Question

Check my work Problem 9-18 10 points Assume that the risk-free rate of interest is 4% and the expected rate of return on the market is 13%. I am buying a firm with an expected perpetual cash flow of $2,000 but am unsure of its risk. If I think the beta of the firm is 0.6, when in fact the beta is really 1.2, how much more will I offer for the firm than it is truly worth? (Do not round Intermediate calculations. Round your answer to 2 decimal places.) eBook Amount offered in excess Print References

Answer 1

Risk-free rate = RF = 4%

Expected rate of return on market = RM = 13%

Case I : Beta for the firm is 0.6

Expected return for the firm can be calculated using the CAPM equation

Expected return = r1 = RF + β*(RM-RF) = 4% + 0.6*(13%-4%) = 9.4%

Prepetual Cashflow = C = $2000

Present value of a prepetuity = C/r

Value of the firm if beta is 0.6 = V1 = C/r1 = 2000/9.4% = 21276.5957446809

Case II: Beta of the firm is 1.2

Expected return for the firm can be calculated using the CAPM equation

Expected return = r2 = RF + β*(RM-RF) = 4% + 1.2*(13%-4%) = 14.8%

Perpetual cashflow = C = $2000

Value of the firm if beta is 1.2 = V2 = C/r2 = 2000/14.8% = 13513.5135135135

Actual value of the firm = V2 = $13513.5135135135

Value offered by me = V1 = $21276.5957446809

Amount oferred in Excess = V2 - V1 = 21276.5957446809 - 13513.5135135135 = 7763.08223116734 ~ 7763.08 (Rounded to two decimals)

Therefore, I am offering $7763.08 more for the firm than its truly worth

Answer -> Amount offered in excess = 7763.08