Present value, also known as present discounted value, is the value on a given date of a payment or series of payments made at other times.

If the payments are in the future, they are discounted to reflect the time value of money and other factors such as investment risk. If they are in the past, their value is correspondingly enhanced to reflect that those payments have been (or could have been) earning interest in the intervening time. Present value calculations are widely used in business and economics to provide a means to compare cash flows at different times on a meaningful “like to like” basis.

If offered a choice between 100 today or 100 in one year and there is a positive real interest rate throughout the year ceteris paribus, a rational person will choose 100 today. This is described by economists as time preference. Time preference can be measured by auctioning off a risk free security—like a US Treasury bill. If a 100 note, payable in one year, sells for 80 now, then 80 is the present value of the note that will be worth 100 a year from now. This is because money can be put in a bank account or any other (safe) investment that will return interest in the future.

An investor who has some money has two options: to spend it right now or to save it. But the financial compensation for saving it (and not spending it) is that the money value will accrue through the compound interest that he will receive from a borrower (the bank account on which he has the money deposited).

Therefore, to evaluate the real value of an amount of money today after a given period of time, economic agents compound the amount of money at a given (interest) rate. Most actuarial calculations use the risk-free interest rate which corresponds the minimum guaranteed rate provided by a bank’s saving account for example. To compare the change in purchasing power, the real interest rate (nominal interest rate minus inflation rate) should be used.

The operation of evaluating a present value into the future value is called a capitalization (how much will 100 today be worth in 5 years?). The reverse operation—evaluating the present value of a future amount of money—is called a discounting (how much will 100 received in 5 years—at a lottery for example—be worth today?).

It follows that if one has to choose between receiving 100 today and 100 in one year, the rational decision is to choose the 100 today. If the money is to be received in one year and assuming the savings account interest rate is 5%, the person has to be offered at least 105 in one year so that two options are equivalent (either receiving 100 today or receiving 105 in one year). This is because if 100 is deposited in a savings account, the value will be 105 after one year.

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