"ART Company just paid a dividend of $2.00. The dividend is expected to grow by 10% this year, 9% in year two and 6% in year three. Then, beginning in year four, the dividend will begin growing at a constant rate of 4%. With a required return of 10%, what is the stock worth today

The stock is worth $38.99 per share today

Explanation:

We can calculate the value of the stock using the dividend discount model approach (DDM). The DDM values the stock based on the present value of the expected future dividends from the stock. To calculate the price of the stock today, we simply discount back all the future expected dividends and terminal value (calculated when the growth rate in dividends become constant) to their present value using the required rate of return as the discount factor.

The value of ART company's stock today will be,

P0 or V0 = 2 * (1+0.1) / (1+0.1)  + 2 * (1+0.1)*(1+0.09) / (1+0.1)^2  +  

2 * (1+0.1)*(1+0.09)*(1+0.06) / (1+0.1)^3  +  

[( 2 * (1+0.1)*(1+0.09)*(1+0.06)*(1+0.04)) / (0.1 - 0.04)] / (1+0.1)^3

P0 or V0 = $38.9939 rounded off to $38.99

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