Question

You are considering acquiring a firm that you believe can generate expected cash flows of $12,000 a year forever. However, you recognize that those cash flows are uncertain.

a.	Suppose you believe that the beta of the firm is 0.5. How much is the firm worth if the risk-free rate is 4% and the expected market risk premium is 8%? (Round your answer to the nearest cent.)
	The value of the firm    $

b.	By how much will you misvalue the firm if its beta is actually 0.8? (Round your answer to the nearest cent. Enter your answer as positive value.)
	By underestimating beta, you would (Click to select) undervalueovervalue the firm by $_____

Answer 1

Answer a

Step 1: Calculation of cost of equity using Capital Asset Pricing Model

Using Capital Asset Pricing Model

Cost of Equity Ke = Rf + b ( Rm – Rf )

Where,

Rf – Risk free return = 4%

b – Beta = .5

Rm – Expected return on market portfolio

Rm-Rf – Market risk premium = 8%

Cost of Equity Ke = 4 + .5*8

= 4 + 4

= 8%

Value of Firm = Perpetual Cash flow / Cost of Equity

= 12000/.08

= 150000

Answer b

Cost of Equity Ke = 4 + .8*8

= 4 + 6.4

= 10.4%

Value of Firm = Perpetual Cash flow / Cost of Equity

= 12000/.104

= 115384.62

By underestimating beta, you would overvalue the firm by $34615.38 (150000-115384.62)