New Schools is an all-equity company with an expected EBIT of $94,000 every year forever. The company can borrow at 7.4 percent while its cost of equity is 13.9 percent. What will be the value of the company if it converts to 50 percent debt given its total tax rate of 24 percent?
A) $500,916
B) $575,632
C) $477,407
D) $480,690
E) $532,408

Question

Quizplus · Accepted Answer

To calculate the value of the company if it converts to 50 percent debt, we use the Modigliani-Miller Proposition I with taxes. The value of the levered firm (V_L) is equal to the value of the unlevered firm (V_U) plus the tax shield on debt (Tc*D), where Tc 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 = EBIT(1-Tc) / r_0, where r_0 is the cost of equity for an all-equity firm. Here, EBIT = $94,000, Tc = 24%, and r_0 = 13.9%.V_U = $94,000 * (1 - 0.24) / 0.139 = $66,160 / 0.139 = $476,115.83Since the firm converts to 50 percent debt, we calculate the tax shield on debt. Assuming the firm's value is initially similar to the unlevered firm's value, half of this would be debt, so D = $476,115.83 / 2 = $238,057.91. The tax shield on debt is Tc*D = 0.24 * $238,057.91 = $57,133.90.Finally, calculate the value of the levered firm (V_L) = V_U + Tc*D = $476,115.83 + $57,133.90 = $533,249.73.The closest answer provided is E) $532,408, but due to a slight discrepancy in rounding or calculation steps, the exact answer calculated here doesn't match perfectly with the provided options. However, based on the methodology and closest match, the intended correct answer seems to be E.

New Schools Is an All-Equity Company with an Expected EBIT