Question

Green Gadgets Inc. is trying to decide whether to cut its expected dividend for next year from $7 per share to ​$4 per share in order to have more money to invest in new projects. If it does not cut the​ dividend, Green​ Gadgets' expected rate of growth in dividends is 7 percent per year and the price of their common stock will be ​$105 per share. ​ However, if it cuts its​ dividend, the dividend growth rate is expected to rise to 10 percent in the future. Assuming that the​ investor's required rate of return for Green​ Gadgets' stock does not​ change, what would you expect to happen to the price of its common stock if it cuts the dividend to ​$4​? Should Green Gadgets cut its​ dividend? Support your answer as best you can.

a.  What is the​ investor's required rate of return for Green​ Gadgets' stock? (?)% ​(Round to two decimal​ places.)

Answer 1

Answer (a) : Investor's Required Rate of Return:

~ If the expected dividend is not cut, then -

Expected Dividend = D₁ = $7

Growth Rate = g = 7%

Price of the stock = V₀ = $105

Required rate of return = "r" = ?

Therefore, as per Gordon Growth Model,

r = ( D₁ / V₀ ) + g

= ( $7 / $105 ) + 0.07

= 0.13666 = 13.67%

Therefore, Investor's Required Rate of Return = 13.67%

"What would you expect to happen to the price of its common stock if it cuts the dividend to ​$4​? Should Green Gadgets cut its​ dividend?"

Answer:

~ If the expected dividend is cut to $4, then -

Expected Dividend = D₁ = $4

Growth Rate = g = 10%

Required rate of return = "r" = 13.67%

Price of the stock = V₀ = ?

Therefore, as per Gordon Growth Model,

V₀ = D₁ / (r - g)

= $4 / (0.1367 - 0.10)

= $108.99

Therefore, if it cuts the dividend, the price of the stock will rise to $108.99 ($109) per share.

~ Green Gadgets company should cut its dividend from $7 to $4 per share, because it results in increase in value of the firm from $105 to $109 per share.

~ By cutting down the dividend, and investing the saved funds into new projects, the company's earnings and dividends growth increases from 7% to 10%, thereby, resulting in higher value of the company's equity.

~ Hence, the company should cut its dividend.