Multistage Growth Question

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!

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.

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

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).

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

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