Question

Assume that the risk-free rate of interest is 6% and the expected rate of return on the market is 11%. 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 0.3, when in fact the beta is really 0.6, how much more will I offer for the firm than it is truly worth

Answer 1

Answer:

$4445

Explanation:

Given: Risk Free Rate of Return $R_{f}$ = 6%

          Market Rate of Return $R_{m}$ = 11%

          Beta $B_{1}$ = 0.3

          Actual Beta $B_{2}$ = 0.6

Cost of Capital $K_{e} =$ $R_{f}\ + B_{1} (R_{m}\ -\ R_{f})$

Cost of Capital using estimated Beta = 6 + 0.3 (11 - 6) = 7.5%

Cost of capital using actual Beta = 6 + 0.6 (11- 6) = 9%

Cash flows are received till perpetuity i.e $2000

Valuation of the firm = $\frac{Cash\ Flows}{Cost\ Of\ Capital}$

Valuation using Cost of capital 7.5% = $\frac{2000}{.075}$ = $26,667 approx.

Valuation using Cost of Capital 9% = $\frac{2000}{.09}$ =  $22,222 approx.

Excess value over true worth to be offered = 26,667 - 22,222 =  $4445