Question

Starskeep, Inc., is a fast growing technology company. The firm projects a rapid growth of 40 percent for the next two years and then a growth rate of 20 percent for the following two years. After that, the firm expects a constant-growth rate of 8 percent. The firm expects to pay its first dividend of $1.25 a year from now. If your required rate of return on such stocks is 20 percent, what is the current price of the stock?

a.$15.63
b.$30.30
c.$4.70
d.$22.68

Answer 1

To calculate the current price of the stock, use the constant-growth formula to find the present value of future dividends and the terminal value. The current price is the sum of the present values of the dividends and the present value of the terminal value.

Step-by-step explanation:

To calculate the current price of the stock, we need to use the constant-growth formula. First, we calculate the dividends for the next two years:

Year 1: Dividend = D1 = D0 * (1 + g1) = $1.25 * (1 + 0.40) = $1.75

Year 2: Dividend = D2 = D1 * (1 + g2) = $1.75 * (1 + 0.40) = $2.45

Next, we calculate the present value of the dividends:

PV(D1) = D1 / (1 + r) = $1.75 / (1 + 0.20) = $1.45833

PV(D2) = D2 / (1 + r)^2 = $2.45 / (1 + 0.20)^2 = $1.83940

Finally, we calculate the present value of the constant growth period:

PV(Terminal value) = D2 * (1 + g) / (r - g) = $2.45 * (1 + 0.08) / (0.20 - 0.08) = $28.62069

The current price of the stock is the sum of the present values of the dividends and the present value of the terminal value:

Current Price = PV(D1) + PV(D2) + PV(Terminal Value) = $1.45833 + $1.83940 + $28.62069 = $31.91842 ≈ $30.30