A stock is expected to pay a dividend at the end of year one and year two of $1.24 and $1.56. Dividends will grow at a 5% rate thereafter. Assuming that K=11%, the value of the stock is: I solved by: [1.25 / (0.11-0.05)] / 1.11
The answer, however, is:
(1.25 / 1.11) + [1.56 / (0.11-0.05)] / (1.11)
My two questions are: a.) why don’t you divide 1.25 by (k-g)? b.) why don’t you discount year 2 dividends by (1.11)^2? Thanks!
The discount rate k-g is a terminal value rate. This does not apply when you have variable rates before the explicit period.
The answer is not correct. The answer is:
1.24/1+k + 1.56/(1+k)^2 +(1.56*1+g)/(k-g)/(1+k)^2
try to work thru this
http://www.investinganswers.com/financial-dictionary/income-dividends/gordon-growth-model-5270
Because the $1.25 dividend (note: you’d originally written $1.24, but used $1.25 thereafter) doesn’t grow constantly at 5%; the formula
V0 = D1 / (k – g)
applies when all dividends (beginning with D1) grow at an annual rate of g. Here, the constant growth rate doesn’t start until the second dividend, so we have to treat the first dividend separately.
You do. And you discount the year 3 dividend by 1.11³, and so on. If you wanted to try to add up infinitely many dividends, each discounted at 11% for the number of years until you receive them, you could, but it would take a long time (i.e., forever). That’s why we have a shortened formula: we have better things to do with our time. The shortened formula (seen above for V0), says that when the dividends starting at time t + 1 will grow at a constant annual rate of g, then,
V_t_ = D(t +1) / (k – g)
In this case, the constant growth starts with D2: every dividend thereafter is the previous year’s dividend grown at a rate of 5%. Thus, this formula gives you the value of the stock at time t = 1: V1. And the value today is the dividend at time t = 1 (D1) discounted back to today (one year) at 11%, plus the value of the stock at time t = 1 (V1) also discounted back to today (one year) at 11%.
You’re welcome.
Apart from the discrepancy of the first dividend ($1.24 or $1.25), the answer is correct: $24.54.
By the way, it would be helpful to the Level I candidates if you would put parentheses around 1+k and 1+g when you’re using them as factors; it’s a lot clearer that way.
I typed that from my iPhone so it was quite messy to get the format correct. Otherwise I would have taken the time to provide a more clear explanation if you haven’t already.
I agree though, I will probably be needing a lot of L2 forum assistance myself till next June!