Present Value & the Time Value of Money

The time value of money is another very important investing 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.

A Dollar Today Is Better Than a Dollar Tomorrow

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 could have $100,000 today or $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 return you could earn in one year by putting the $100,000 in an alternate investment. You could easily answer the question if you knew that you could 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. If you collect $100,000 today, you can deposit it in the bank and earn 10% interest for the year, or $10,000, 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.

If we told you that you could 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 could earn by investing $100,000 in the bank for one year.

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 expect a year from now should be higher than the money you are offered today. 

Future Value and Present Value

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 asked you how much money you’d require today such that you’d give up the $100,000 you could receive in a year. Once again, this would depend on how much you could earn by investing the money you would get today for one year. Let’s go through the numbers.

Assume again that the interest rate you would get by putting your money in a bank is a 10% yearly compound rate. The question you have to ask yourself is: how much would I have to put in a bank account that pays 10% yearly compound interest such that at the end of one year, I’d have $100,000? Mathematically, the equation to solve is as follows:

        Future Value = (Present Value) + (Present Value) x (Rate on Investment)

Where Future Value is the amount of money you would get in the future, which is $100,000 in our example.
Where Present Value is the amount of money you would need today such that if you invested it in a bank today, you would end up with the Future Value. 
Where Rate on Investment is the interest rate you would be paid for your investment, which is 10% in our example.

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. Present Value has a very special meaning in the world of investing and finance so you should make sure you understand the concept thoroughly here and now. 

The Present Value amount can be solved my manipulating the equation above to get the following:

Present Value = Future Value / (1 + Rate 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 not have to be paid $100,000 one year from now? As you can see from the formula above, the answer is that you should require at least $90,909.09 today, and we can prove it. With $90,909.09 on hand today, 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

If we changed the original question and asked how much cash you would require today such that you would not have to be paid $100,000 two years from now, the answer gets slightly more complicated, but the basic principle is the same. You just need to know how much money you would need today such that if you earn 10% interest in the first year, and another 10% interest in the second year, you would end up with $100,000. Without going through the mathematics, the answer is $82,644.63.