PRESENT VALUE: WHAT IT IS, HOW IT IS CALCULATED AND EXAMPLES - ECONOMY - 2025

The present value (PV) is the present value of a future sum of money or cash flow, given a specific rate of return from the valuation date. It will always be less than or equal to the future value, because money has the potential to earn interest, a characteristic known as the time value of money.

The concept of present value is one of the most fundamental and widespread in the world of finance. It is the basis for the prices of stocks and bonds. Also of financial models for banking and insurance, and valuation of pension funds.

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This is explained by the fact that the money received today can be invested to obtain a return. In other words, present value represents the time value of money

In either case, present value provides an estimate of what should be spent today for an investment to be worth a certain amount of money at a specific point in the future.

What is present value?

Present value is also known as discounted value. It is based on the fact that receiving $ 1,000 today is worth more than $ 1,000 in five years, because if the money were obtained now it could be invested and receive an additional return during those five years.

Future value can be related to future cash inflows from investing today's money, or the future payment required to repay money that is borrowed today.

Present value is used in reference to future value. Comparing present value to future value better illustrates the time value of money principle and the need to charge or pay additional risk-based interest rates.

Value of money over time

That is, today's money is worth more than the same tomorrow's money due to the passage of time. In almost all scenarios, a person would rather have $ 1 today versus the same $ 1 tomorrow.

A dollar today is worth more than a dollar tomorrow because this dollar can be reversed and earn one day's interest. This causes the total to accumulate, giving a value of more than a dollar for tomorrow.

Interest can be compared to rent. Just as a tenant pays rent to a landlord, without ownership of the asset being transferred, interest is paid by a borrower who gains access to the money for a time before returning it.

By allowing the borrower access to the money, the lender has sacrificed the exchange value of this money and is compensated in the form of interest. The initial amount of funds loaned, the present value, is less than the total amount of money paid to the lender.

How is it calculated?

The most commonly applied present value model uses compound interest. The standard formula is:

Present value (VP) = VF / (1 + i) ^ n, where

VF is the future amount of money to be discounted.

n is the number of compound periods between the current date and the future date.

i is the interest rate for a compounding period. Interest is applied at the end of a compounding period, for example, annually, monthly, daily).

The interest rate i is given as a percentage, but it is expressed as a number in the formula.

For example, if $ 1,000 is to be received in five years, and the effective annual interest rate during this period is 10%, then the present value of this amount is:

PV = $ 1,000 / (1 + 0.10) ^ 5 = $ 620.92.

The interpretation is that for an effective annual interest rate of 10%, a person would not care to receive $ 1,000 five years from now, or $ 620.92 today.

Other uses

With the same formula, it is also possible to calculate the purchasing power in today's money of an amount VF of money, n years in the future. In this case, i would be the assumed future rate of inflation.

The present value calculation is extremely important in many financial calculations. For example, net present value, bond yields, spot rates, and pension obligations depend on present or discounted value.

Learning how to use a financial calculator to do present value calculations can help you decide whether to accept offers such as a cash back, 0% financing on a car purchase, or pay points on a mortgage.

Examples

Example 1

Suppose Paul wanted to put his money into an account today to make sure his son has enough money in 10 years to buy a car.

If you want to give your child $ 10,000 in 10 years, and you know you can get 5% annual interest from a savings account during that time, how much should you put into the account now? The present value formula says:

PV = $ 10,000 / (1 + 0.05) ^ 10 = $ 6,139.13

So, $ 6,139.13 today will be worth $ 10,000 in 10 years if you can earn 5% interest each year. In other words, the present value of $ 10,000 in this scenario is $ 6,139.13.

It is important to note that the three most influential components of present value are time, the expected rate of return, and also the size of the future cash flow.

To take inflation into account in the calculation, investors should use the real interest rate. This is the nominal interest rate minus the inflation rate.

Present value provides a basis for evaluating the appropriateness of any future financial benefit or obligation.

Example 2

An investor must decide in which financial project he is going to invest his money. Present value offers a method for making such a decision. A financial project requires an initial outlay of money. This money will be to pay the share price or the price of a corporate bond.

The project intends to return the initial outlay, as well as some surplus, such as interest or future cash flows.

The investor can decide which project to invest in by calculating the present value of each project, using the same interest rate for each calculation, and then comparing them.

The project with the smallest present value, with the lowest initial outlay, will be chosen. This is because it will offer the same return as the other projects for the least amount of money.

References

1. Will Kenton (2018). Present Value - PV. Taken from: investopedia.com.
2. Wikipedia, the free encyclopedia (2019). Present value. Taken from: en.wikipedia.org.
3. Investing Answers (2019). Present value (PV). Taken from: investinganswers.com.
4. Harold Averkamp (2019). Present Value of a Single Amount. Accounting Coach. Taken from: accountingcoach.com.
5. My Accounting Course (2019). What is Present Value (PV)? Taken from: myaccountingcourse.com.