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Hi
Would you be able to help me figuering out the correct answer for this question, please?Dominique Company’s capital structure consists entirely of long-term debt and common equity. The cost of capital for each component is shown below.
Long-term debt 8%
Common equity 15%
Dominique pays taxes at a rate of 40%. If Dominique’s weighted average cost of capital is 10.41%, what proportion of the company’s capital structure is in the form of long-term debt?Select one:
a. 55%
b. 34%
c. 45%
d. 66%I tried to rearrange WACC = Ke(E/E+D) + Kd(D/E+D), but do not get the same answer as the sample explanation where they use WACC= .15X + .048 (1-X) = .1041.
I don’t understand why if (E/E+D) equals X, why (D/E+D) becomes (1-X)?I greatly appreciate your help!
Jenny
Its only john who explain you the correct way to deal with this Mcq..
But i just want to confirm that the correct Option is C=45%The cost of equity is 15%, the cost of debt is 8% x (1 – 0.4) = 4.8%
With regard to the proportions, just suppose that debt was 10% (or 0.1) of the total capital. That would mean that equity was 100% – 10% = 90% (or 1 – 0.1 = 0.9) of the total capital.
So if debt is a proportion X of the total, then equity is a proportion (1 – X) of the total.
(Your printed answer has let X be the proportion of equity and therefore the proportion of debt is 1-X. You end up with the same final answer, but since the question asks for the proportion of debt I would let X be the proportion of debt and therefore 1-X is the proportion of equity).I assume you are happy with the rest of the workings in the answer, but for khuramch’s benefit…..
If x is the proportion of debt, then:15(1-x) + 4.8x = 10.41
15 – 15x + 4.8x = 10.41
10.2x = 4.59
x = 4.59/10.2 = 0.45 or 45%
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