I am buying a firm with an expected perpetual cash flow of $1,500 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 6% and the expected rate of return on the market is 16%. (Input the amount as a positive value.) Present value difference $
Present value difference $ 12,750 0.1%
Explanation
If beta is zero, the cash flow should be discounted at the risk-free rate, 6%:
PV = $1500/0.06
= $25,000
If, however, beta is actually equal to 1, the investment should yield 16%, and the price paid for the firm should be
: PV = $1500/0.16
= $9,375
The difference ($15,625) is the amount you will overpay if you erroneously assume that beta is zero rather than 1
If beta Last for one year
Pv (b=0) = 1500/1.06=1415
Pv (b=1) = 1500/1.16 =1213
With the difference of 122
