Question

First and Ten Corporation’s stock returns have a covariance with the market portfolio of .0456. The standard deviation of the returns on the market portfolio is 19 percent and the expected market risk premium is 7.1 percent. The company has bonds outstanding with a total market value of $55.8 million and a yield to maturity of 6 percent. The company also has 5 million shares of common stock outstanding, each selling for $43. The company’s CEO considers the firm’s current debt-equity ratio optimal. The corporate tax rate is 23 percent and Treasury bills currently yield 3.4 percent. The company is considering the purchase of additional equipment that would cost $53 million. The expected unlevered cash flows from the equipment are $17.6 million per year for 5 years. Purchasing the equipment will not change the risk level of the firm.

  

Calculate the NPV of the project.

Answer 1

Variance = 0.19*0.19 = 0.0361

Beta of the security = Covariance with the market portfolio/Variance of the market return

= 0.0456/0.0361

= 1.26

Cost of Equity using CAPM = Rf + β(Rm - Rf)

= 3.4 + 1.26*7.1

= 3.4+8.96

= 12.36%

YTM of the Bond = 6%

Market value of the common stock = 5 millions * $ 43

= $ 215 millions

WACC = (12.36*215+6*55.8)/(215+55.8)

= 2992.2/270.8

= 11.05%

PV of Cash inflows = $ 17.6 millions (PVIFA11.05%, 5yrs)

                                     = $ 17.6 millions * 3.7924

                                     = $ 66.75 millions

NPV = PV of Cash Inflow – Cash Outflow

= $ 66.75 millions – $ 53 millions

= $ 13.75 millions