Common stock value All growth models Personal Finance Problem You are evaluating
ID: 2542118 • Letter: C
Question
Common stock value All growth models Personal Finance Problem You are evaluating the potential purchase of a small business currently generating $41,500 of after-tax cash flow (Do $41,500). On the basis of a review of similar-risk investment opportunities, you must earn a rate of return of 18% 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. 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 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 12% for the first 2 years, followed by a constant annual rate of 9% from year 3 to infinity?Explanation / Answer
A.
Firms value = Next year cash flow D1/ required rate
= 41500/.18
= 230555.56
B.
Firms value = Next year cash flow D1/ required rate – dividend growth rate
= 41500 (1 + 0.09)/ (.18 – 0.09)
= 45235/0.09
= 502611.11
C.
Year 1 cash flow = 41500* 1.12 = 46480
Year 2 cash flow = 46480 * 1.12 = 52057.6
Year 3 cash flow = 52057.6 * 1.09 = 56742.78
After year 2 dividend will grow in the form of a perpetuity.
PV of perpetuity = 56742.78/.18 – 0.09
= 630475.33
Year
Cash flow
PV factor @ 18%
PV of cash flow
1
46480
0.84746
39389.83051
2
52057.6
0.71818
37386.95777
2
630475.33
0.71818
452797.5654
Total
529574.35
Firms value = 529574.35
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Year
Cash flow
PV factor @ 18%
PV of cash flow
1
46480
0.84746
39389.83051
2
52057.6
0.71818
37386.95777
2
630475.33
0.71818
452797.5654
Total
529574.35
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