Question

Suppose DeepMind Inc. will pay $1.50 per share in dividends next year. The require return on the stock is 10% and its dividends will grow by 2% per year indefinitely. Under which of the following scenarios would you be willing to pay more than $18.75 today?A.All else being equal, the required return is more than 10%.B.All else being equal, the dividend next year will be $1.20.C.All else being equal, the growth rate of the dividends is greater than 2%.

Answer 1

C. All else being equal, the growth rate of the dividends is greater than 2%

Step-by-step explanation:

The formula to calculate the fair price of a stock with a constant growth in dividends is as follows,

• P = D1 / r-g
• Where D1 is the dividend next period
• r is the required rate of return
• g is the growth rate in dividends
• P = 1.5 / 0.1 - 0.02 = 18.75
• We are taking 1.5 as D1 as it is the dividend per share DeepMind will pay next year.

So, we will be willing to pay more than 18.75 if the fair price per share today is greater than 18.75. We check all the 3 options.

A. say the required rate is 10.1%

• P = 1.5 / (0.101 - 0.02) = 18.52
• So if the required rate of return increases from 10%, the fair price per share is falling and we will be willing to pay less than 18.75 per share.

B. P = 1.2 / (0.1 - 0.02) = 15

• If D1 = 1.2,the fair price per share will be 15 which is less so we will not be willing to pay more than 15 for such share.

C. Say the growth rate in dividends is 2.1%

• P = 1.5 / (0.1 - 0.021) = 18.99
• The fair price per share increased to 18.99 if the growth rate in dividend increases by 0.1 percentage point. Thus, C is the correct answer