Gray Manufacturing is expected to pay a dividend of $1.25 per share at the end of the year (D₁ = $1.25).The stock sells for $22.50 per share,and its required rate of return is 10.5%.The dividend is expected to grow at some constant rate,g,forever.What is the equilibrium expected growth rate?

Question

Quizplus · Accepted Answer

We can use the constant growth model to solve for the equilibrium expected growth rate:

P0 = D1 / (r - g)

where:
P0 = current stock price
D1 = expected dividend at the end of the year
r = required rate of return
g = expected growth rate

Plugging in the given values:

$22.50 = $1.25 / (0.105 - g)

Simplifying:

$22.50 x (0.105 - g) = $1.25
2.3625 - $22.50g = $1.25
-$21.25g = -$1.1125
g = 0.052 or 5.2%

Therefore, the equilibrium expected growth rate is 5.2%. None of the answer choices match exactly with this calculation, but the closest one is E) 4.94%.

Gray Manufacturing Is Expected to Pay a Dividend of $1