H model is another form of Dividend Discount Model under Discounted Cash flow (DCF) method which breaks down the cash flows (dividends) into two phases or stages. It is similar or one can say a variation of a two-stage model however unlike the classical tw0- stage model, this model differs in how the growth rates are defined in the two stages.
In the two-stage model, it is assumed that the first stage goes through an extraordinary growth phase while the second stage goes through a constant growth phase. In H model, the growth rate in the first phase is not constant but reduces gradually to approach the constant growth rate in the second stage. The key point to note here is that the growth rate is assumed to reduce in a linear way in the initial phase till it reaches stable growth rate in the second stage. The model also makes an assumption that dividend payout and cost of equity remain constant. Let us take an example illustrating firm value using H model dividend discount model.
Example of Valuation using H Model – Dividend Discount Model
Let us take an example of a company ABC Ltd. that has paid a dividend of $ 4 this year. Assuming a growth for next 3 years at 13%, 10% and 7% respectively in the first stage and a stable growth of 4% thereafter; let us calculate the firm value using H model dividend discount model.
The dividend values will be as follows:
Current Dividend = $ 4.00
Dividend after 1^{st} year will be = $ 4.52 ($ 4.00 x 1.13 – growing at 13 %)
2^{nd} year will be = $ 4.972 ($ 4.52 x 1.10 – growing at 10%)
3^{rd} year will be = $ 5.32 ($ 4.972 x 1.07 – growing at 7%)
The dividend declared after the first stage will be $ 5.32 as calculated above.
$ 5.32 x 1.04 = $ 5.5328.
Assuming this as the constant dividend for the rest of the life of the company, we arrive at the present values as follows
P_{0 }= D/ (i – g)
Where, P_{0} = Value of the stock/equity
D = per- share dividend paid by the company at the end of each year
i = discount rate, which is the required rate of return which an investor wants for the risk associated with the investment in equity as against investment in a risk-free security.
g = growth rate
Now using the formula for calculating the value of the firm, we can arrive at the present value at the end of 3^{rd} year for all future cash flows as follows:
Value = $ 5.5328 / (10% – 4%)
= $ 92.21
Assuming a constant discount rate of 10%, now the value of the firm can be calculated as the present value of future cash flows.
Tenor | Cash Flow | Discount Rate | Present Value |
1 | 4.52 | 10% | 4.11 |
2 | 4.972 | 10% | 4.11 |
3 | 5.32 | 10% | 3.99 |
3 | 92.21 | 10% | 69.28 |
Total Present Value | 81.49 |
Present value calculations arrived as follows:
$ 4.11 = $ 4.52 / (1 + 10%) ^1
$ 4.11 = $ 4.972 / (1 + 10%) ^2
$ 5.32 = $ 5.32 / (1 + 10%) ^3
$ 69.28 = $ 92.21 / (1 + 10%) ^3
The sum of all the present values will be the value of the firm which in our example comes to $81.49.
The H model tries to do away with some of the problems/shortcomings associated with the classical two-stage model; let us have a comparative look to enable the better understanding of the H Model.
H Model V/s Two Stage Model
- The classical two-stage model assumes an extraordinary rate of growth (constant) in the initial stage while the H model is free to use an increasing or declining rate in the initial phase and then align itself with the constant second stage growth rate.
- In the two-stage model, the growth rate drops suddenly from a very high rate to a stable rate as stages change, however in H model; the growth rate reduces linearly to reach the stable growth rate thereby avoiding any sudden jumps or falls.
- Like the two-stage model, the H model also assumes constant dividend payout ratio and cost of equity which may not be a real world scenario and may lead to estimation errors.
The main limitation of H Model is that it assumes linear fall in growth rates from extraordinary growth rate period in stage 1 to stable growth rate period in stage 2.
In cases where the transition happens faster from extraordinary phase to stable growth rate phase, a three-stage model may behave same as in the same way as H model and so would the value of the firm using either model. As a result, a good number of cases for H model yield similar results as the three stages model.
References:
http://pages.stern.nyu.edu/~adamodar/pdfiles/valn2ed/ch13.pdf
http://banner.thebrennergroup.com/2009/08/24/alternate-valuation-model/