# Winter Time Adventures is going to pay an annual dividend of $2.72 a share on its common stock... ## Question: Winter Time Adventures is going to pay an annual dividend of$2.72 a share on its common stock next week. This year, the company paid a dividend of $2.60 a share. The company adheres to a constant rate of growth dividend policy. What will one share of this common stock be worth 12 years from now if the applicable discount rate is 9.0%? a.$139.82

b. $98.56 c.$106.61

d. $101.90 e.$115.30

## Dividend Growth Model:

The dividend growth model also termed as the constant growth model is a valuation model that is used to determine the current intrinsic value of the stock by considering the future dividends expected to be issued on the stock. The model assumes that the dividends grow at a constant growth rate to perpetuity and the discounted value of these future dividends is the current price of the stock.

Correct answer: Option c) $106.61 Explanation: As per the data provided by Winter TIme Adventures: • Next dividend, D1 =$2.72
• Last dividend, D0 = $2.60 • Required return, r = 9% • Constant rate, g = ? • Price in year 12, P12 = ? Computation: The first step is to determine the constant growth rate: • Constant growth rate = (D1 - D0) / D0 • Constant growth rate = ($2.72 - $2.60) /$2.60
• Constant growth rate = 4.62%

The second step is to determine the current stock price, P0:

• P0 = D1 / (r - g)
• P0 = $2.72 / (9% - 4.62%) • P0 =$62.10

The last step is to determine the price in year 12, P12:

• P12 = {eq}P0 * (1 + g)^{12} {/eq}
• P12 = {eq}$62.10 * (1 + 0.0462)^{12} {/eq} • P12 = {eq}$62.10 * 1.719398 {/eq}
• P12 = {eq}\$106.77 {/eq}

Note: The answer is closest to option c. 