Question

Computech Corporation is expanding rapidly and currently needs to retain all of its earnings; hence, it does not pay dividends. However, investors expect Computech to begin paying dividends, beginning with a dividend of $0.75 coming 3 years from today. The dividend should grow rapidly-at a rate of 49% per year-during Years 4 and 5; but after Year 5, growth should be a constant 5% per year. If the required return on Computech is 18%, what is the value of the stock today? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

The value of the stock today is $7.64.

Step-by-step explanation:

This can be calculated as follows:

Since required return is 18% (or 0.18), we have:

Present value (PV) of year 3 dividend = $0.75 / (1 + 0.18)^3 = $0.456473154509468

Year 4 dividend = Year 3 dividend * (1 + growth rate in year 4) = $0.75 * (1 + 0.49) = $1.1175

PV of year 4 dividend = $1.1175 / (1 + 0.18)^4 = $0.576394067982294

Year 5 dividend = Year 4 dividend * (1 + growth rate in year 5) = $1.1175 * (1 + 0.49) = $1.665075

PV of year 5 dividend = $1.665075 / (1 + 0.18)^5 = $0.727819628214931

Year 6 dividend = Year 5 dividend * (1 + growth rate in year 6) = $1.665075 * (1 + 0.05) = $1.74832875

Using the Gordon growth model (GGM) formula, we can calculate stock price year 5 as follows:

Stock price at year 5 = Year 6 dividend / (rate of return - Constant annual growth rate after year 5) = $1.74832875 / (0.18 - 0.05) = $13.4486826923077

PV of stock price at year 5 = $13.4486826923077 / (1 + 0.18)^5 = $5.87854315096675

Value of the stock today = PV of year 3 dividend + PV of year 4 dividend + PV of year 5 dividend + PV of stock price at year 5 = $0.456473154509468 + $0.576394067982294 + $0.727819628214931 + $5.87854315096675 = $7.64

Therefore, the value of the stock today is $7.64.