Common stock value — Variable growth Newman manufacturing is considering a cash

Question

Common stock value—VariablegrowthNewman manufacturing is considering a cash purchase of the stock of Grips Tool. During the year just completed, Grips earned $4.15 per share and paid cash dividends of $2.45per share(D0=$2.45). Grips' earnings and dividends are expected to grow at 30% per year for the next 3 years, after which they are expected to grow 5% per year to infinity. What is the maximum price per share that Newman should pay for Grips if it has a required return of 16% on investments with risk characteristics similar to those of Grips?What is the maximum price per share that Newman should pay for Grips?

Common stockvaluel—All growth modelsPersonal Finance ProblemYou are evaluating the potential purchase of a small business currently generating$42,000 of after-tax cash flow (D0=$42,000). 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 00% from now to infinity?

b.What is the firm's value if cash flows are expected to grow at a constant rate of 77% 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 7% from year 3 to infinity?

Explanation / Answer

D0 = 2.45,

constant growth (g) = 5%,

required return (r) = 16%

D1 = 2.45*(1+30%) = 3.185

D2 = 3.185*(1+30%) = 4.1405

D3 = 4.1405*(1+30%) = 5.38265

Termianl value = D3*(1+g) / (r-g)

Terminal = 5.38265 *(1+5%) / (16%-5%) = 51.3798

maximum price = Present value of next 3 dividends and terminal value

Price = 3.185/(1+16%) + 4.1405/(1+16%)2 + 5.38265/(1+16%)3 + 51.3798/(1+16%)3

Price = 42.1881

2)

cash flow = 42000,

required return (r)= 17%

a)

growth of 0% says cashflow will be constant till perpetuity

Firm value = cash flow / required return

Firm value = 42000/0.17 = 247058.82

b)

constant growth rate (g) = 7% (given as 77% , think it is 7%, you cant solve for 77% rate)

Firm value = cashflow*(1+g) / (r-g)

Firm value = 42000*(1+7%) / (17%-7%) = 449400

3)

FCF1 = 42000*(1+11%) = 46620

FCF2 = 46620*(1+11%) = 51748.2

terminal value = 51748.2*(1+7%) / (17%-7%) = 553705.74

Firm value = 46620/(1+17%) + 51748.2/(1+17%)2 + 553705.74/(1+17%)2 = 482138.46

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