P. Daves Inc's stock is currently sells for $45 per share. The stock's dividend is projected to increase at a constant rate of 4% per year. The required rate of return on the stock, rs, is 12%. What is Daves' expected price 6 years from now? a. $52.68 b. $55.12 c. $54.41 d. $56.94 e. $53.71

The price of the stock six years from now will be $56.94

Explanation:

To calculate the price of a stock that pays a dividend which grows at a constant rate forever, we use the constant growth model of DDM. The current price of stock using the constant growth model is calculated as follows,

P0 = D1 / r - g

As, we don't know the D1, that is dividend expected for the next year, we will calculate it first,

45 = D1 /  (0.12 - 0.04)

45 * (0.12-0.04)  =  D1

45 * (0.08) = D1

3.6 = D1

We use the D1 to calculate the price today. Thus, we will use D7 to calculate the price six years from now.

D7 = D1 * (1+g)^6

P6 = 3.6 * (1+0.04)^6  /  (0.12 - 0.04)

P6 = $56.939 rounded off to $56.94

$56.94

Explanation:

Growth rate=4%

Current stock price=$45

Time in year=6

Future value of stock=45*1.04^6=56.94

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