What proportion of the firm is financed by debt for a firm that expects a 15% return on equity, a 12% return on assets, and a 10% return on debt? The tax rate is 25%.

Question

Quizplus · Accepted Answer

We can use the formula for calculating the weighted average cost of capital (WACC) to find out the proportion of the firm that is financed by debt:
WACC = (E/V)Re + (D/V)Rd(1-T)
Where:
E = Market value of equity
D = Market value of debt
V = Total market value of the firm (= E + D)
Re = Cost of equity
Rd = Cost of debt
T = Tax rate

We can rearrange the formula to solve for D/V:
D/V = (WACC - Re) / (Rd(1-T) - WACC + Re)
Plugging in the given values, we get:
WACC = 0.15
Re = 0.15
Rd = 0.1
T = 0.25

D/V = (0.15 - 0.15) / (0.1(1-0.25) - 0.15 + 0.15)
D/V = 0.67, or 2/3

Therefore, 2/3 of the firm is financed by debt. Answer is D).

What Proportion of the Firm Is Financed by Debt for a Firm