# Dividend Pricing Model – Part 3 (Math Concepts)

In this video, we continue to discuss the Dividend Pricing Model!

VIDEO SUMMARY

In this video we’re going to continue talking about the Dividend Pricing Model and I’m going to focus on talking about the math concepts behind the equation. There is some really interesting math going on here and if you understand the math you can really do some pretty cool things with your money.

Before we get started, I’m actually going to start with talking about a math trick that a lot of accountants use and it has to do with calculating out percentages. Accountants have to calculate a lot of percentages in their day to day job and I’d like to just review the basic percentage equation that we all know. So if you take the full value of something and multiply it by a percentage you get the percentage value of that thing. So to use an example, 100 times twenty-five percent equals 25. We all know this. It is a pretty simple concept. What happens is accountants often have to do this equation backwards. So what you can do is you just flip the equation around and say 25 divided by 25 percent gives you a hundred. It is important to just realize you can go backwards and forwards in this equation. So if you have the portion of the percentage of the whole you can find the whole value by dividing by the percentage. What happens is you might be creating a financial report and you might say you are dealing with a segment of revenues. Say the segment you are dealing with is twenty-five thousand dollars of revenue. You know it is twenty-five percent of the total revenue. Well, you can quickly figure out the total revenue by taking 25 thousand divided by twenty-five percent gives you a hundred thousand. So that’s your total revenue. This is just an example but the idea is when you are dealing with percentages, you can go backwards and forwards through this equation.

So what does that have to do with the Dividend Pricing Model? Well let us look at the math of the Dividend Pricing Model. Just to review the concept, we are talking about a string of dividends or a string of cash flows out into the future and we are trying to figure out a price of an appropriate value that I am going to pay for this opportunity to collect these cash flows. So you are going to receive your first dividend, your second dividend, your third dividend, your fourth dividend, out into the future and those dividends are specific values. Well how much is that worth to you? That is what we are figuring out and how you would go about figuring that out is you know all these cash flow values based on your assumptions. What you do is you take the present value of each one of those cash flows. So if you take the first cash flow, the present value of that is going to be the cash flow divided by the present value equation which is 1 plus R to the power of the number of periods. So for the first dividend, it is the dividend divided by 1 plus R to the power of one. That gives you the present value of that cash flow. Let us go to the second cash flow. We can do it again. Dividend 2 divided by 1 plus R to the power of 2. And we add that to the first cash flow. We continue on forever. So we do that for dividend three, dividend four, dividend five, and the total sum of all those dividends which should be the price you are willing to pay. It is the sum of the economic value of this opportunity to receive these cash flows. The Dividend Pricing Model is just a simplification of that. It is saying in this equation that dividends / risk- growth is equivalent to doing that whole long mathematical process out forever to the future. There is a mathematical proof that proves this that will go from one equation to the other and you can find it in pretty much every finance textbook so I am not going to go through it here with you but go ahead and look that up. It is pretty interesting. But it is important to realize that that is what we are doing here. We are taking the present value of each one of these cash flows. What happens is, as you go further and further out into the future, you are discounting cash flows more and more and more because cash flows get riskier and riskier and more uncertain the farther into the future you go. So you would be willing to pay less money for each of those opportunities. What happens is when you get somewhere out into a hundred periods into the future, you are discounting so much, there is so much uncertainty, that it is pretty much zero with the further out you get. So we are really talking about a hundred periods into the future. We are discounting from period one way out into the future and that is how you determine your price.

So let us take this a step further. Now we have a different pricing model equation. What happens if we push this to an extreme. Let us say that growth equals zero. That is going to be your assumption. Growth is zero. Then you are left with the equation D divided by R equals P, your price. So you are saying your assumption is that your dividends or your cash flows are going to be equal forever into the future. What would you be willing to pay for that opportunity? Well let us throw some numbers in here. Let us say your cash flow is going to be fifteen dollars. Your assumption of risk is fifteen percent. If that is the case you would be willing to pay a hundred dollars for that opportunity if there is zero growth. So this should be interesting to you and you should draw the connection between the accounting math trick we were talking about earlier in multiplying percentages because your cash flow is exactly the same percentage of your risk of your total price. There is a relationship there between your cash flow and the price you would be willing to pay for that. Your cash flow just happens to be the same percentage as the risk you are assuming. You should be asking, “Why would that be? Why would the price be related to the cash flow at exactly the correct proportion as my risk?” That is exactly the point with this equation and this should be your “aha moment” because your dividend payments are essentially an interest rate based on the risk you are assuming.

Let us use the example of a loan. Let us say you are going to loan money to somebody to buy a house or any other type of loan. So you are going to give somebody a sum of money. You should expect interest payments back each period based on the riskiness of that individual. So the more risky that person is, the higher the interest rate you are going to charge. So when you are buying a stock it is essentially the same thing. You are giving somebody money for the opportunity to get a series of cash flows and that series of cash flows is based on an assumption of the risks you are going to take on. So the price you would be wanting to pay for that opportunity should reflect that risk and those payments are essentially interest payments you are receiving for holding that level of risk. That is the “aha moment.” So investing is really not about buying a stock or buying a company. It is really about buying a certain level of risk. Investing is buying and managing risks and when you understand this concept, that it is about this theoretical idea of risk, it takes you to a whole other level of understanding finance because you start to realize that it is a really about your assumptions and understanding the prices that you are paying for things and how that relates to your assumptions about the future.

I hope this was helpful in discussing what the math is saying in the Dividend Pricing Model. We started by talking about an accounting math trick and how you can calculate percentages backwards or forwards. Then we walk through the Dividend Pricing Model and talked about the math. Then we talked about the concept of why risk is important in the relationship between your cash flow and the price you are willing to pay is proportional related to the risk you are assuming. So there is more to talk about the Dividend Pricing Model and in the next video we are going to talk about the implications of what this all means for you.

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Neither Zach De Gregorio or Wolves and Finance Inc. shall be liable for any damages related to information in this video. It is recommended you contact a CPA in your area for business advice.