Question

Common stock value-All growth models Personal Finance Problem You are evaluating the potential purchase of a small business currently generating $46,000 of after-tax cash flow Do-$46,000). On the basis of a review o s m ar risk nvestmen op or n tes you must ea arate of teum 2% on he ro osed 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 11% for the first 2 years, followed by a constant annual rate of 6% from year 3 to infinity?

Answer 1

Using dividend growth model,

Firm's value, V = D0 x (1 + g) / (r - g)

a) if g = 0%, V = 46,000 x (1 + 0%) / (22% - 0%) = $209,090.91

b) if g = 6%, V = 46,000 x (1 + 6%) / (22% - 6%) = $304,750

c) D1 = D0 x (1 + g) = 46,000 x (1 + 11%) = 51,060, D2 = D1 x (1 + g) = 51,060 x (1 + 11%) = 56,676.6, D3 = D2 x (1 + g) = 56,676.6 x (1 + 6%) = 60,077.2

=> Value in year 2, V2 = D3 / (r - g) = 60,077.2 / (22% - 6%) = $375,482.48

Value today, V0 = D1 / (1 + r) + (D2 + V2) / (1 + r)^2

= 51,060 / (1 + 22%) + (56,676.6 + 375,482.48) / (1 + 22%)^2

= $332,203.89