# Present value

The present value (PV) is the value that a certain flow of money has today that we will receive in the future.

That is, the present value is a formula that allows us to calculate what is the value of today that has an amount of money that we will not receive right now, but later.

To calculate the VP we need to know two things: the money flows that we will receive (or that we will pay in the future since the flows can also be negative) and a rate that allows discounting these flows.

## Present value concept

Present value seeks to reflect that it is always better to have an amount of money today than to receive it in the future.

In effect, if we have the money today we can do something to make it productive, such as investing it in a company, buying shares or leaving it in the bank to pay us interest, among other options.

Even if we don’t have a certain plan to invest the money, we can simply spend it to satisfy our tastes and we don’t have to wait to receive it in the future.

Considering the above, receiving an amount of money later (not today) implies an opportunity cost and this is what is reflected in the calculation of the present value. Thus, we discount (write off) the value of future flows to bring them to the present.

The concept of VP is commonly used to determine whether or not it is convenient to invest in a certain project, to value the assets that already exist, to calculate the value of the pension that we will receive in old age, etc.

## Present value formula

Suppose we will receive an amount of money in the future (n years in the future or periods in the future) and our discount rate is r%, which reflects our opportunity cost. Then the present value is:

VP = Fn / (1 + r) n

Now, if we receive several money flows in different periods we have:

VP = F0 + F1 / (1 + r) + F2 / (1 + r) 2 +… .. + Fn / (1 + r) n

Where:

Fi = Flows (i = 0,1,2,3… .n)

r = discount rate

## Present value calculation example

When we want to value an investment project , we discount the flows that we will receive at a certain rate. If the VP of the project is greater than zero, then the investment is profitable, otherwise we will not gain anything or we will lose money.

Let’s see an example: Juan asks Pablo to rent his vehicle for 3 months at a monthly payment of 5,000 euros (the first payment is today). After this time, it will be bought for 45,000 euros. Juan’s opportunity cost is 5% per month. What is the VP of the project?

We calculate the VP:

PV = 5,000 + 5,000 / (1 + 5%) + 5,000 / (1 + 5%) 2 + 45,000 / (1 + 5%) 3

PV = 53,170 euros (approximate value)