Suppose your firm has decided to use a divisional WACC approach to analyze projects. The firm currently has 2 divisions, A and B, with betas for each division of 0.5 and 1.5, respectively. If all current and future projects will be financed with half debt and half equity, and if the current cost of equity (based on an average firm beta of 1.0 and a current risk-free rate of 5 percent) is 14 percent and the after-tax yield on the company's bonds is 6 percent, what are the WACCs for divisions A and B?
A) 7.75 percent; 12.25 percent
B) 8.75 percent; 12.00 percent
C) 9.25 percent; 11.00 percent
D) 8.95 percent; 10.15 percent

Question

Quizplus · Accepted Answer

The WACC for each division can be calculated using the formula: WACC = (E/V) * Re + (D/V) * Rd * (1 - Tc), where E is the market value of the equity, D is the market value of the debt, V is the total market value of the firm (E + D), Re is the cost of equity, Rd is the after-tax cost of debt, and Tc is the corporate tax rate. Given that the financing is half debt and half equity (E/V = D/V = 0.5), and assuming a corporate tax rate of 0%, the formula simplifies to WACC = 0.5 * Re + 0.5 * Rd. For division A, with a lower beta of 0.5, the cost of equity would be lower than the firm's average, and for division B, with a higher beta of 1.5, the cost of equity would be higher. Given the provided cost of equity (14%) is based on an average beta of 1.0, and the risk-free rate is 5%, we can adjust the cost of equity for each division using the CAPM model: Re = Rf + beta*(Rm-Rf), where Rm - Rf is the market risk premium. Assuming the market risk premium is 9% (14% - 5%), for division A, Re = 5% + 0.5*(9%) = 9.5%, and for division B, Re = 5% + 1.5*(9%) = 18.5%. Plugging these into the simplified WACC formula: Division A WACC = 0.5 * 9.5% + 0.5 * 6% = 7.75%, Division B WACC = 0.5 * 18.5% + 0.5 * 6% = 12.25%.

Suppose Your Firm Has Decided to Use a Divisional WACC