Since in my last post I discussed inflation and why people invest in the stock market, I decided that a natural next concept to introduce would be something called time value of money or TVM for short. This concept is the basis for most everything in finance. Stock investing, private equity, venture capital, bond investing, savings and loans, capital budgeting and much more hinge on the concept of TVM so I’ll try to explain it as clearly as possible.
At the base of it, time value of money means that 1 dollar today is worth more than 1 dollar in the future, and conversely 1 dollar today is worth less than 1 dollar one year ago. It may be tempting to attribute this to inflation but that is not the reason that this is true. The reason that a dollar today is worth more than the same amount in the future is because a dollar today can be invested until next year at which point it that dollar plus the return from investing would be more than just the one dollar being given to you one year from now. If this does not make sense to you, that’s okay, the followinf example will help clarify.
You have two people James and Sally. I tell them each that I’ll give them $100, they can receive it now(March 29, 2014) or they can receive it exactly one year from now (March 29, 2015). Naturally Sally takes her $100 now, James decides that he would rather receive his $100 exactly one year from now. Sally goes home and puts her money in her bank account which we’ll say pays 5% interest compounded annually. On March 29 2015, one year from the starting point, I give James his $ 100 dollars and he puts it in his bank account. At this point Sally has $105 in her account while James has only $100. Time value of money is true because any money that a person receives today can be invested and earn returns.
In the case of James and Sally, we would say that the presesnt value of both James and Sally’s money was $100. We would also say that the Future Value of James’s money was $100, while the Future value of Sally’s money was $105 because she earned interest on her money.
In order to further understand this concept we must consider the TVM formulas. OH NO MATH!!!!! Relax, there is no reason to panic when it comes to this math, it’s really easy to understand and it applies the same way across all areas of finance.
The future value formula is as follows.
FV is your future value and in the case of this formula, the number that we are trying to find. PV is the present value of money, as I said before this is the amount of money that you have right now, or in other words the amount of money is being invested. The variable r is your interest rate if you are lending money or your rate of return if the money is invested in stocks. The variable n is the number of compounding periods per year, which means the amount of times you take the returns you’ve made and reinvest them. Finally, the variable t is the number of years that you are keeping your money invested.
In the case of Sally if we substitute in the appropriate numbers into the formula we get the result shown below.
And of course when we work this out we do get $105.
The other formula used in TVM is when we are told what our future value will be and we have to figure out what that would be worth toady. For that we would use something called the present value formula which is shown below.
As you can see all I did was use algebra to isolate the PV variable from the previous formula. Suppose we knew that Sally had $105 in 2015 and that her bank paid 5% interest compounded annually and we wanted to find out how much she started with. All we’d have to do is fill out the formula.
And when this is simplified we do get our $100 starting amount.
I understand that all of the math in this might come off as boring now, but it is a necessary evil and it will come in use when I discuss things like dividend discount and discounted cash flow valuation techniques for stock valuation. It will also come in use when learning what it means to beat the market or to beat a benchmark.
If you have any questions please post them in the comments below and I will attempt to get back to you.
As always, thanks for reading!,
Mohit D. Patel, Author
The author is a student, not an attorney at law or finance professional. As such, this article is not intended to constitute legal or finance advice and is offered as is for purely educational purposes. The author is not liable for any decisions a reader makes based on the content this article.
If you have any questions please post them in the comments below and I will attempt to get back to you!