 # H-model formula

Does anybody understand the rationale behind the valuation formula for the H-model, or its derivation? I hate having arbitrary formulae thrown at me like this.

Not sure about the rational behind it but the text does mention where to find the technical details. The way i think of it is the formula is broken into two parts. the first is the lng term growth in normal years and the second is the additional growth in the short term (since you already have the long term growth factored in, taking the short term growth as a whole instead of differencing it would cause you to double count it) . Its easier to think of it when you think of how it plots in a graph…

2 Fuller, R.J. and C. Hsia, 1984, A Simplified Common Stock Valuation Model, Financial Analysts Journal,

v40, 49-56

The formula adds the value that comes from an assumed linear decline from the super-growth rate to the long-term growth rate. I don’t think that it has a rational unless you learn the derivation of the formula… it is just like that because that equals what you would get if you actually did the calculation of that linear decline the manual way. Unfortunately derivation is beyond our scope. Try understanding it by making a graph. It assumes linear decline in growth from super normal to normal growth periods and accumulates the effect of linear decline with the long term stable growth. Regarding supernormal growth it is more like area under the graph of growth at y-axis and time at x-axis for 1\$ of dividends and multipled with D0 to get the actual effect. But derivation is beyond our scope, for exams perspective its better to retain it.

See Schweser Library for good intuition.

As pointed out above, the first part of the formula is what the value would have been if the dividends were to grow indefinitely at the long-term normal rate (G_L_), and the second part is the value coming from the short-term supernormal growth (G_S_). I don’t really understand how this formula is derived, but I tried to think of this second portion like this:

• [D0(G_S-G_L)x(t/2)]/(R-G_L_) can be algebraically rearranged as:
• [D0(1+G_S_)/(R-G_L_) - D0(1+G_L_)/(R-G_L_)]x(t/2)

Ignoring (t/2), what is inside the brackets above is the difference between the values of two different firms whose dividends at Time 1 are D0(1+G_S_) and D0(1+G_L_), respectively, In other words, this is the additional value of a firm that experiences super growth for the next 1 year and grows at the long-term normal rate thereafter. Now you can take this additional value of 1-year super growth and multiply it by t (because the super growth lasts for t years) and divide it by 2 (because the rate of the growth declines in linear fashion over those t years).