Assume that a stock is expected to pay at the end of ya 1 and year 2 of $1.25 and $1.56. Dividends are expected to grow at a 5% rate thereater. Assuming that k is 11%, the value of the stock is cloests to which of the following? A) $22.30 B) $23.42 C) $24.55 My answer: A. Their answer: C. You can obviously the solution to this without me having to write it down. The issue is that the $26 ($1.56/(11%-5%)) is discounted back only one period and not two, which I thought was the correct thing to do considering it was in year two.
THink about the perpetuity formula : Po = D1 / k-g . So using this formula based on the 1.56 dividend gets you the price at time 1, which then must be discounted back only 1 period. I always draw a timeline. Seems to help.
My ansa was $23.49 which obviously closewr to C. I worked it out as follows: 1) Price @ Y2 = $1.56/(.11-.05)=26. The discounted everything as (1.25/(1.11))+(26+1.56)/1.11^2 Alternatively you get $23.56, again which is closest to C, calculated as follows: 2) Calculate Price at Y3 as $1.56*1.05/.11-.05=$27.3 with Dividends at Y3 being 1.64, then you discount it for 3 years 1.25/1.11+1.56/1.11^2+(27.3+1.64)/1.11^3.
Unfortunately however the solution is supposed to come out to exactly $24.55 according to the readings
Like what PatBateman said, the easiest (which is also the answer) is actually discounting the PV at Time 1 i.e. ((1.56/0.06) + 1.25)/1.11 which is $24.55 exactly.