Basic Business Concept: The Time Value of Money

Basic Business Concept: The Time Value of Money

 

Author: Emmanuel Modu ( eumodu@gmail.com )

The time value of money is a very important business concept. The application of this idea is what determines your parents' monthly mortgage, car loan payment, or installment loan payments. It also has an effect on the price of stocks.

Time value of money simply says that a dollar received today is worth more than a dollar received in one day, one month, or a year because the dollar received today can start earning interest immediately. It is such a simple idea that you probably already know it, but you just 
haven't thought about how it can affect your actions. Let's consider an example of how this idea can be applied.

Suppose someone told you that you can have $100,000 today or you can have $105,000 a year from now (assuming you have no immediate need for the money). Which would you prefer?

You cannot really answer this question until we supply you with one more piece of information: the interest you can earn in one year by putting the $100,000 in an alternate investment such as a bank account. You can easily answer the question if you know that you can put the $100,000 you'd receive today, in a bank account paying 10% yearly compound interest.

Think about the choices again: receive $100,000 today or receive $105,000 one year from now. For those of you who would rather have the $105,000 one year from now, you would have cheated yourself out of $5,000. And here is how.

If you collect $100,000 today, you can deposit it in the bank and earn 10% interest for the year, or $10,000 ( = 10% of $100,000), on that money. In one year, you would have a principal and interest total of $110,000. This is $5,000 more than you would get if you'd opted to receive $105,000 one year in the future.

Let's be a bit more precise in our calculations and use the proper terms for the analysis. In business school, the $110,000 you would earn in the future based on the 10% interest rate is called the Future Value. The $100,000 you are offered today to forego the Future Value is called the Present Value. The equation to go from the Present Value to the Future Value is as follows:

Future Value = (Present Value) + (Present Value) x (Return On Investment)

Future Value = ($100,000) + ($100,000) * (10%) = $110,000

If we told you that you can have $100,000 today or $110,000 one year from now, both choices are equivalent because the extra $10,000 we would give you one year from now exactly equals the amount of money you can earn by investing $100,000 in the bank for one year. Therefore you should demand more that $110,000 a year from now in order to make out better in the deal. 

This time value of money idea means that if you have a choice of receiving money today or a year from now, the money you should expect a year from now (by investing the money you received today) should be higher than the money you are offered today.

Turning the situation around a bit, suppose someone told you that you are eligible to receive $100,000 one year from now. At the same time, she asks you how much money you'd require today such that you'd give up the $100,000 money you can receive in a year? Once again, this would depend on how much you can earn by investing the money you would be getting today for one year. Let's go through the numbers.

Assume again that the interest rate you can get by putting your money in a bank is 10% yearly compound rate. The question you have to ask yourself is this: how much will I have to put in a bank account which pays 10% yearly compound interest such that at the end of one year I'd have $100,000 or more? We begin with our Future Value equation:

Future Value = (Present Value) + (Present Value) x (Return On Investment)


What we are trying to figure out in the equation above is Present Value—how much you would need today such that if you invest it, you would end up with $100,000 in a year. We can easily solve the equation using basic math in the following steps:

 Future Value = (Present Value) + (Present Value) x (Return On Investment)

Future Value = Present Value * (1 + Return On Investment)

Present Value = Future Value / (1 + Return On Investment)

Substituting the numbers in our example, we get the following equation:

Present Value = $100,000 / (1 +10%) = $100,000/(1 + .1) = $100,000 /1.1

Present Value = $90,909.09


Remember the original question: how much cash would you require today such that you would forgo $100,000 one year from now? As you can see from the formula above, the answer is that you should require more than $90,909.09 today if you can invest the money you receive today at an investment that would earn you a 10% return. We can prove this.

With exactly $90,909.09 on hand today (Present Value), you could put it in a bank account earning 10% per year. The total amount of money you would have in one year if you invest this money in the bank (Future Value) would be calculated as follows:


Future Value = $90,909.09 + ($90,909.09) x (10%)

Future Value = $90,909.09 + $9090.909 = $100,000

So if you received exactly $90,909.09 today, it would be exactly the same as receiving $100,000 one year from now if you could invest the money you received in a bank account earning 10% interest.

However, if you receive anything more than $90,909.09, you will be better off taking the money today. Let's assume that you were offered $93,000 today (the Present Value) versus receiving $100,000 a year from now (the Future Value). The future value of the $93,000 would be as follows. 

Future Value = Present Value * (1 + Return On Investment)

Future Value = $93,000 * (1 + 10%) 

Future Value = $93,000 * (1.1) = $102,300

So if you received exactly $93,000 today, you should take it instead of receiving $100,000 a year from now if you can earn 10% interest on the $93,000 because you will end up with $102,300 instead.

Therefore, you should always take the deal if you receive any amount over $90,909.09 in the scenario we just described.

Things get slightly more complicated if the investment period is multiple years versus our one-year example but we will save this for another time.