Schweser Q on Security Valuation discount, understand, practice, question, recent

SWASH

I dont understand this practice question (Book 4, SS14, Pg. 226)
17) An analyst feels that Brown Company’s earnings and dividends will grow at 25% for two years after which growth will fall to a marketlike rate of 6%. If the projected discount rate is 10% and Brown’s most recent paid dividends was $1, value Brown’s stock using the supernormal growth (multistage) dividend discount model.
A. $31.25
B. $33.54
C. $36.65
The Correct Answer: C
$1(1.25) / 1.11 + [$1(1.25^2 / (0.100.06)] / 1.1 = $36.65
My attempt:
Since growth was 25% for 2 years starting at $1, then the next two dividends would be
$1(1.25) = $1.25 and,
$1(1.25^2) = $1.56, with the final dividend with normal growth
$1.56(0.06) = $1.66
Using this dividend, find the FV of the stock: ($1.66 / kg) = $1.66/(0.10.06) = $41.41
Now we have to present value these numbers…
$1.25/1.1 + $1.56/(1.1^2) + ($1.66 + $41.41)/(1.1^3) = 33.51 which would be answer B.
How come in the official answer they never present valued more than the 1 year? and how come since the DDM should be the first year with the constant dividends they used $1.56 and not the year after since the formula is PV(0) = D(1)/(kg)?
Thanks for the help!

Elliotbay

You have to bear in mind that it is 2ND YEAR DIVIDEND which will grow at a constant rate of 6%.
That is D2 of 1.56 will grow constantly at 6%.
So, we need to calculate P1 and not P2.
P1 = D2/(k  g) = 1.56/(.10  .06) = 39.06
P0 = 1.25/1.1 + 39.06/1.1 = 36.65
It is a little tricky in the beginning. ALWAYS see which is the FIRST dividend figure grwoing at a constant rate and then calculate for Price, 1 yr before that.

TheMBAGlover

Ahh ok I see now… I’ll have to keep that in mind, I had assumed its the first divident that grew at the constant rate, not the first divident that will grow at the constant rate. Thanks!