The Brassy Co. has expected EBIT of $910, debt with a face and market value of $2,000 paying an 8.5% annual coupon, and an unlevered cost of capital of 12%. If the tax rate is 34%, what is the value
Of the Brassy's equity?
A) $3,258
B) $3,685
C) $5,685
D) $6,325
E) $7,005

Question

Quizplus · Accepted Answer

The value of the firm's equity can be calculated using the Modigliani-Miller Proposition with taxes. First, calculate the value of the firm as if it were unlevered: V_unlevered = EBIT * (1 - tax rate) / unlevered cost of capital = $910 * (1 - 0.34) / 0.12 = $5,000. Then, calculate the tax shield on debt: Tax shield = tax rate * debt = 0.34 * $2,000 = $680. The value of the levered firm is V_levered = V_unlevered + Tax shield = $5,000 + $680 = $5,680. The value of equity is V_levered - debt = $5,680 - $2,000 = $3,680, which is closest to option B ($3,685).