Question

You are given the following information: EBIT (for firms L and U in perpetuity) = $300,000; corporate tax rate (T) = 30%; cost of equity for firm U (K_su or r_su) = 10%; cost of debt for firm L (K_d or r_d) = 8%; level of debt for firm L (D) = $1,200,000.

What are the WACCs of firms U and  L, respectively, under M&M theory with corporate taxes?

	1.	10% (U), 8.53% (L)
	2.	10%(U), 8.10% (L)
	3.	11.33% (U), 10.53% (L)
	4.	10% (U), 11.33% (L)

Answer 1

Answer is “10% (U), 8.53% (L)”

Firm U:

Value of Firm U = EBIT * (1 - Tax Rate) / Unlevered Cost of Equity
Value of Firm U = $300,000 * (1 - 0.30) / 0.10
Value of Firm U = $300,000 * 0.70 / 0.10
Value of Firm U = $2,100,000

WACC of Firm U = Unlevered Cost of Equity
WACC of Firm U = 10.00%

Firm L:

Value of Firm L = Value of Firm U + Tax Rate * Value of Debt
Value of Firm L = $2,100,000 + 0.30 * $1,200,000
Value of Firm L = $2,100,000 + $360,000
Value of Firm L = $2,460,000

Value of Equity = Value of Firm L - Value of Debt
Value of Equity = $2,460,000 - $1,200,000
Value of Equity = $1,260,000

Weight of Debt = Value of Debt / Value of Firm L
Weight of Debt = $1,200,000 / $2,460,000
Weight of Debt = 0.4878

Weight of Equity = Value of Equity / Value of Firm L
Weight of Equity = $1,260,000 / $2,460,000
Weight of Equity = 0.5122

Debt-Equity Ratio = Value of Debt / Value of Equity
Debt-Equity Ratio = $1,200,000 / $1,260,000
Debt-Equity Ratio = 0.95238

Levered Cost of Equity = Unlevered Cost of Equity + (Unlevered Cost of Equity - Cost of Debt) * Debt-Equity Ratio * (1 - Tax Rate)
Levered Cost of Equity = 0.10 + (0.10 - 0.08) * 0.95238 * (1 - 0.30)
Levered Cost of Equity = 0.10 + 0.0133
Levered Cost of Equity = 0.1133 or 11.33%

WACC = Weight of Debt * Cost of Debt * (1 - Tax Rate) + Weight of Equity * Levered Cost of Equity
WACC = 0.4878 * 0.08 * (1 - 0.30) + 0.5122 * 0.1133
WACC = 0.0853 or 8.53%