Hello everyone, I’m seriously confused about this, how it’s laid out on paper and how it should be entered into the calculator to make it come out right. The question reads as follows: A stock that currently does not pay a dividend is expected to pay its first dividend of $1.00 5 years from today. Thereafter, the dividend is expected to grow at an annual rate of 25% for the next 3 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. A.20.65 B.20.95 C.22.72 D.23.87
C. Nasty as a lot of “future” in there; but it’s still basically a multistage DDM question. The best way to do this is to lay out the CF (dividends) and discount back to the present. I make it: Yr 4 - $1 (5 years from now is at the end of period 4, beginning of period 5) Yr 5 - $1.25 Yr 6 - $1.56 Yr 7 - $1.95 Yr 8 - $2.05 (5% growth) So the value of the perpetual growth from Yr 9 on in Yr 8 is: D1 / (k - g) = 2.05 / (10.3% - 5) = 38.7 Total CF to be discounted are thus: Yr 4 - $1 Yr 5 - $1.25 Yr 6 - $1.56 Yr 7 - $40.6 = (1/(1.103^4))+(1.25/1.103^5)+(1.56/1.103^6)+(40.6/1.103^7) = 22.75 ~ 22.72
The paper solution goes like this: ($1.00/1.103)^5 + ($1.0*1.25)/(1.103)^6 + ($1.25 * 1.25)/(1.103)^7 + [(1.25^3) / (.103 - .05)(1.103)^7] There are a few different steps coming together. I know that there are 2 steps. The 25% growth period, and then the constant grow dividend discount model. I understand the equation up till it tries to combine the last accelerated growth period with the constant growth period. I feel like it should be… Accelerated Growth Period ($1.00/1.103)^5 + ($1.0*1.25)/(1.103)^6 + ($1.25 * 1.25)/(1.103)^7 + (1.25^3) /(1.103)^8 + Constant Growth Period 1.25^3/ (.103 - .05) Have I lost my mind? Any thoughts? Thank you!
Book Says answer is A… 
Yeah…I was going to say… When you use the perpetual growth model, you use the dividend for P1. So, you need to add it in with the last dividend of 25% growth when discounting back, and not make it’s own cash flow…if that makes any sense at all… So, for C5 (1.25)^3 + [(1.05)(1.25)^3]/(.103-.05) / (1.103)^8 Using the CF Function CFo = 0 C1 = 0 F1 = 4 C2 = 1 F2 = 1 C3 = 1.25 F3 = 1 C4 = 1.5625 F4 = 1 C5 = 40.6471 F5 = 1
Year 5 1 Yr 6 1.25 Yr 7 1.5625 Yr 8=1.953125 Yr 8 1.953125*1.05/(.103-0.05) = P8 = 38.69 Now back -> CF0=0 CF1=0 F1=4 CF2=1 F2=1 CF3=1.25 F2=1 CF4=1.5625 F3=1 CF5=1.953125 + 38.69 F5=1 NPV, I=10.3 CPT NPV NPV=20.65
With these problems I often find it less confusing to a) draw a quick time line and b) solve for the period before the first payment is made - so in this case P4. I would then solve as per a normal multistage DDM and then discount the result back by the cost of equity 4 periods. I think it might be a little more intuitive but what ever works for you.