5F.12
12. Let's say Nike wants to diversify its business. It is planning on buying Wild Oats Markets (the company that owns Oasis Grocery Markets). Nike is financed 34% with debt and 66% with equity. Wild Oats is financed 58% with debt and 42% with equity. Nike's equity beta is 1.20 and Wild Oats' beta is 0.97. They both have debt betas that are 0. The risk-free rate is 4% and the expected return on the market is 14%. What should be your discount rate for discounting the cash flows for the decision of whether to buy Wild Oats? Justify your choice. [8]
You want Wild Oats' asset beta, since you're discounting Wild Oats' cash flows. You know what Wild Oats' equity and debt betas are and what Wild Oats' capital structure looks like, so you can figure out WO's asset beta:
Now you can use the CAPM to map the risk (beta) into required return:
E[Rwo]=0.04+.4074(.14-.04)=0.08074
so your discount rate should be 8.074%