# Estimating the fair value of a firm

You are evaluating the potential purchase of a small business currently generating $42,500 of after-tax cash flow (D=42,500). On the basis of a review of similar-risk investment opportunities, you must earn an 18% 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 7% from now to infinity?

c. What is the firm's value if cash flows are expected to grow at an annual rate of 12% for the first 2 years, followed by a constant annual rate of 7% from year 3 to infinity?

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#### Solution Preview

a. What is the firm's value if cash flows are expected to grow at an annual rate of 0% from now to infinity?

Growth Rate=g=0%

Required rate of return=r=18%

Current Cash Flow=Do=$42500

Value of firm=Do*(1+g)/(r-g)=42500*(1+0%)/(18%-0%)=$236,111.11

b. What is the firm's value ...

#### Solution Summary

Solution describes the steps to estimate the firm's value under different conditions/assumptions.