# H-model

Hi, Could anyone please help me with a demonstration of the H-model formula which is part of the DDM valuation? I couldn’t find it in the books. There was just a rough approximation with an integral of the linear function over the decreasing growth period. Thanks a lot !

It should be in the books. check the index

well i took LII in 2008, and there was not demonstration of this model there. maybe in the new ones… thanks anyway.

a demonstration?

higgmond, there we have just the end formula, Value = D0(1 + gt)/(r – gt) + D0H(gs – gt)/(r – gt). the idea is how can we obtain it starting from the GG model and the sum of discounted dividends in the declining growth period

Not sure if you’re looking for the algebraic proof, but via the long method if you discount back each dividend during the declining growth period and use the GG model at the end to get a terminal value and then discount that back you’ll get your P0. What the H model does is use the GG model from time zero in term 1 and the incremental value added due to the higher short-term growth period in term 2, and simplifies the math so you don’t have to discount these interim dividends individually.

yap, thanks sundevl21, i was looking for the proof… the part with the GG model it’s clear, but the incremental part, mathematically speaking, i just don’t seem to grasp. i’m not able to link the sum of decremental growth dividends to the second term of the equation. I just get the numerator as a sort of integral over the triangle formed by the downard slope corresponding to to growth and the time axis. But the denominator… i need it to make a presentation to some people, and i wanted to show the calculations to them.

The H-model seems to have been presented in the September/October 1984 issue of the Financial Analysts Journal, so you may want to take a look at that. The article includes a footnote that says “The formal derivation of the H-model . . . is available from the authors. . . .”, however.

thanks CW, i’ll look into that

If you’re using it in a presentation, unless they’re uber math geeks I wouldn’t recommend including the mathematical proof. Wouldn’t it suffice to make a graph with time on the x-axis and dividend growth rate on the y-axis? Then you could could shade in a rectangular area (technically there’d be no upper bound on time but make a simplifying assumption) that represents the first term, then shade in a triangle on top of the rectangle representing the decremental dividends in the H period to graphically display the value of the 2nd term.

it’s a presentation of valuation methods to some students who have graduated from an engineering class. but i guess you’re right, a graphical representation would be the way to go. i thought that being engineers, they wouldn’t just buy the formula as it is. but then again, it’s not their core activity, so i guess they’ll let it pass.