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

sabina

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 market-like 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 / (0.10-0.06)] / 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 / k-g) = $1.66/(0.1-0.06) = $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)/(k-g)?

Thanks for the help!

MonkeyBusiness

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.

FVPV

My own way - The Correct Answer: C

D1/ (1+k) + D2/(1+k)^2 + P2/k - g (remember constant g rate)

$1(1.25) / 1.10 + [$1(1.25^2 + $44.41/ (0.10-0.06)] / 1.10^2 = $36.65

So terminal price = P2 = D3/k-g and you know D3 = D2(1+g) . Here you must use perpetual g rate