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!
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.
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!
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