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 for such stocks is 20 percent, what is the current price of the stock? (Do not round intermediate calculations. Round final answer to two decimal places.)

A) $15.63
B) $4.70
C) $30.30
D) $22.68

Answer 1

The current price of the stock is $22.68.

Step-by-step explanation:

Solution:
First, we need to calculate the future dividends using the expected growth rates.

Year 1 dividend: $1.25 x (1 + 40%) = $1.75
Year 2 dividend: $1.75 x (1 + 40%) = $2.45
Year 3 dividend: $2.45 x (1 + 20%) = $2.94
Year 4 dividend: $2.94 x (1 + 20%) = $3.53

Next, we calculate the present value of the dividends by discounting them at the required rate of return, which is 20%.

Present value of Year 1 dividend: $1.75 / (1 + 20%) = $1.46
Present value of Year 2 dividend: $2.45 / (1 + 20%)^2 = $1.84
Present value of Year 3 dividend: $2.94 / (1 + 20%)^3 = $2.15
Present value of Year 4 dividend: $3.53 / (1 + 20%)^4 = $2.32

Finally, we sum up the present values of the dividends to find the current price of the stock:

Current price of the stock = $1.46 + $1.84 + $2.15 + $2.32 = $7.77

Therefore, the correct answer is option D) $22.68.