Suppose two firms are exactly the same except Firm A has no debt in its capital structure and Firm B has 50% debt in its capital structure. Firm A has a WACC of 15%. If Firm B's cost of debt is 10% (after-tax value), what must Firm B's cost of equity be to have the same WACC as Firm A?

Question

Quizplus · Accepted Answer

For Firm A: WACC = Cost of Equity
For Firm B: WACC = (E/V) * Cost of Equity + (D/V) * Cost of Debt * (1-tax rate)
where E= equity, D= debt, V= total value of the firm = E + D, tax rate = assumed to be 0.

Since Firm B has 50% debt in its capital structure, D/V = 0.5 and E/V = 0.5 as well. Given that WACC is same for both firms, we have:

15% = 0.5 * Cost of Equity + 0.5 * 10%
=> Cost of Equity = (15% - 0.05) / 0.5 = 0.20 (or 20%) after-tax value.
Therefore, the best choice is B.

Suppose Two Firms Are Exactly the Same Except Firm a Has