A ﬁrm has zero debt in its capital structure.Its overall cost of capital is 10%.The ﬁrm is considering a new capital structure with 60% debt.The interest rate on the debt would be 8%.Assuming there are no taxes or other
Imperfections, its cost of equity capital with the new capital structure would be ______ .
A)9%
B)10%
C)13%
D)14%
E)None of the above.

Question

Quizplus · Accepted Answer

To find the cost of equity capital with the new capital structure, we can use the following formula:

Cost of Equity = Risk-Free Rate + Beta * Equity Risk Premium

Since the firm has no debt in its current capital structure, the overall cost of capital is equal to the cost of equity capital, which is 10%.

With the new capital structure of 60% debt, we can use the following formula to find the new cost of capital:

Cost of Capital = Weight of Equity * Cost of Equity + Weight of Debt * Cost of Debt

We know that the weight of debt is 60% and the cost of debt is 8%. The weight of equity is 40% (100% - 60%). We can plug in these values and solve for the new cost of equity:

0.10 = 0.4 * Cost of Equity + 0.6 * 0.08
0.10 = 0.4 * Cost of Equity + 0.048
0.052 = 0.4 * Cost of Equity
Cost of Equity = 0.052 / 0.4
Cost of Equity = 0.13 or 13%

Therefore, the answer is C) 13%.

A ﬁRm Has Zero Debt in Its Capital Structure