September 02, 2020

# How to Calculate the Present Value of a Single Amount

The present value of money plays an important role in business and personal financial decisions to invest money. It is also used in the financial world to value stocks, to find out what is the better deal and what financially is a better thing to do. The present value provides a basis for assessing the fairness of any future financial benefits or liabilities. It is important for investors to decide upon whether to accept or reject a proposal because a sum payable in the future is worth less today than the stated amount.

## Present Value Definition

Present value is defined as today’s value of a single payment or series of payments to be received at a later date, given a specific interest rate. For example, if someone offered you 1 million dollars today versus 1 million dollars 20 years from now. You know how much \$1 million is worth today (it is worth \$1 million), but how much is \$1 million worth in 20 years? If we calculate how much money that future sum is in current money, it will be easier to make the right decision.

## Present Value of Money Formula

When we look for a present value of a single amount, we want to determine the value of cash flow in the future. The time value of money tells us that future money is worth less than the current money. We can find out exactly how much less it is worth using a specific formula.

The future value of a single amount is equal to the amount we save or invest today, the present cost of an item, and such multiplied by one plus the interest rate to the nth power, where n is the number of compounding periods we hold that principle in the bank or the number of periods that we invest the money. If there is more than one compounding per year, you would divide the interest rate by the number of compoundings per year to get the i value and multiply the number of years by the number of compoundings per year to get the n value.

Let’s modify the future value formula and figure out the present value. What we see is that the present value of future cash flow is equal to that future cash flow divided by one plus the interest rate to the nth power. This is the calculation of the value today of an amount you will have in the future. At a specific interest rate, you will be able to calculate what it is worth currently.

It should be noted that we are not earning interest. We are giving it up by receiving the money in the future. Thus, you might see it often referred to as a discount rate, which is the rate that the individual discounts future cash flows. Thus, the final investment decision will depend on how impatient you are, how risky the business environment is, how much interest you could earn during that period, and how much inflation you expect.

There is a relationship between all the factors involved in the calculation. For a given interest rate, the longer the time period, the lower the present value. For a given time period, the higher the interest, the smaller the present value.

## How to Calculate Present Value?

Let’s return to our example of being proposed \$1 million today or 20 years from now and use the formula explained above to calculate the present value. Since we do not know an interest rate value, we will assume it is 10%.

PV = 1,000,000 / (1 + 0.1)20

PV = \$148,643.63

As you can see, if the 10% discount was relevant, your 1 million dollars will be worth a lot less in 20 years. That \$1 million has depreciated due to the time value of money.

Now, we are going to review another example where the same formula is used for a slightly different purpose. For instance, Jake wants to have \$1,500 in ten years in order to buy a camera for his future plans. He wants to invest in an account that earns 8% interest compounded annually. How much should he invest today in order to achieve this goal? We are going to input the data given into the formula and calculate the answer.

PV = 1,500 / (1 + 0.08)10

PV = \$694.79

According to our calculation, Jake would need to invest \$694.79 today to have \$1,500 in ten years. There is also an easier way to calculate the present value with the help of a present value factor that can be looked up in a special table. For this calculation, you would simply multiply the future value by the factor to get the present value. The result, as you can see below will be exactly the same.

PV = 1,500 x 0.4632

PV = \$694.8