A question about Gordon growth model

Hey everyone:

If i understand this growth model correctly, it is P0=D1/(r-g)

Which means, price at the current date depends on the dividend the next period, correct?

If a stock is expected to pay a dividend of 2.6$ per share two years from now, we have D2=2.6.

The divident payout ratio at that time is expected to be 40%, which means Retention ratio is 0.6.

The return on equity will be 13%. Therefore we have g=roe*rr=0.078.

We have a required return of 10%. What would be today’s stock value?

I have: P0*1.1=P1=D2/(k-g)=2.6/(0.1-0.078)=118.18, P0=118.18/1.1=107.43$

Let me know if my answer is correct and if you have other value of today’s stock value.

Thx in advance! smiley

Howdy!

That’s correct.

That’s not quite correct.

Your calculation that P1 = $118.18 is correct.

Your calculation that P0 × 1.1 = P1 is incorrect; 10% is the required rate of return on common stock, but it is not the growth rate of dividends. That rate is g = 7.8%.

The proper equation is P0 × 1.078 = P1, or P0 = $118.18 ÷ 1.078 = $109.63.

Perhaps a better way to look at it is that D1 × 1.078 = D2 (= $2.60), so D1 = $2.60 ÷ 1.078 = $2.412. Then P0 = D1 / (rg) = $2.412 / (0.10 – 0.078) = $109.63.

You’re quite welcome.

It wasn’t clear whether dividends start next year or the following year. I had believed – perhaps unwisely, in retrospect – that there was a D1.

If D2 is the first dividend, then $107.43 is correct.

If there’s a D1, then 109.63 is correct.

Good observation!

Hey! The question implies the first dividend will be paid 2 years from today. So glad to hear my calculation is correct! smiley