Assume that the risk-free rate of interest is 3% and the expected rate of return on the market is 14%. 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 0.9, when in fact the beta is really 1.8, how much more will I offer for the firm than it is truly worth

$‭3,365.98‬

Explanation:

Value of firm with beta of 0.9.

First use CAPM to find the required return:

= Risk free rate + beta * (Market return - risk free rate)

= 3% + 0.9 * (14% - 3%)

= 12.9%

Firm Value = Perpertual cashflow / Required return

= 1,000 / 12.9%

= $7,751.94

Value of firm with beta of 1.8.

Required return = 3% + 1.8 * (14% - 3%)

= 22.8%

Value of firm = 1,000 / 22.8%

= $4,385.96

Difference = 7,751.94 - 4,385.96

= $‭3,365.98‬

You would be paying $‭3,365.98‬ than the firm is worth.

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