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CFAHouston

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A stock is not expected to pay dividents until three years from now. The dividend is then expected to be $2.00 per share, the divident payout ratio is expected to be 40%, and the return on equity is expected to be 15%. If the required rate of retun is 12%, the value of the stock today is closest to:

A. $27
B. $33
C. $53
D. $67
 
hmm i wish i had my calculator on me ... but lets see if i can get the steps right

D1= 2
g = .60*.15
K= .12

once the price is determined it wd be discounted back 3 yrs using a dsic. rate of 12 %
 
D/E = 0.4
RR = 1-D/E 0.6
ROE = 0.15
g = ROE*RR = 0.12*0.6 = 0.072
k = 0.12

If you get dividend in year 3, D_3 = 2

Price for year 2 = D_3 /K-g = 2/(.12-0.072) = 41.66

Price today = P2/(1+K)^2 = 33.2
 
until three years from now



so we disc it back 3 yrs or 2 yrs ..??
 
if we have dividend for year 3, then we find price for year 2, so we discount the price at year 2.
 
Vir - your method is right, but look at the question again. Your answer isn't right.
 
Oh I thought we are getting div in year 3. But not, so 41.66 /(1.12)^3
 
nope, you were right about that as well.

you had used K are your ROE to calculate g.

:) I made the same mistake.
 
look at your ROE. it should be .15 and not .12. that changes the calculation. when i do that i calculated it the same method but got $53.14 for the PV when i used it. is the correct discount rate 12%?

thanks
 
its C.

yes, discount rate is 12%. Vir had it right, except he used discount rate instead of ROE on g.
 
why it's c?

D1= 2
g = .60*.15 = 0.9
K= .12

P =D1/(k-g) = 2/(.12-.09) = 67,
why not d?
 
wxyz - because $2 dividend is for period 3 since they aren't paying out dividend until then.

So if we find price with that dividend, its the price for year 2. Therefore, discount it back.
 
For any of these I scribble a little time line especially problems like mid-year depreciation and TVM and FSA (started in the year ended in this year) all you have to do is mess up by 1 period and you just wasted your time

The timeline is pretty straight forward

0--------1---------2--------3

@ period 3 you receive the dividend (D1) so the formula (D1/k-g) will give you the price of the stock @ the end of year two. Just discount that value back two periods @ 1+k...to get the price today.
 
Thanks Houston for pointing out the mistake. Even if the fundamentals are right it wouldnt count if I make such stupid mistakes.
 
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