# H-Model in DDM

Regarding the H model in Discounted Divident Model in SS11, Reading 34, I don’t quite understand the formula:

V0 = D0*[1+g(l)] / [r-g(l)] + D0*H*[g(s)-g(l)]/[r-g(l)] (Sorry I don’t know how to make it prettier)

I understand the first term is to calculate the value assuming the company grow at g(l) forever, got it, so 2nd term should mean the additional effect when the growth rate drop from g(s) to long term sustainable rate g(l) across the first few years. Since this process won’t last forever, why would we use [r-g(l)] in the denominator as if it’s in Gordan Growth model?

Thanks!

you cannot use Gs since that is a short term growth rate.

say gs = 10%, gl = 5%

and r = 12%

using gs would use 2% to discount all that intermediate growth - which would overstate the price.

using an average of 7.5% would use 4.5% to discount that growth

and using 5% would use 7% to discount. to discount that growth

7% would give you a most conservative #.

It’s a good question and I dont have an answer to it. I see where you come from, but since this is not an annuity, I’d say denominator should be [1+ (gs+gl)/2]^H or something like that? i.e. something more close to discount rate.

Does it make sense?

you are using the more conservative number - it will give you a lower valuation with a higher rate (gl) in this case.

I asked you a question - and answered it already … as to why it should be gl.