The question is as follows: An analyst feels that Brown Company’s earnings and dividends will grow at 25% for two years, after which growth will fall to a constant rate of 6%. If the projected discount rate is 10%, and Brown’s most recently paid dividends was $1, the value of Brown’s stock using the multistage dividend discount model is closest to:
A. $31.25 B. $33.54 C. $36.65 The solution provided was: $1(1.25) / 1.1 + [$1(1.25)2 / (0.1 - 0.06)] / 1.1 = $36.65 Because the second dividend is in the second year shouldn’t this be the correct formula? $1(1.25) / 1.1 + [$1(1.25)2 / (0.1 - 0.06)] / (1.1)2 = $33.42
OK, buckle up: I’m gonna use first principles here. Yes, you are correct that we need to discount by 2 years interest, but with modification.
The value at time 0 is 1.25/1.1 +(1.252/1.12) + {[(1.252)*1.06]/(0.1-0.06)}/1.12. The first 2 terms are the individual dividends for years 1 and 2, while the last expression is the value of dividends for years 3 and on, i.e. the long-term growth phase of 6%.
Oh, thank you! I have convinced myself that the formula you presented above is correct and arrives at the same conclusion as the solution provided. I would have understood the solution much more clearly if they presented the formula as you have: 1.25/1.1 +(1.252/1.12) + {[(1.252)*1.06]/(0.1-0.06)}/1.12. How did you manage to see so many steps ahead of the solution?
I just went back to square one: lay out the CFs during the supercompound phase, then plug in the DDM at time 2 for years 3, 4, 5, … It didn’t hit me until later that the solution showed it as of time 1. That’s when I rubbed the third brain cell together.
