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 $46, 000 of after tax cash flow (D_0 = $46, 000). On The basis of a review of similar-risk investment opportunities, you must earn a rate of return of 12% on the proposed purchase. Because you are relatively uncertain about future cash flows, you decide to estimate the firm's value using two possible assumptions about the growth rate of cash flows. What is the firm's value if cash flows are expected to grow at an annual rate of 0% from now to infinity? What is the firm's value if cash flows are expected to grow at a constant rate of 7% from now to infinity? What is the firm's value if cash flows are expected to grow at an annual rate of 10% for the first 2 years. followed by a constant annual rate of 7% from year 3 to infinity? The firm's value if cash flows are expected to grow at an annual rate of 0% from now to infinity is $ (Round to The nearest dollar.) The firm's value if cash flows are expected to grow at a constant rate of 7% from now to infinity is (Round to The nearest dollar.) The farm's value if cash flows are expected to grow at an annual rate of 10% for the first 2 years, followed by a constant annual rate of 7% from year 3 to infinity is $ (Round to the nearest dollar.)

Explanation / Answer

CF0=46000 r=12% a) g=0% hence Firm's Value= CF1/(r-g)=46000/(0.12-0)= 383333.3 b) g=7% hence Firm's Value= CF1/(r-g)=46000*1.07/(0.12-0.07)= 984400 c) Growth rate (g) Year 1& 2 (g1)= 10% Year 3 onwards(g2)=7% hence Firm's value=CF1/(1+r) +CF2/(1+r)^2+CF3/((r-g)(1+r)^2) CF1=CF0*(1+g1)=46000*(1+0.1)= 50600 CF2=CF0*(1+g1)^2=46000*(1+0.1)^2= 55660 CF3=CF2*(1+g2)=55660*(1+0.07)= 59492 Firm's Value=50600/(1.12)+55660/(1.12^2)+59492/((1.12^2)*(0.12-0.07))= 1038084

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