Question

Suppose your firm operates a chain of video rental stores in South Bend. Your firm’s beta is 1.35, its cost of debt is 6.25% at its current D/E ratio of 0.30, and its marginal tax rate is 21%. Assume a risk-free rate of 3.2%, a market risk premium of 5.8%.

a. You are planning to expand through the purchase of a privately-held rival chain of video rental stores in the SB area. What discount rate should you use for your analysis of this expansion?

b. You are also considering acquiring a privately-held takeout pizza business. A comparable public firm (Pizza World) has a stock beta of 0.95, a D/E ratio of 0.20, and tax rate of 20%. If you will finance the acquisition with your usual mix of debt and equity, what cost of capital should you use for your analysis of this acquisition?

Please show formulas and work!

Answer 1

a]

discount rate = risk free rate + (beta * market risk premium)

discount rate = 3.2% + (1.35 * 5.8%)

discount rate = 11.03%

b]

First, we calculate the appropriate beta to use by unlevering the beta of Pizza World and relevering it for your firm.

Unlevered beta = levered beta / (1 + (1 - tax rate) * (D/E ratio))

Unlevered beta of Pizza World = 0.95 / (1 + (1 - 20%) * 0.20)

Unlevered beta of Pizza World = 0.8190

Levered beta = Unlevered beta * (1 + (1 - tax rate) * (D/E ratio))

Levered beta of your firm = 0.8190 * (1 + (1 - 21%) * 0.30)

Levered beta of your firm = 1.0131

discount rate = risk free rate + (beta * market risk premium)

discount rate = 3.2% + (1.0131 * 5.8%)

discount rate = 9.076%