 # DDM question (2 different correct ways gives different answers?)

A stock is not expected to pay dividends until 3 years from now. The dividend is then expected to be \$4.00 per share, the dividend payout ratio is expected to be 30%, and the ROE is expected to be 15%. If the required rate of return is 12%, the value of the stock today is closest to: A. 189.81 B. 212.59 C. 234.91 D. 265.32 any ideas? I think there are two ways to solve this, but each way have different answers and only one of them is listed.

CFo=0 C01=0 F01=2 C02=4/(0.12-0.15*0.7) I=12, NPV: A. 189.81

is it D? 0 dividends for 2 years, a dividend of 4 at the end of year 3, and the price of the stock at year 3 is 4*(1+.15*.7)/(.12 -. 15*.7)=294.67, dividend +P=298.67, pv = 298.67/1.12^3=266.67, say D.

The problem does not say (when it should) that dividends are growing at the growth rate, or not. Assuming growing dividend: P0 = D1/Rce-g g=0.15 * 0.70 = 0.105 Rce= 0.12 P0=\$4.42/0.12-0.105 = \$294.67 at end of yr 3 curent price = \$294.67/1.12^3 = \$209.74

Ah, the \$4 dividend, so answer should be B.

you have it right map1, but you mis-clculated the final answer.

Yeap, it should be 298.67/1.12^3=212.585~B Thank you Dreary

4/(1.12^2)+ (4(1.105)/.015)/(1.12^3)) = 212.59…B

4/(1.12^3)…NOT 4/(1.12^2)

Does the DDM give you the price at the beginning of the period?

it gives you the price for the year you calculate the next dividend.

I get 212.59 too B) (4/(0.12-0.105))/(1.12^2)

It’s B

Hi All, Thanks for the quick replies. The answer is indeed B. The answer book shows us to find P(2) , where you are given D(3). In this case, P(2) = D(3) / r - g g = Retention Ratio x ROE = 70% x 15% = 10.50% r = 12% r-g = 1.50% P(2) = 4 / 1.5% = 266.67 Since P(2) is at year 2, we PV back to time zero: 266.67 / (1+12%)^2 = 212.59, hence B. HOWEVER Has anyone tried finding P(3) then discounting it back to P(0)? I get a different (but close) answer: P(3) = D(4) / r - g D(4) = 4 x (1+g) = 4 x 1.105 = 4.42 P(3) = 4.42 / 1.5% = 294.67 Now discount P(3) at time 3, back to time zero, we get: 294.67 / (1+12%)^3 = 209.74. Am I assuming something wrong here? 209.74 is around 3 dollars off from the answer, but I’m very curious to know why no one use this method. any ideas?

is it a valid rationale to say since the question doesn’t say if the growth rate’s the same for dividend OR that dividend payout ratio’s continuous in the future, then we have to find and use P2?

read above…you left out the \$4. Thanks for the question.

toniwestern : You get a different answer because you ignored the dividend payment on the year 3. So the total payoff should be 4 + 294.67 . The price you get is therefore 298.67/(1.12^3) = 212.59 !!!

ahh yes that makes sense - I left out the \$4 dividend which should be included. Thanks alot for your help!

you missed the dividend of year 3 which is 4 \$. present value = 4/1.12^2=3.188 so P0 = 3.188+309.74 =212.92

rahulv Wrote: ------------------------------------------------------- > you missed the dividend of year 3 > > which is 4 \$. present value = 4/1.12^2=3.188 > > so P0 = 3.188+309.74 =212.92 sorry, 4/1.12^3 =2.847 p0=313.59