Common stock value long dash— All growth models Personal Finance ProblemYou are

Question

Common stock

valuelong dash—All

growth modelsPersonal Finance ProblemYou are evaluating the potential purchase of a small business currently generating

$44500

of after-tax cash flow

(Upper D 0D0equals=$44,500).

On the basis of a review of similar-risk investment opportunities, you must earn a rate of return of

17%

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

6%

from now to infinity?

c.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

6%

from year 3 to infinity?

Explanation / Answer

A

D0 = $44500

Rate of return = 17%

Present value of perpetuity = D/r = $44500/0.17 = $261764.71

---------------------------------------------------------

Constant Growth rate = 6%

Using formula for Constant Growth rate Dividend model,

Present value = D0 * (1+ Growth rate)/(Rate of return - Growth)

= $44500 * (1+6%)/(17%-6%) = $428818.18

------------------------------------------------------------------

Cashflow for year 1 = D0 * (1+growth rate) = $44500 * 1.1 = $48950

Cashflow for year 2 = D0 * (1+growth rate)2 = $48950 * 1.1 = $53845

Cashflow for year 3-infinity = D0 * (1+growth rate)2 *(1+ constant growth rate) / ( rate of return -constant growth rate) = $44500 * 1.12 * (1+6%)/(17%-6%) =$53845 *1.06/ 0.11 = $518870

Discount these cashflows at rate of 17% to calculate present value of the firm

Firm's value = $48950/ (1+17%) + $53845/(1+17%)2 + $518870/(1+17)2

= $460213.675

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.