A common method of estimating the unlevered cost of capital is to use an unlevered beta in a CAPM formulation. An unlevered beta is the beta for the company's equity if there were no debt financing. A discussion and example of levered and unlevered betas is given on pp. 716 .
12.
The methods of estimating the growth rate are given as follows:
a. The simple growth rate between two successive periods is estimated as follows:
where EPSt = earnings per share at time t.
b. The arithmetic growth rate estimate is just the arithmetic average of individual growth rates calculated for short periods according to the simple growth rate formulation defined above. Specifically,
c. The compound growth rate is estimated as g in the following equation:
d. The fourth growth rate estimation procedure is obtained using ordinary least squares.
loge(EPSt) = a0 + a1t + εt,
The time indicator is t. Instead of EPS, DPS can be used in the equation.
13.
The Chase Manhattan Model defines the cost of capital without leverage as follows: