# Why use present value?

Jul 6, 2015

Many circumstances require knowing what money is worth in a previous time period.

#### Explanation:

The best way to think of money (cash flow) is that exists somewhere on a time line. It could be a gift of $5,000 you expect to receive from your grandparents when you graduate in 5 years. It could be the monthly salary you expect to receive when you start working 5 years from today or the monthly payments you will have to make on your car loan when you buy a car. These amounts exist somewhere on a time line. Time line for the graduation gift. Here is the time line for your graduation gift. T_0/(?).......T_5/(+5000) ${T}_{0}$is today and ${T}_{5}$is 5 years from now. We see that at ${T}_{5}$you will have a cash inflow of$5,000.

But you don't want to wait. You suggest to your grandparents that you can use the money now. They say, "Fine, but we are not going to give you the full amount." But they would agree to give you an equivalent amount today. Here is where it is important to know the present value of the future gift of $5,000. Using the present value formula,you can make the calculation. $P V = \left(\frac{F V}{1 + r} ^ n\right)$FV=$5,000
n=the number of years until you receive the future value of $5,000. r=a reasonable rate of return you can receive on any invested money. Here (as in many cases) we will make an assumption - 3%. $P V = \left(\frac{5000}{1.03} ^ 5\right)$Solving for PV, we arrive at the equivalent amount of$4,313. (Fortunate for you, interest rates are low right now.)

Your grandparents should be indifferent between giving you $5,000 in 5 years or$4,313 today. If they set aside $4,313 in a savings account that pays 3% interest, after 5 years they would have the$5,000.

Present value is used in many instances related to economics, finance, investments, and personal finance. It is important for calculating things like car payments, retirement goals, the price of bonds, and Net Present Values.