Assume that the risk-free rate of interest is 5% and the expected rate of return on the market is 15%

Assume that the risk-free rate of interest is 5% and the expected rate of return on the market is 15%. 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 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? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

amount offered in excess=

Solutions

Expert Solution

Value of the firm= PV of perpetual cash flow = C/R_e

Where C= Perpetual cash flow (given as $1,000) and Re= Expected return on equity.

As per CAPM, required rate of return on equity (R_e) = R_f + Beta*(R_m-R_f)

Where R_f= Risk free rate (given as 5%) and R_m= expected return of market (given as 15%)

Plugging the inputs,

If Beta=0.3,

Re= 0.05 + 0.3*(0.15-0.05) = 8%

Value ascertained= $1000/8%= $12,500

If beta= 0.6,

Re= 0.05 + 0.6*(0.15-0.05) = 11%

Value ascertained= $1000/11%= $9,090.91

Amount paid in excess= $12500-$9090.91 = $3,409.09.

It appears that the second part of the question is repetition and hence not attended.

jeff jeffy answered 2 years ago

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