2 Stage Dividend Discount Model - Inconsistencies in texts

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cleverCFA

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Hi,
I’m trying to get my head around what I see as inconsistencies in the explanation of calculating the 2 stage dividend discount model.
In the schweser mock exam 1 morning session, question 94.
Assume the Wansh Corporation is expected to pay a dividend of $2.25 per share this year. Sales and profit for Wanchsch are foreceasted to grow at a rate of 20% for 2 years after that, then grow at 5% per year forever. Dividend and sales growth are expected to be equal. If Wansh’s shareholder require a 15% return, the per share value of common stock based on the ddm model is closest to:
a. 22.75
b. 26.00
c. 28.50
The answer given is C and explanation is as follows:
P2 = D3 / (k-g) = (2.25 * (1.2)^2 ) / (0.15 - 0.05) = 32.40
P0 = 2.25 /1.15 + 2.70/(1.15^2) + 32.40/ (1.15^2) = 28.5
This just smells of an errata of some kind. Firstly the calculation for D3 seems wrong, their calc looks ot be like they are calculation D2 only.
So I looked in Schweser on 309 and in their explantion, they calculate the future stock price by using the last dividend result before the change in growth (i..e D2 / (k- g) to calculate P1). So my interpretation of their example to the mock example question would be:
P1 = D2 / (k - g) = (2.25 * (1.2)^2) / (0.15 - 0.05) = 32.4 (note the answer is the same but calc is for P1, not P2)
P0 = PV(D1) + PV(P1)
P0 = 2.25/1.15 + 32.4 /1.15 = 30.13
So I was stil confused and so I looked in the CFAI text (p284 of equities book)
The way they do it is to calculate all the dividend up to the first dividend that has grown at the 2nd growth rate.
So, using this methodology I would do the following:
D3 = 2.25 * (1.2^2) * (1.05) = 3.402 (grows at 20% for 2 years, then 5% for 1 year)
P2 = D3 / (k- g) = (2.25 / (0.15 - 0.05) = 34.02
P0 = PV(D1) + PV(D2) + PV(P2)
P0 = (2.25 *1.2) / 1.15 + (2.25 * 1.2^2) / (1.15^2) + 34.02 / (1.15^2) = 30.52
So 3 different answer to the same problem from 3 different sources. Which is right? I just don’t get it.
 
I can’t help but I’m with you entirely on this one… never quite sure what to do as I’ve seen conflicting explanations. Some help would be greatly appreciated.
 
I don’t think its a discrepancy. You just have to assume that the 20% growth occurs after the next dividend payment, so the first dividend is 2.25. the second is 2.25*1.2, etc. Here are the proper calculations:
1. 2.25/1.15
2. 2.25*1.2/1.15^2
3. 2.25*1.2*1.2/1.15^3
4. 2.25*1.2*1.2*1.05/.15-.05/1.15^3
sum=28.497
if you just map out the cash flows, it is more straightforward: you’ll receive 3 dividend payments (1-3)-discount each to get the PV. Then in 3 years, the stock will be worth number 4, so discount that back and sum all CFs. Hope this helps
 
Thanks Babba. I think my mistake comes from a misunderstanding of the timeline involved. When they say “Wansh Corporation is expected to pay a dividend of $2.25 per share this year” I read this as a D0 dividend, not as a D1 (i.e. 1 year out). You are discounting that 2.25 div out 1 year which seems a long discount period when someone says “this year”. I guess the way to read it is to consider anything question that says “just paid” or “last year” as a D0 div and anything that implies “next div” or “this year” as a 1 year out dividend. I understand the multi-stage DDM mechanics once this is sorted
Thanks for helping me clarify this.
 
I have developed a process to answer all sorts of questions so that its quick n easy to answer these ones.
For DDM questions - I would punch in the dividends into calculator memory buttons 4-6 with their respective discount rates stored in buttons 1-3. I would also add the terminal value into button 6 as these get discounted by the same factor as the last dividend.
It is a case of what works for yourself - but I find that having a process to apply the knowledge and answer these question in a short amount of time has worked really well for me in the practice exams I have done.
Even when I have lost focus in the afternoon session I will say the word “question” in my mind before reading the actual question as I find it helps me re-focus instantly…its sad but it reminds me a of gameshow somewhat.
See you all in Sydney - I am the guy who will be head and shoulders above everyone else.
 
Thanks Kailas. That’s the best effort I’ve seen on this forum to help other candidates. Appreciate it.
By the way, what software/mouse do you use to create that whiteboard video? I often find it difficult to explain myself, but if I could create videos like that it would really help.
 
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