Equity risk premium

  1. Ryan Myers, a financial analyst, has been appointed the task of developing a valuation estimate for Colors Fashion Label (CFL), a private, U.S. based firm operating in the fashion industry of the country. Myers gathered the following information to aid his analysis: • The long-term yield on U.S. government bonds is 3.5%. • The historical equity risk premium in the U.S. is 5.6%. • A comparable firm has a beta of 1.35, a debt-to-equity ratio of 1.20, and a tax rate of 40%. • CFL’s tax rate is 33%. • CFL’s Debt/Equity ratio is 0.75. Given the aforementioned information, Myers estimate of CFL’s cost of equity should be closest to: A. 7.896%. B. 9.874%. C. 10.105%. Correct Answer: C 1.35/(1+[(1-0.4)(1.20)] = 0.785 Levered beta for private company: 0.785[1+(1-0.33)(0.75)] = 1.179 Cost of equity: 3.5+ 1.179(5.6) = 10.105%

I though that equity risk premium= beta* (e(rm) - rf)… so why would you multiply your leveraged beta for the equity risk premium… what I did in this problem was identicall from the answer , I had my leverage beta of 1.179 and I calculated the Rm so I made this 1.179 * (Rm - 0.035) = 0.056 --> E(Rm)= 0.0825 and then 0.035 + 1.179 * ( 0.0825 - 0.035 ) = 0.091… obviously is wrong… but I dont understand the why would they multiply levered beta with equity risk premium… I would believe it if it said Market risk premium, right???

Thank you!!! 20 days to go…

Equity risk premium (ERP) = (rm - rf)

The definition of ERP is the excess of market over risk-free return.

CAPM = rf + Beta (ERP)

Thus, answer C is correct.