WACC Approach

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 Fs leverage, firm Fs probability of default is zero.

Regardless of firm Fs leverage, the covariance between firm Fs 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: WACC = 1/(1+L)rS+L/(1+L)(1-Tc)rB, where B is the firms debt, S is the firms equity, L = B/S is the firms leverage, rS is the firms cost of equity, rB is the firms cost of debt, and Tc is the firms corporate tax rate.

(a) Compute the Weighted Average Cost of Capital (WACC^F1 ) when firm Fs leverage is L = 1.

(b) What is todays value of firm F(A^F1 ) if firm Fs 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) Compute the Weighted Average Cost of Capital (W ACC^F2 ) when firm Fs leverage is L = 2.

(d) What is todays value of firm F (A^F2 ) if firm Fs 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) If you were a manager of firm F, would you choose a leverage of 1 or 2? Justify.

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

Assume from now on that firm Fs leverage is optimal and therefore equal to L.

(g) Show that the optimal Weighted Average Cost of Capital is W ACC^F*= 1.6%

(h) What is todays value of firm F (A^F*)? 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) What is todays value of firm Fs debt (B^F*)?

(j) What is todays value of firm Fs equity (S^F* )?

(k) 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.