The Shore Hotel just paid a dividend of $2 per share. The company will increase its dividend by 6 percent next year and will then reduce its dividend growth rate by 2 percentage points per year until it reaches the industry average of 2 percent dividend growth, after which the company will keep a constant growth rate forever.
Required:
(a) What is the price of this stock today given a required return of 12 percent?

The price of the stock today is $21.58

Explanation:

The price of the stock can be calculated using the dividend discount model approach. The dividend discount model bases the stock price on the present value of the expected future dividends. The formula for price today under DDM of such a stock is,

P0 = D1 / (1+r)  +  D2 / (1+r)^2  +  [ (D2 * (1+g)  /  (r - g)) / (1+r)^2 ]

The growth rate in year 1 will be 6%

The growth rate in year 2 will be (6-2) = 4%

From year 3 the growth rate will be a constant 2%

P0 = 2 * (1+0.06) / (1+0.12)  +  2 * (1+0.06) * (1+0.04)  /  (1+0.12)^2  +  

[ (2 * (1+0.06) * (1+0.04) * (1+0.02)  /  (0.12 - 0.02)) / (1+0.12)^2 ]

P0 = $21.578 rounded off to $21.58

answer; niosh, the national institute for occupational safety and health;