Walter's Distributors have a cost of equity of 13.84% and an unlevered cost of capital of 12%.The company has €5,000 in debt that is selling at par value.The levered value of the ﬁrm is €12,000 and the tax rate is 34%.What is the pre-tax
Cost of debt?
A)7.92%
B)8.10%
C)8.16%
D)8.84%
E)9.00%

Question

Quizplus · Accepted Answer

Step 1: Calculate the value of equity using the levered value of the firm and the amount of debt:

Equity = Levered Value of the Firm – Debt
Equity = €12,000 – €5,000
Equity = €7,000

Step 2: Calculate the weighted cost of capital using the cost of equity, the unlevered cost of capital, and the pre-tax cost of debt:

Weighted Cost of Capital = Cost of Equity * (Equity / Levered Value of the Firm) + Unlevered Cost of Capital * (Debt / Levered Value of the Firm) * (1 – Tax Rate)
Pre-tax Cost of Debt = (Weighted Cost of Capital – Cost of Equity * (Equity / Levered Value of the Firm)) / (Debt / Levered Value of the Firm)

Plugging in the given values:

Weighted Cost of Capital = 13.84% * (€7,000 / €12,000) + 12% * (€5,000 / €12,000) * (1 – 34%)
Weighted Cost of Capital = 8.57%

Pre-tax Cost of Debt = (8.57% – 13.84% * (€7,000 / €12,000)) / (€5,000 / €12,000)
Pre-tax Cost of Debt = 8.10%

Therefore, the correct answer is B) 8.10%.

Walter's Distributors Have a Cost of Equity of 13