Question: You are evaluating the potential purchase of a small business currentl

Question

Question: You are evaluating the potential purchase of a small business currently generating $41,500 of after-tax cash flow (D0 = $41,500). 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 firms value using several possible assumptions about the growth rate of cash flows.

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

b. What is the firms value if cash flows are expected to grow at a constant annual rate of 9% from now to infinity?

c. What is the firms value if cash flows are expected to grow at an annual rate of 14% for the first 2 years, followed by a constant annual rate of 9% from year 3 to infinity?

Explanation / Answer

Required Rate of Return = 18% Current After Tax Cash flow =D0=               41,500 a Firm value when after tax cash flows expected to grow @0% till infinity = 41500/18%= $ 230,555.56 b If the after Tax cash flow grows @9% (g=9%) till infinity   Firm Value = 41500*1.09/(0.18-0.09)= $ 502,611.11 c when g=14% for 2years and 9% from yr 3 to infinity Year 0 Year 1 Year 2 Year 3 After Tax Cash Flow               41,500          47,310            53,933               58,787 Terminal Value of After Tax cash flow at Yr 3 end=58787*1.09/(0.18-0.09)             711,981 Total Future Cash flows          47,310            53,933             770,768 PV factor @18%                         1            0.847              0.718                 0.609 PV of Cash flows            40,093            38,734             469,113 Total PV of cash flows=Firm Value= $ 547,940.68

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