# Equity / Implied Growth Rate

For the below question :

“Tamara Ltd stock currently trading at 38.25 per share. Company recently paid a dividend of 1.5, which is expected to grow at a constant rate forever. Given a required rate of return of 10% and that the stock is fairly valued, the implied growth rate is closest to…”

Am I factoring in growth to the dividend (1.5 *1+g) because the dividend was already paid and we are referring to future dividends? If it stated that the dividend paid will be 1.5 would I then not use the future growth in equation? Hope this is clear, thanks!

According to Gordon Growth:

V0 = D1 / (r – g)

V0 = D0 × (1 + g) / (r – g)

V0 × (r – g) = D0 × (1 + g)

(V0 × r) – (V0 × g) = D0 + (D0 × g)

(V0 × r) – D0 = (V0 × g) + (D0 × g) = (V0 + D0) × g

g = [(V0 × r) – D0] / (V0 + D0)

Given:

• V0 = 38.25
• D0 = 1.50
• r = 0.10

we get:

g = [(38.25 × 0.10) – 1.50] / (38.25 + 1.50)

= 2.325 / 39.75

= 5.849%

We can check this easily:

(1.50 × 1.05849) / (0.10 – 0.05849)

= 1.5877 / 4.151%

= 38.25

S2000magician comment says it 110%. In general, it all depeneds on when the dividend given is paid. If the question says that the dividend was just paid then it definitely means D0 is given. Even if I am told that the company is planning to pay a dividend in the nearest future it is still D0. Only if the question says that in one year the company is planning to pay the dividend I would consider it to be D1.

Thanks!