# Dividend Growth Model

Can anyone help on this question?

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

Correct answer: V3 = 0.5/(10%-5%) = \$10. Then V0 = \$7.51

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.

Can anyone help me to understand here?

Thanks a bunch!

Sophie

it is a constant growth rate from year 4 onwards.

and year 4 had a dividend of \$0.5.

So V3 = D4 / (r-g)

and then V0 = V3 / (1+r)^3

you need to get your subscript right.

If you use D4 is the numerator - then the value you obtain after the initial calculation is V3 …

(Timeline again is useful till you get this understanding).

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?

Any help?

Thanks,

Sophie

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.

Now everything makes sense!! Thanks a lot!!

You’re welcome - glad it helped.