# Two Period Dividend Discount Model

The next step towards understanding the dividend discount model is to extend the conclusions derived from the single step dividend model. This brings us to the two period dividend discount model. In this model we will use the same logic. However, we will extend the assumption regarding the holding period. Instead of selling his stock at the end of period 1, the investor holds on to the stock and only sells it at the end of period two. The question arises, how the investor should value the stock this time.

Once again, we will understand this with the help of an example:

*Example:*

**An investor is confident that a certain stock can be sold off for $100 if it is held on to for 2 years. He has a required rate of return of 10%.He is also confident that the company will pay a $4 dividend in the first year and a $6 dividend in the second year. However, he is not certain about what the price of the stock should be today? **

*Calculation:*

Once again, the value of the stock is only equal to the present value of all future cash flows that can be derived from that stock. In this case, we will receive three different cash flows.

- The first cash flow is dividend 1. Let’s call it D1
- The second cash flow is dividend 2. Let’s call it D2
- Lastly, the third cash flow is the final selling price i.e. P2

Also, note that the first cash flow will be received at the end of year 1. However, the second and third cash flows will be simultaneously received at the end of year 2.

Hence, we will discount the first dividend of $4 at 10% for 1 period only. However, second dividend plus the final sale proceeds i.e. $6 and $100 are to be received after two years, therefore they will be discounted for 2 periods.

The formula for the two period dividend discount model is:

= [D1/(1+r)]+ [D2+P2/(1+r)2 ]

= [$4/(1.1)]+ [$6+$100/(1.1)2 ]

= $3.7 + $87.6

=$91.3

Thus, from the given assumptions the value of this investment should be equal to $91.3 in present value terms

### Interpretation:

Once again,

- If the current market price is $91.3, the investor should be indifferent
- If the current market price is less than $91.3, the investor should buy the share as it is undervalued
- If the current market price is greater than $91.3, then the investor should not buy the share as it is overvalued

### Difficulties in Implementation:

This model too cannot be used on its own for very accurate results. Once again the reason is that it uses hard to predict variables like future price and future dividends as inputs. However, the two step dividend discount model is proof that the concept of discounting dividends can be extended to several years.

This proof will be used in the next article, to finally arrive at the generic dividend discount model. The assumptions in the generic model are comparably more realistic which makes it usable. In fact it is amongst the most preferred equity valuation models used by cautious investors.

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