### CFA Practice Question

There are 191 practice questions for this study session.

### CFA Practice Question

A stock is not expected to pay dividends until three years from now. The dividend is then expected to be \$2.00 per share, the dividend payout ratio is expected to be 40%, and the return on equity is expected to be 15%. If the required rate of return is 12%, the value of the stock today is closest to ______.
A. \$27
B. \$53
C. \$67

User Comment
kalps Ans: 2(0.12-0.09) = 66.67 Discount factor = 1/1.12(2) = 53
kaym ans is 66.666 calculated as- 2/(0.12-0.09)
kalps no your answer is wrong as the div starts in two years time you have not discounted it
KD101 Well I think here how is goes -
PV of \$2 after 2 years is (remember you use expected dividends so use t-1 years) 1.5944

Now 1.5944 / (0.12-0.09) = \$53.14
mm04 It says '3 years from now'. So:

2/0.12-0.09 = 66.67 This is the price at the beginning of the 3rd year/end of the 2nd year.
Discount back for 2 years:

66.67/1.12^2 = 53
llgoms thanks mm04 -that's the clearest explanation
ThePessimist Remember the distinction between dealing with a perpetual growth calculation and an individual dividend. If you were calculating the value of that first dividend, you'd discount by three years. When you calculate the GGM as mm04 showed, you're calculating the value of dividends as of the year *before* the first dividend is paid, and thus it only gets discounted by two years. (V0 is based on D1.)
NinaB CF0 = 0, CF1 = 0, CF2 = 67, I = 12, NPV cpt = 53
Bibhu In case of delayed dividends, g = ROE*(1 - dividend payout ratio)= .15*.6=.09 .
So CF2= D2/k-g= 2/(.12-.09)= 67.
Then before starting in BA II plus CF + 2nd + Clear work. Then follow up what is given by NinaB
lazio Thanks a lot, Bibhu, this is much of a relief.
miene Ok, I think this is the most logic answer:

Growth Rate (g)= ROE x Retention Rate
Retention Rate = 1- Div.Payout Ratio
Therefore: g = 0.15 x (1-0.4)
g = 0.09

Now 2.00/0.12-0.09 = 66.67
Now we need to discount 66.67 to get to t0 (note its only 2 periods discounting)

66.67/(1.12)(1.12) = 53.14
copus why are there only two discounting periods and not three?
dcfa this is how i did it:
D= 2/1.12(3) = 1.4236

g=0.15x0.6=0.09
after 3years it is supposed to grow at 0.09
P3=D4/k-g=2(1.09)/(0.12-0.09)=72.667 (remember P0=D1/k-g)

discount P3 term to now = 72.667/1.12(3)=51.7227

V0=51.7227+1.4236=53.1463
Jurrens At copus: It's only two periods because that formulas uses the NEXT dividend to calculate the price, therefore, if it had only been one year, it would be calculating the stock price at the beginning of the year. Hope that helps.
maria15 Where did .09 come from?
maria15 Never mind. I got it. Thanks!
dipu617 It says "until three years from now"!! Does it mean at the end of 2nd year or at the end of 3rd year?? Anybody!!
DaniD13 You do discount 3 years, but you also have to multiply the dividend first by 1.09 to get D1 not D0
2.18/(.12-.09) then discount by 1.12^3
gill15 Dani - No

Dividend starts Year 3 and it is 2 at that point. When using Gordon the dividends are discounted back to Time = 2. At time = 2 P = 2/(.12 - .09)

Now we're at time two and discount it back two more years and you got 53
liana Is the answer correct? check example from pg 283 CFA!
jgonzalez Thanks miene!