You are considering acquiring a firm that you believe can generate expected cash flows of

You are considering acquiring a firm that you believe can generate expected cash flows of $28,000 a year forever. However, you recognize that those cash flows are uncertain.

a.	Suppose you believe that the beta of the firm is 2.2. How much is the firm worth if the risk-free rate is 5% and the expected rate of return on the market portfolio is 8%? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Value of the firm

$

b.	How much is the overvalue of the firm if its beta is actually 2.5? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Overvalue

$

Explanation:

Some values below may show as rounded for display purposes, though unrounded numbers should be used for the actual calculations.

a.

The expected cash flows from the firm are in the form of a perpetuity. The discount rate is:

rf + β(rm − rf) = 5% + [2.2 × (8% − 5%)] = 11.6%

Therefore, the value of the firm would be:

P0 =	Cash flow	=	$28,000	= $241,379.31
	r		0.116

b.

If the true beta is actually 2.5, the discount rate should be:

rf + β(rm − rf) = 5% + [2.5 × (8% − 5%)] = 12.5%

Therefore, the value of the firm is:

P0 =	Cash flow	=	$28,000	= $224,000.00
	r		0.125

By underestimating beta, you would overvalue the firm by:

$241,379.31 − $224,000.00 = $17,379.31