I am buying a firm with an expected perpetual cash flow of 5

I am buying a firm with an expected perpetual cash flow of $560 but am unsure of its risk. If I think the beta of the firm is zero, when the beta is really 1, how much more will I offer for the firm than it is truly worth? Assume the risk-free rate is 7% and the expected rate of return on the market is 14%. (Input the amount as a positive value.)

Present value difference $____

Solution

If beta = 0

ke = Rf + beta(Rm-Rf)

ke = 7% + 0(14% - 7%) = 7% + 0 = 7%

present value of firm = perpetual cash flow/ ke = 560/0.07 = $8000

If beta = 1

ke = Rf + beta(Rm-Rf)

ke = 7% + 1(14% - 7%) = 7% + 7% = 14%

present value of firm = perpetual cash flow/ ke = 560/0.14 = $4000

Answer : Present value difference = $8000 -$4000 =$4000

$4000 is more offered errorneously