Question: At the end of Year 4, dividend payout is $0.5. Assuming the constant growth rate is 5%, and the cost of equity is 10%. Calculate the current stock value.
My answer: D4 = $0.5, Gc = 5%, Ke = 10%, So V4 = 0.5*(1+5%)/(10%-5%) = $10.5. Then V0 = $10.5/ (1+10%)`4 = $7.17
I can see the points on both calculations, but I think my answer makes more sense. Based on my understanding of DDM, the constant growth is happening since from Yr 0 to Yr 1. That’s why D1 = D0 * (1+Gc). If we use the $0.5 as the D1 as the correct answer shows, it becomes that the growth rate starts from Yr 1 to Yr 2.
You are saying V3 = D4 / (r-g) and V0 = V3 / (1+r)^3. I understand this part. But why can’t I do V4 = D4(1+g) / (r-g) and V0 = V4/(1+r)^4 ??
You mentioned the constant growth rate from year 4 onwards. That’s what I am confused. If it starts from year 4, why should i calculate V3 instaed of V4? In the original formula, V0 = D1/(r-g), is the constant growth rate starts from year 1 or year 0?
This is probably one of the most common areas of confusion, and I think it’s due to the way the topic is taught in most textbooks. When valuing a growing perpetuity, you assume that, STARTING WITH THE NEXT DIVIDEND, all SUBSEQUENT dividends grow at a constant rate. So it’s irrelevant what the growth rate is that occurs between D(0) and D(1).
Remember - the price is a present value (the constant growth formula is the formula for the PV of a growing perpetuity). And in calculating present value, we care about FUTURE cash flows.
I suspect the reason so many get confused is that when discussing the constant growth model, it often starts with D(0) and makes you calculate D(1) as D(0) x (1+g). So that concept gets anchored in their minds. But all that’s necessary is that everything AFTER D(1) grows by the constant rate.