Consider a firm F with the following features:

EBIT is 200 at time 1 Then, EBIT grows at a 1% annual rate (perpetuity).

Regardless of firm F's leverage, firm F's probability of default is zero.

Regardless of firm F's leverage, the covariance between firm F's stock return and the market return is 0.01. The corporate tax rate is 20%.

The expected market return is 10%. The volatility of the market return is 15%. The risk-free rate is 2%.

The so-called Weighted Average Cost of Capital (WACC) is defined as follows: W ACC = S S + B rS + B S + B (1 Tc)rB = 1 1 + L rS + L 1 + L (1 Tc)rB, where B is the firm's debt, S is the firm's equity, L = B S is the firm's leverage, rS is the firm's cost of equity, rB is the firm's cost of debt, and Tc is the firm's corporate tax rate.

a) (2 points) Compute the Weighted Average Cost of Capital (W ACCF1 ) when firm F's leverage is L = 1.

(b) (2 points) What is today's value of firm F (AF1 ) if firm F's leverage is L = 1? Hint: 1) Compute the cash-flows to the shareholders of a comparable (exact same features as F except the capital structure) unlevered firm. 2) Assume that discounting these cash-flows at the WACC provides the value of the firm.

c) (2 points) Compute the Weighted Average Cost of Capital (W ACCF2 ) when firm F's leverage is L = 2.

(d) (2 points) What is today's value of firm F (AF2 ) if firm F's leverage is L = 2? Hint: 1) Compute the cash-flows to the shareholders of a comparable (exact same features as F except the capital structure) unlevered firm. 2) Assume that discounting these cash-flows at the WACC provides the value of the firm.

(e) (2 points) If you were a manager of firm F, would you choose a leverage of 1 or 2? Justify

(f) (2 points) More generally, what is the optimal choice of leverage (L )

Assume from now on that firm F's leverage is optimal and therefore equal to L .

(g) (2 points) Show that the optimal Weighted Average Cost of Capital is W ACCF = 1.6%

h) (2 points) What is today's value of firm F (AF )?

Hint: 1) Compute the cash-flows to the shareholders of a comparable (exact same features as F except the capital structure) unlevered firm. 2) Assume that discounting these cash-flows at the WACC provides the value of the firm.

(i) (2 points) What is today's value of firm F's debt (BF )?

(j) (2 points) What is today's value of firm F's equity (S F )?

(k) (2 points) Provide a general formula/expression for the Weighted Average Cost of Capital of firm F (W ACC )? Hint: the formula should depend on the corporate tax rate, Tc, and the risk-free rate, rf , only.

Answer rating: 100% (QA)

Here are the answers to the questions a 2 points Compute the Weighted Average Cost of Capital WACC F... View the full answer