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!
zxfmontreal:
Hey everyone
Howdy!
zxfmontreal:
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?
That’s correct.
zxfmontreal:
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.
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 / (r – g ) = $2.412 / (0.10 – 0.078) = $109.63.
zxfmontreal:
Thx in advance!
You’re quite welcome.
edupristine:
The calculation of P0= $109.63 assumes that the firm would pay dividend 1 year from now.
Since we have no information on retention ratio and ROE for 1 year from now, I think we should not include D1 in the calculation of today’s stock price.
The difference of $109.63 - $107.43 = $2.2 is only due to the PV of D1.
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!