Present value, also known as present discounted value, is the value on a given date of a future payment or series of future payments, discounted to reflect the time value of money and other factors such as investment risk. 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, then the present value of $100 one year in the future is $80. This is because you can invest your money today in a bank account or any other (safe) investment that will return you interest.
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 interest that he or she 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 your bank’s saving account for example. If you want to compare your change in purchasing power, then you should use the real interest rate (nominal interest rate minus inflation rate).
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 that I receive 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 you cash $100 today and deposit in your savings account, you will have $105 in one year.
Choice of interest rate
The interest rate used is the risk-free interest rate. If there are no risks involved in the project, the rate of return from the project must equal or exceed this rate of return or it would be better to invest the capital in these risk free assets. If there are risks involved in an investment this can be reflected through the use of a risk premium. The risk premium required can be found by comparing the project with the rate of return required from other projects with similar risks. Thus it is possible for investors to take account of any uncertainty involved in various investments.