Santa Klaus Toys just paid a dividend of $3.10 per share. The required return is 9.2 percent and the perpetual dividend growth rate is 4.0 percent. What price should this stock sell for five years from today?

The price of the stock 5 years from today will be $75.43

Explanation:

The perpetual dividend growth means that the stock's dividends will grow at a constant rate forever. For such a stock, we use the constant growth model of DDM. The formula for price today using the constant growth model is:

P0 = D1 / r - g

Where D1 is the dividend in the next period or Year 1 or D0 * (1+g).

To calculate the price of the stock 5 years from now, we will use D6.

The price of the stock 5 years from now is:

P = 3.1 * (1+0.04) ^6 / 0.092 - 0.04

P = $75.432 rounded off to $75.43

Five years form today the stock will sell for $75.38

Explanation:

Given D0 $3.10, r 9.2%, g 4.0%

Stock price? 5 years from today

The DDM will be used as it derives the stock price by discounting future dividends at the required return.

Need to discount future dividends to year five to find stock price

Find D6

3.10 * (1.04) ^6 = $3.92

DDM formula : Sp = D1 / r - g

= 3.92/0.092-0.04

=$75.38