Question

In Problems 21–23 below, assume the risk-free rate is 8% and the expected rate of return on the market is 18%.

I am buying a firm with an expected perpetual cash flow of $1,000 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?

Short answer

The correct answer would be: $ 6,944.44

Step-by-step solution

Given Information

P ₀ = $ 1,000

If beta is zero, the cash flow should be discounted at the risk-free rate, 8%:

PV = Perpetual cash flow/ Discount Rate

PV = $1,000/0.08 = $12,500

Calculation of PV if beta is equal to 1 and finding difference

If beta is actually equal to 1, the investment should yield 18%, and

The price paid for the firm should be:

PV = Perpetual cash flow/ Discount Rate

PV = $1,000/0.18 = $5,555.56

The difference in amount in case of erroneous overpayment: $5,555.56 - $12,500 = $ 6944.44

Therefore the overpayment in the above scenario = $ 6944.44