Question

Free cash flow valuation You are evaluating the potential purchase of a small business with no debt or preferred stock that is currently generating ​$41 comma 300 of free cash flow ​(FCF 0​= ​$41,300​). On the basis of a review of​ similar-risk investment​ opportunites, you must earn​ a(n) 18​% rate of return on the proposed purchase. Because you are relatively uncertain about future cash​ flows, you decide to estimate the​ firm's value using several 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 annual rate of 8​% 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 7% from year 3 to infinity?

Answer 1

a. $229,444.44

b. $446,040

c. $438,326.23

Step-by-step explanation:

a. Value of the firm will be calculated as the present value of the perpetuity. The perpetuity is FCF0 = 41,300. => Value of firm = 41,300 / 0.18 = $229,444.44 ;

b. Apply the constant growth model for calculation value of the firm : FCF1 / ( Required return - Growth rate) = ( FCF0 x 1.08) x ( 18% - 8%) = ( 41,300 x 1.08 )/ 10% = $446,040;

c. Value of the firm = FCF1 / 1.18 + FCF2 / 1.18^2 + [FCF3/(18% -7%)]/1.18^2

in which: FCF1 = FCF0 x 1.12 = $46,256; FCF2 = FCF1 x 1.12 = $51,807; FCF3 = FCF2 x 1.07 = $55,433

Value of the firm = $438,326.23