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!

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!

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.