Multistage Growth Question

CFA Level I Equities
#1

I am looking at Kaplan, book 4, page 318, questions #8 & 9. I’m trying to figure out why the answer does not discount the year 2 constant growth to the 2nd power. This is the question #9 from the book:

Q9) Dividend grows at 25% for two years, after which growth will fall to a constant rate of 6%. If the discount rate is 10%, and most recently paid dividend was $1 the value of the Brown’s st ock using the multistage dividend discount model is:

Answer per the book: $36.65 (because they divided the constant dividend model by 1.1, not 1.1 squared as I think it should be).

What I think the answer should be:

D1: 1.25

D2: 1.56

Value: $1.25/1.1 + (1.56 / (.1 - .06)) / (1.1) squared = 33.54

Thanks in advance for looking into this!

#2

The formula for a constant growth stock says P(t) = D(t+1)/(r-g). In other words, either

  1. the price at any point in time is based on the NEXT expected dividend, or (Alternately)

  2. If you use a dividend to calculate a price using the constant growth formula, you’ll get a price that is as of one period before the dividend.

So, since you’re using the “time 2” dividend, you get a “time 1” price (i.e. what the stock will be worth one year from today. That’s why it is discounted one year instead of two.

#3

Yes here the Answer by book is correct 36.65.

Caculation is 1.25/1.1 + 1.25*1.25/(1.1)^2 + (1.25)^2 * 1.06/10%-6%/(1.1)^2

Here the answer comes 36.65

#4

ok, so i got the same answer first that the original poser got.

I left out the step, where to get the numerator, you need to do 1.56*1.04.

I had just did 1.56/(.10-.06).

#5

@busprof, thanks so much! finally clicking now haha!

#6

My pleasure. It’s one of those concepts that are confusing at first but simple after the fact - like many things.