Common stock valuelong dash—All growth modelsPersonal Finance ProblemYou are eva

Question

Common stock

valuelong dash—All

growth modelsPersonal Finance ProblemYou are evaluating the potential purchase of a small business currently generating 44,000 of after-tax cash flow (Upper D 0D0equals=$44,000). On the basis of a review of similar-risk investment opportunities, you must earn a rate of return of 14% 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 5%

from now to infinity?

c.What is the firm's value if cash flows are expected to grow at an annual rate of 9%

for the first 2 years, followed by a constant annual rate of 5%

from year 3 to infinity

Explanation / Answer

a) Value of the firm = CFAT1 / Re

Where Cash flow after tax (CFAT1) = 44,000

Re = 14%

Value of the firm = 44000 /.14 = $ 314,285.71

b) Value of the firm = CFAT1 / Re-g

CFAT1 = CFAT0 * (1+g)

= 44000 * 1.05 = 46, 200

Re= 14%

g = 5%

Value of the firm = 46200 / (.14 - .05) = 513,333.33

c)

For constant growth period

IV 2 = CFAT 3 / ( Re-g)  

Where

CFAT 3 = 52,276.40*1.05 = 54,890.22

Re= 14%

g = 5%

IV 2 = 54,890.22 / (.14-.05) = 6,09,891.33

PV @14% for 2 years of IV2

609,891.33 / (1.14)2

= 469,291.58

Value of the firm = 82,295.50 + 469,291.58

= 551,587.08

Year CFAT PV factor @ 14% PV of CFAT 1 47,960.00 0.8772 42070.51 2 52,276.40 0.7695 40224.99 TOTAL 82,295. 50

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