# Two-stage DDM

This is from 2008 Schweser Book6. Exam2.am. #96 A stock that currently does not pay a dividend is expected to pay its first dividend of \$1.00 five years from today. Thereafter, the dividend is expected to grow at an annual rate of 25% for the next three years and then grow at a constant rate of 5% per year thereafter. The required rate of return is 10.3%. what is the value of the stock today. My answer is also A. I calculated as this : D5/(1.0103)^5 + D6/(1.0103)^6 + D7/(1.0103)^7+(D8+P8)/(1.0103)^8 D5=1, D6=D5*1.25 … to D8=1.25^3 P8=D9/(k-gc) where D9=D8*1.05 Their explaination is to calculate until year 7, the first 3 period is sames as mine : [D5/(1.0103)^5 + D6/(1.0103)^6] The discounted price for year 7 is D7/[k-gc]*[(1.0103)^7] I need help to understand : why D7/[k-gc]*[(1.0103)^7] = D7/(1.0103)^7+(D8+P8)/(1.0103)^8 Thanks!

Seems to me that the Schweser book screwed up. You Should have - D5 = 1 D6 = 1.25 D7 = (1.25)^2 D8 = (1.25)^3 P = [(1.25^3)(1.05)]/(.103-.05) Then D5/(1+R)^5 + D6/(1+R)^6 + D7/(1+R)^7 + (D8+P)/(1+R)^8 If you want to be effecient for the exam, use the CF feature of your calculator CFo = 0 C01 = 0 F01 = 4 C02 = 1 F02 = 1 C03 = 1.25 F03 = 1 C04 = 1.5625 F04 = 1 C05 = 40.6471 F05 = 1 CPT NPV

i got the schweser answer. Just did it a bit differently with geometric series formula: For the first 4 periods: a = 1/1.103^5 r = 1.25/1.103 sum1 = a(r^4-1)/(r-1) Remaining infinite series: a = 1.25^3/1.103^8 r = 1.05/1.103 sum2 = a / (1-r) sum1 + sum2 comes to 20.64684

Sorry - I don’t have the schweser books, but I get 20.65, so I’m assuming it’s right then. To the OP - Were you merely questioning their methods vs. yours? If thats the case, I wouldn’t worry about it - Mathematically there a lot of ways to compute this, so long as you’re getting the right answer your way…

agree with nodoubt… 19.33 + .69 + .61… but I arrive @ 18.70 using 0-5;1.25-1;36.85-1 cf keys… however, rplcing above 0-5 with 0-4 gives me the answr… any “remember” suggestions?

draw a timeline…

I guess my problem is identifying key words such as “5yrs from now”. How to identify 5 years from now should mean beginning of the 5yr or end of 5th yr.

I think it’s safe to assume that now is time = 0

I asked because I was wordering if this is supported by some theroy (mathimatically?), can we down cal it to yr5, that should be much simpler than the original one. The turn point is at yr 8. So what we usually do is to cal D9/(k-gc) to get P8. The answer however used D8’/(k-gc) where D8’ = D7(1+r1) --(r1=0.25) I agree with hoffmag2 that we should use CF in the exam (and it is simple enough.)

hoffmag2 Wrote: ------------------------------------------------------- > Seems to me that the Schweser book screwed up. > You Should have - > > D5 = 1 > D6 = 1.25 > D7 = (1.25)^2 > D8 = (1.25)^3 > P = [(1.25^3)(1.05)]/(.103-.05) > > Then > > D5/(1+R)^5 + D6/(1+R)^6 + D7/(1+R)^7 + > (D8+P)/(1+R)^8 > > If you want to be effecient for the exam, use the > CF feature of your calculator > > CFo = 0 > C01 = 0 > F01 = 4 > C02 = 1 > F02 = 1 > C03 = 1.25 > F03 = 1 > C04 = 1.5625 > F04 = 1 > C05 = 40.6471 > F05 = 1 > > CPT NPV shouldn’t you include the dividend of \$1.95 in there after C04?

Yes you should. It’s included in the 40.6471 (the perpetual portion is only a FV of 38.69, plus the 1.95 for that dividend)

here’s a guide that might help: ftp://ftp.cba.uri.edu/classes/dadalt/Classes/FIN322/Miscellaneous/VALUING_NONCONSTANT_DIVIDEND_GROWTH_STOCKS.pdf