### CFA Practice Question

The management of Clay Industries have adhered to the following capital structure: 50% debt, 45% common equity, and 5% perpetual preferred equity. The following information applies to the firm:

Before-tax cost of debt = 9.5%
Combined state/federal tax rate = 35%
Expected return on the market = 14.5%
Annual risk-free rate of return = 6.25%
Historical Beta coefficient of Clay Industries Common Stock = 1.24
Expected annual preferred dividend = \$1.55
Preferred stock net offering price = \$24.50
Annual common dividend (expected) = \$0.80
Common stock price = \$30.90
Expected growth rate = 9.75%

Given this information, and using the discounted cash flow (DCF) approach, what is the weighted average cost of capital for clay industries?
A. 8.96%
B. 9.97%
C. 12.34%
Explanation: The calculation of the weighted average cost of capital is as follows: {fraction of debt * [yield to maturity on outstanding long-term debt][1- combined state/federal income tax rate]} + {fraction of preferred stock * [annual dividend/net offering price]} + {fraction of common stock * cost of equity}. The cost of common equity can be calculated using three methods, the capital asset pricing model (CAPM), the dividend-yield-plus-growth-rate (or discounted cash flow) approach, and the Bond-Yield-Plus-Risk-Premium approach. In this example, you are asked to calculate the cost of common equity using the discounted cash flow, or dividend-yield-plus-growth-rate approach.

To calculate the cost of equity using this approach, take the expected annual dividend on common equity (\$0.80) divided by the market price of common stock (\$30.90), and add the expected growth rate (9.75%) to this figure. Using this method, the cost of common equity is found to be 12.34%. The after-tax cost of debt can be found by multiplying the yield to maturity on the firm's outstanding long-term debt (9.5%) by (1 -tax rate). Using this method, the after-tax cost of debt is found as 6.175%. The calculation of the cost of perpetual preferred stock is relatively straightforward, simply divide the annual preferred dividend by the net offering price. Using this method, the cost of preferred stock is found as 6.327%. Incorporating these figures into the WACC equation gives the answer of 8.957%.

User Comment
masha are we not supposed to take D1 and thus adjust the annual common dividend by the growth rate?
shasha Q said it's ANNUAL common dividend, means the company keeps dividend unchanged every year. for g, it's the company's business growth rate, of course, quite often, it's the same as dividend growth rate, IF, its dividend does grows yearly, which is not the case in this Q.
Franz Yes you must use D1 - multiply D0 * 1+g
fanfare shasha, with some elementary series math it can be shown that the g applies to growth of dividend not the growth of the business. The latter is irrelevant in DCF mehtod.
danlan 12.34%*0.45+6.175%*0.5+6.327%*0.05
wollogo Not necessarily fanfare, this is only the case if you assume a constant dividend payout ratio. Otherwise you can have a different growth rate from earnings and dividends.
ricardo152 whya cannot wbe used the CAPM formula for cost of equity?
SSPatel the question says using the DCF approach
Kuki agreed the question asks for DCF approach. I'm just curious as to why the cost of equity ke is different under the 2 approaches. Shouldn't they be the same.. ANYONE?
dlukas No, they're not the same under all the approaches. You're using totally different and unrelated inputs, so the output is going to be different.
CFunder I agree with dlukas...the method is the dividend discount model.
JeffAu the key word is "expected"......damn it
SCBAnalyst why do we add the growth rate?
farhan92 my brain was way too frazzled to have a proper shot at this!
stevo no way this take 90 sec
Mjw1095 Farhan completely agree this question is a pucke