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. 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 dividend is growing by three different growth rates. Thus, the three stage growth model of DDM will be used to calculate the price of the share today. Under DDM approach, we discount the expected dividends by the required rate of return to estimate the fair value of the stock today. The terminal value is calculated when the dividend growth becomes constant forever. To calculate the price of the stock today, we use next period's dividend D1.

The price per share = D1 / (1+r)  +  D2 / (1+r)^2 + ... + [(Dn * (1+g) / r - g) / (1+r)^n]

Price per share = 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]

Price of stock today = $21.578 rounded off to $21.58

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