You are evaluating the potential purchase of a small business currently generati

Question

You are evaluating the potential purchase of a small business currently generating $45,000 of after-tax cash flow (D0 = $45,000). On the basis of a review of similar-risk investment opportunities, you must earn an 19% rate of return on the proposed purchase. Because you are relatively uncertain about future cash flows, you decide to estimate the firm’s value using several possible assumptions about the growth rate of cash flows.
a. What is the firm’s value if cash flows are expected to grow at an annual rate of 0% from now to infinity?
b. What is the firm’s value if cash flows are expected to grow at a constant annual rate of 9% from now to infinity?
c. What is the firm’s value if cash flows are expected to grow at an annual rate of 13% for the first 2 years, followed by a constant annual rate of 9% from year 3 to infinity?

Explanation / Answer

a) Value of the company woudl be given by

= Cashflows/requires arte of return

=45000/.19

=

b) Value of the company woudl be given by

Cashflow in year 1/(R-g)

=45000*1.09/(.19-.09)

=490500

c) First let us calculate the present value for first two cashflows

Present value of cashlows =91017.23

Cashflows in year 3 =

Value of the cashfows to infinit at year 2 = 62631.95/(.19-.09)

=626319.5

The value of at year 0 of these cashflows ==

626319.5/(1.19)^2 =

Value ofthe firm =

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