Question

Assume that the risk-free rate of interest is 3% 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 0.8, when in fact the beta is really 1.6, 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.)

Answer 1

Given,
Risk free rate (Rf)	3%
Market return (Rm)	15%
Perpetual cashflow	$1,000
Offered beta	0.8
Actual beta	1.6
We know,
As per CAPM,
Required return= Rf+(Rm-Rf)*Beta
Required return based on the offered beta
Required return= 3+(15-3)*0.8
	12.60%
Required return based on the actual beta
Required return= 3+(15-3)*1.6
	22.20%
Value of the firm= Perpetual cashflow/Required return
Value of the firm based on offered beta= 1000/12.60
	$79.37	(rounded off to two decimal places)
Value of the firm based on actual beta= 1000/22.20
	$45.05	(rounded off to two decimal places)
Therefore,
Extra offered= $(79.37-45.05)
	$34.32	(rounded off to two decimal places)