Question

 

Using the constant-growth dividend discount model, comment on the following statement: “If the shareholders’ expected rate of return were always twice the growth rate on future dividends, then the value of the dividend next period will always equal the current stock price times the growth rate on future dividends.”                      

Group of answer choices

True and the dividend next period would have a direct relationship to both the current stock price and the growth rate on future dividends percent.

False because the dividend next period would have a direct relationship to the current stock price, but an inverse relationship to the growth rate of future dividends.  

True and the dividend next period would equal the current dividend plus the current growth rate on future dividends.  

False because the dividend next period would equal the current dividend plus the current dividend times the growth rate on future dividends.

None of the above comments or statements are correct

Answer 1

The constant-growth dividend discount model says that the intrinsic value of a stock is based on a future series of dividends that grow at a constant rate.

The formula given is:

P = D1 / (r - g)

where: P=Current stock price
g=Constant growth rate expected for dividends, in perpetuity
r=Constant cost of equity capital for the company (or rate of return)
D1​=Value of next year’s dividends​

Now if we go by the given statement, that is, “If the shareholders’ expected rate of return were always twice the growth rate on future dividends, then the value of the dividend next period will always equal the current stock price times the growth rate on future dividends.”

Then,

P = D1/ (2g - g)

p = D1/ g

D1 = P*g

This shows that the given statement is true and it is observed that future dividend has a direct relationship to both current prcie and growth rate.

Therefore the statement is true and the dividend next period would have a direct relationship to both the current stock price and the growth rate on future dividends percent.