The Coffee Shop has expected earnings before interest and taxes of $14,600, an unlevered cost of capital of 12%, and debt with both a book and face value of $18,000. The debt has an annual 8.25% coupon. The tax rate is 35%. What is the value of the firm?
A) $81,640
B) $85,383
C) $87,778
D) $90,114
E) $92,309

Question

Quizplus · Accepted Answer

The value of the firm can be calculated using the Modigliani-Miller Proposition I with taxes. The formula is: $V_L = V_U + T_cD$, where $V_L$ is the value of the levered firm, $V_U$ is the value of the unlevered firm, $T_c$ is the corporate tax rate, and $D$ is the value of debt. First, calculate the value of the unlevered firm ($V_U$) using the formula: $V_U = \frac{EBIT(1-T_c)}{r_u}$, where $EBIT$ is the earnings before interest and taxes, $T_c$ is the tax rate, and $r_u$ is the unlevered cost of capital. So, $V_U = \frac{14600(1-0.35)}{0.12} = \frac{9490}{0.12} = 79083.33$. Then, calculate the tax shield ($T_cD$): $T_cD = 0.35 \times 18000 = 6300$. Finally, calculate the value of the levered firm ($V_L$): $V_L = 79083.33 + 6300 = 85383.33$. Rounded to the nearest whole number, the value of the firm is $85,383.

The Coffee Shop Has Expected Earnings Before Interest and Taxes