Question

A stock paying $5 in annual dividends sells now for $80 and has an expected return of 10%. What would be the stock price eight years from now

Answer 1

Answer:

P8 = $105.5994 rounded off to $105.60

Explanation:

The constant growth model of DDM is used to calculate the price of a stock whose dividend growth rate is constant. The DDM values a stock based on the present value of the expected future dividends from the stock. The formula for the price of stock today under this model is,

P0 = D0 * (1+g) / (r - g)

Where,

• D0 * (1+g) is the dividend for the next period of D1
• r is the required rate of return
• g is the growth rate in dividends

80 = 5 * (1+g) / (0.1 - g)

80 * (0.1 - g) = 5 * (1+g)

8 - 80g = 5 + 5g

8 - 5  =  5g + 80g

3 =  85g

3/85 = g

g = 0.03529 or 3.529% rounded off to 3.53%

To calculate the price today, we use D1. Thus, to calculate the price 8 years from now or P8, we will use D9

P8 = 5 (1+0.0353)^9  /  (0.1 - 0.0353)

P8 = $105.5994 rounded off to $105.60