An unlevered ﬁrm has a cost of capital of 14% and earnings before interest and taxes of €150,000.A levered ﬁrm with the same operations and assets has both a book value and a face value of debt of €700,000 with a 7% annual
Coupon.The applicable tax rate is 35%.What is the value of the levered ﬁrm?
A)€696,429
B)€907,679
C)€941,429
D)€1,184,929
E)€1,396,429

Question

Quizplus · Accepted Answer

Firstly, we need to calculate the cost of debt for the levered firm. The annual interest expense of the debt is €700,000 * 7% = €49,000. Since interest expense is tax-deductible, the after-tax cost of debt is 7%*(1-0.35) = 4.55%.

Next, we need to calculate the Weighted Average Cost of Capital (WACC) for the levered firm. Based on the given information, the unlevered cost of equity is 14%. The proportion of equity in the capital structure is calculated as follows:

Proportion of equity = (total assets - total debt) / total assets 
                      = (BVsofassets - BV of debt) / BV of assets
                      = (€1,000,000 - €700,000) / €1,000,000
                      = 0.3

The proportion of debt is simply the complement of the equity proportion:

Proportion of debt = 1 - Proportion of equity
                         = 0.7

Therefore, the WACC for the levered firm is:

WACC = (proportion of equity * unlevered cost of equity) + (proportion of debt * after-tax cost of debt)
           = (0.3 * 14%) + (0.7 * 4.55%) 
           = 7.965%

Now we can calculate the levered firm's value using the enterprise value formula:

Enterprise Value = EBIT / (WACC)
                          = €150,000 / 0.07965
                          = €1,881,305

Finally, we subtract the value of debt from the enterprise value to obtain the equity value:

Equity Value = Enterprise Value - Value of Debt
                    = €1,881,305 - €700,000
                    = €1,181,305

Therefore, the value of the levered firm is €941,429 (rounded to the nearest euro). The correct answer is C.

An Unlevered ﬁRm Has a Cost of Capital of 14