Time Value of Money Part 2 (Equation and Application)

In this video, I continue the discussion on the Time Value of Money.

VIDEO SUMMARY

Let’s talk about the equation for the Time Value of Money. I’m going to put it up, and you can see that there are four different variables. You have present value, future value, rate, and the number of periods. So present value and future value actually use the same equation. You can just flip the equation around depending on what you are trying to calculate. In the example we did previously with the dollar today and the dollar tomorrow, we were talking about one period, so we didn’t consider the variable N. N was equal to 1. But when you get into more periods, you would raise it to the power of the number of periods you are dealing with. The reason why you do this is because of compounding interest. Compounding interest also comes from the idea of the time value of money. That happens because you are experiencing a level of risk period after period after period. So you are not only being compensated for the risk of each period, but for the additional amount that you should receive from the interest in the preceding periods. So one period down the road, you should be receiving interest not only for the risk of that period, but also interest on the interest you received the last period. To make this make more sense, I am going to put up an amortization table. You see these all throughout finance and what this is showing is what is happening each period. This table starts with 10,000 with ten percent risk each period. For the first period, you have 10,000 starting value multiplied by 1.1 to get the effect of ten percent risk. That gives you your ending value. The ending value becomes the starting value for the next period. Then you experience ten percent risk again, and so on through all the periods. This mathematical process is the same thing as raising your risk to the power of the number of periods. So you can either go through and create an amortization table or you can simply use the equation. Both ways are mathematically the same thing. So you are receiving at the end of the five periods, you would receive the 10,000 plus interest to compensate you for holding ten percent risk for five consecutive periods.

Let’s talk about an application because in practice you actually use present value more often than future value. What you are usually doing is evaluating several different options for investments. With an investment, you are going to receive some value in the future. So let’s look at a specific example. Let’s say you have \$50 in the bank and you are looking at three potential investment options. The first option you receive \$50 in one year with 10% risk. The second option you receive \$100 in five years at 5% risk. The third option you receive \$500 in 10 years at 10% risk. So these are three different options. They all have different time frames. They all have different risks. So how do you compare apples with apples to determine what the best option is? Well if you take all three of those options and value them back to today’s dollars then you can compare them. The option with the best value is going to be the best option for you to choose. So in looking at these different options, I’m going to put up the results. You can see that the first option actually loses value. If you have \$50 dollars today and someone says they will give you \$50 five years from now, it’s not actually worth fifty dollars. It would be worth something less, because you are holding risk. Option two and three have dramatically different future values: \$100 and \$500. You might think that \$500 would be preferable to \$100, but it’s actually not. It is actually less valuable, because you are holding so much more risk for such a long period of time. It is more beneficial to you to choose the second option. That gives you the greatest amount of value.

There is a key point here. We say a dollar today is worth more than a dollar tomorrow, but you are always wanting the dollar tomorrow. You don’t want to hoard all your money today. The intention is we want to get rid of our money. We want to put our money out there. So that it goes to work for us, and we get the interest so we get more money in the future. The money comes back to us so we can go out and do the whole thing over again. Year after year, you continue to grow your money. So we don’t want the dollar today. We always want the dollar tomorrow. The question becomes, out of the infinite choices out there on where to invest your money, which is the one that gives you the most value. We figure that out by calculating things back to the present value and comparing them. I hope this gives you a sense that investing is really just swapping money back and forth between parties with different payouts, different time periods, and different levels of risk. If you can write out your assumptions, the time periods, and your assessment of the risks, you can then use this equation to calculate your best option. I use the equation for the time value of money all the time. I actually don’t use my calculator. I’ll just write out the equation and calculate it out. The reason why I write it out, is because it’s so much fun, but also it really helps you understand what your assumptions are. You want to understand your assumptions because that is driving the results. That is driving your understanding of the best decision that you can make.

To recap, we talked about the concept of the time value of money. Then we walked through the equation. And finally, we talked about how you would apply it.