A firm recently paid a $1.00 annual dividend. The dividend is expected to increase by 10 percent in each of the next four years. In the fourth year, the stock price is expected to be $100. If the required rate for this stock is 14 percent, what is its value?

Question

Quizplus · Accepted Answer

The value of the stock is calculated using the dividend discount model for a growing dividend, plus the present value of the stock price in the fourth year. The dividends for the next four years are $1.10 (Year 1), $1.21 (Year 2), $1.33 (Year 3), and $1.46 (Year 4). The present value of these dividends plus the present value of the stock price in the fourth year ($100) discounted back to the present at the required rate of return (14%) gives the value of the stock. The calculation is as follows:Year 1 Dividend: $1.00 * (1 + 0.10) = $1.10 / (1 + 0.14)^1 = $0.96Year 2 Dividend: $1.10 * (1 + 0.10) = $1.21 / (1 + 0.14)^2 = $0.93Year 3 Dividend: $1.21 * (1 + 0.10) = $1.33 / (1 + 0.14)^3 = $0.89Year 4 Dividend: $1.33 * (1 + 0.10) = $1.46 / (1 + 0.14)^4 = $0.85Year 4 Stock Price: $100 / (1 + 0.14)^4 = $59.24Adding these values together gives the stock's value: $0.96 + $0.93 + $0.89 + $0.85 + $59.24 = $62.87.

A Firm Recently Paid a $1