Three-Stage Dividend Discount Models

Valuation models can have as many growth periods as you want.

A two-stage dividend discount model has two different periods of growth. Fair enough. What amazing innovation would you expect from a three-stage dividend discount model?

Right. So the simpler form would just include three constant growth rates. For example, a company with a 10% discount rate pays a USD 10 dividend today. It is expected to grow at 12% for two years, then 8% for two years, and then 4% forever after that. Much as before, the value would be estimated as 213.94. | Year | Dividend | Present Value | |---|---|---| | 1 | 11.20 | 10.18 | | 2 | 12.54 | 10.37 | | 3 | 13.55 | 10.18 | | 4 | 14.63 | 9.99 | | 4 (GGM) | 253.61 | 173.22 | Again, fair enough.

No. There's just a single dividend class considered in each model type.

No. Each dividend discount model uses inputs to arrive at a single valuation estimate.

The second type of three-stage dividend discount model assumes a first-stage constant growth rate, a declining growth rate in the second period, and then a constant growth rate forever in the third period. What do you think would be the best way to model this?

Not quite. It's certainly possible to set up a spreadsheet that will do this for you, but it could be a little more work than another method.

Absolutely! If this sounds like the H-model again, it is. So using that same first example, suppose you have that 12% growth for two years. Then instead of 8% growth in the second period for two years, allow it to decline from 12% to 4% over the course of six years, ending at a 4% growth rate from there on.

No. This would change the valuation, ignoring the assumption of a declining growth rate.

Those first two dividends will be calculated by hand, just as in the first case. | Year | Dividend | Present Value | |---|---|---| | 1 | 11.200 | 10.18 | | 2 | 12.544 | 10.37 | And then the H-model calculation jumps in to take care of all the rest. Nice. Now think carefully about what is being calculated here. Which dividend should be input to the H-model?

No, the H-model doesn't use a next period dividend at all.

Exactly! This is the H-model calculation. $$\displaystyle V_0 = \frac{D_0(1 + g_L) + D_0H(g_S - g_L)}{r - g_L} $$ Today's dividend is used for a current valuation. But since the first and second stages now become the second and third stages, this all has to move forward to Year 2. So you need the dividend of 12.544 from the table, along with the half-life of three, and the other assumptions. $$\displaystyle V_2 = \frac{D_2(1 + g_L) + D_2H(g_S - g_L)}{r - g_L} = \frac{12.544(1 + 0.04) + 12.544(3)(0.12 - 0.04)}{0.10 - 0.04} = 267.61 $$

No. That would be the case if the decline in growth rates started right now.

So now the whole thing has some nice, realistic assumptions and is down to just three terms. Not bad. With this third value, what do you think is the next step in determining the time zero value?

No. The three values aren't all in the same time period, and so they can't be added up yet.

Yes! Add that Year 2 value to the table, discount it as well, and you're all done. | Year | Dividend | Present Value | |---|---|---| | 1 | 11.200 | 10.18 | | 2 | 12.544 | 10.37 | | 2 (H-model) | 267.61 | 221.16 | Estimated present value: 241.71. It's higher this time, since the second stage was expanded from two years to six years. Of course more customization can always be done, but three-stage models like this are pretty popular with firms that use dividend discount models. Keep this tool handy.

No. That would work for finding the Year 2 value, but there's no need to calculate this.

To summarize: [[summary]]

Three growth rates

Three dividend classes

Three valuation estimates

The same way as the first method

Use the H-model for the second and third stages

Use an average growth rate for the second stage

$$D_0$$

$$D_2$$

$$D_3$$

Add them up

Discount the H-model value

Compound the Year 1 dividend

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