which way is correct?

T

the prodigy

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Hi Guys,
Am i missing something here? my answer is there, but it isnt the right answer. even when i checked the book my approach seems right.
company is experincing abnormal growth, last dividend paid was $0.75. next year,anticipated growth in dividends and earning of 25% followed by negative 5% in 2nd year. the company will level offto normal growth rate of 8% in year threeand expected to maintain 8% growth rate for the foreseeable future. investor required rate of return 12% . the value of the stock today is closest to:
A)$20.70
B)$24.05
C)$18.65
my answer was as follow:
D1=0.75X1.25= $0.9375, PV =0.9375/1.12= $0,83705
D2= 0.9375x0.95= $ 0.89, PV= 0.89/(1.12)2= $0.7095
D3= 0.89 x1.08= $0.9612
D/(K-G)= $0.9612/.04= $24.03 , PV= 24.03/(1.12)3 = 17.10
17.10+ D1 + D2= $18.65
The correct answer was A, explained as follow:
D1= 0.75X1.25= $0.9375
D2=0.9375 X0.95= $ 0.89
D2 is the first dividend that will grow at a constant rate. we can use this dividend in the constant grow DDM to get the valu for the stockin period 1
$0.89/(.12-.08)= $22.25
the value of the stock today= 22.25+ 0.9375/1.12= $20.70
good luck on the exam to everyone
 
You must discount the final PV by 2 years not 3. It doesn’t make sense, maybe someone can explain why, but it gets results.
Good luck to you too!
 
Draw a timeline and you will see why what burberry above is saying is correct.
D3/(r-g) is the price of the security due to all future perpetual dividends at time 2 … so it needs to be discounted for 2 periods.
so 24.03 / 1.12^2 + ….
 
When they calculate $22.25, they’re finding the price at time 1 (a perpetual payment growing by 8% and discounted at 12%). It needs to be added to the dividend at time 1 and discounted by 1 year. This way is one correct approach.
In your method, you’re finding the price at time 2 and discounting it by 3 years, and you’re neglecting the dividend in year 3 (if you really want to discount three years). If you want to use your method (which goes out one more year), you need to calculated P3 and add it to D3, and discount them by 3 years.
You find P3 as: (0.962*1.08)/(0.12-.08) = D4/(r-g)= $25.97. Add this with 0.962 to get D3 + P3 = $26.93 discount by 3 years and add to PV of D1 and D2. You will get $20.71707589 without rounding anything. This is also a correct approach.
OR
(from your initial approach, again) you can recognize that you need to only discount P2 and D2 by 2 years and add it to the PV of D1. $24.03 + $0.89 = D2 + P2 and discount at 12% for two years, add to the PV of D1 and you get $20.703125…
Really, there are tons of ways to do this, since these payments are simplified into the model. Just get the hang of keeping cashflows in the proper period, and try to fully understand the concept behind the formula.
Hope this helps!
 
I find an easy way to remember how to do these problems is to simply note the 1st year that the dividend growth is constant (year 3 in this case) as it will usually just outright say it, so then you know when you use the DDM formula, the number the formula spits out is discounted to:
(The year that dividend growth went constant) - (1 year)
In this case, went constant in year 3, so DDM model gives a result discounted to year 2, (3-1).
Now you have:
Year 1: Year 1 Dividend in year 1 terms
Year 2: Year 2 dividend in year 2 terms
Year 2: DDM value in year 2 terms
Then its just basic Sum of all Year 2 terms/(1+R)^2 + Sum of all Year 1 terms/(1+R)^1 = Price in year 0 (today) terms. Hopefuly that isn’t more confusing lol, just thought I’d share how I approach it.
 
Use D3 to find P2, which you plug into the 2-year DDM. The answer is A.
 
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