DEFINITION: The concept of “present value” refers to the worth at the present time of expected future receipts—whether a sum of money or source of cash flow—assuming a given rate of return.
To calculate the present value of expected future receipts, one must discount the expected receipts at an assigned discount rate. The greater the discount rate, the smaller the present value of the future receipts.
The most important factor in accurately assessing present value is the correct determination of a suitable discount rate.
ETYMOLOGY: Most historians trace the origin of the concept of “present value” to work by the American economist Irving Fisher published in his 1930 book The Theory of Interest. However, others argue that the basic idea is already present in the Liber abaci [Book of Calculation] by Fibonacci (Leonardo Pisano), published in 1202.
The English adjective “present” derives, via Middle English and Middle French, from the Latin present participle praesens, praesentis, from the verb praesum, praeesse, meaning “to be before,”
The English noun “value” derives, via Middle English and Middle French, from the Vulgar Latin noun valuta, meaning “value,” which is the feminine form of the adjective valutus (“valued”). The Vulgar Latin forms derive from the classical adjective validus, meaning “strong,” and verb valeo, valēre, meaning “to be strong.”
USAGE: It is a basic principle of economics—which derives from an essential feature of human nature—that a given sum of money has a higher subjective value if one obtains it today than if one must wait until, say, next week to obtain it.
Put differently, a given sum of money that is expected to be obtained in the future does not have the same subjective worth as the very same amount of money received today.
That is why the present value of future receipts is a discounted amount. Namely, it is the amount of receipts that an individual would subjectively consider to be equivalent, if it was obtained today, to the amount of receipts expected in the future.
Opportunity Costs
In addition to the fundamental human preference for the present over the future, there is a further economic reason why money in hand today has a greater value than money expected in the future (especially, the relatively distant future).
The reason is that one may invest money obtained today so that one will have a larger amount of money (principle plus interest) in a year’s time than one would have if one simply received the principal amount in a year’s time.
This additional amount of money that one would forgo by waiting a year to receive the principal amount is a type of “opportunity cost.”
For this reason, the concept of present value should incorporate any opportunity costs that may accrue over a given time period.
Inflation
Inflation consists in the gradual rise of prices for goods and services as time passes.
The money you possess at present entitles you to purchase certain goods at their present prices. However, if it expected that the prices of those goods prices will increase in the future, reducing the buying power of your present quantity of money.
Therefore, it may be foreseen that money left unspent today will decrease in value in the future by an amount linked to the rate of inflation.
The Discount Rate
The concept of the “discount rate” refers to the rate of return on an investment used in computing present value.
Essentially, the discount rate represents the opportunity costs incurred by an investor if it decides to defer its receipts, in inflation-adjusted terms, to the future, as opposed to receiving the same amount today.
The discount rate combines the element of opportunity cost with an applicable interest rate, systematically amplifying future value in a commensurate manner.
On the other hand, the discount rate may be used to calculate the present value of expected future receipts of a given amount to be obtained on a certain date.
Thus, the term “discount rate” alludes to the process of reducing future value to present value. It creates a sort of parity between the larger future and smaller present amounts of money, taking into account the opportunity costs and inflationary erosion associated with waiting for the larger future amount.
The Present Value Formula
For these reasons, the present value of a future amount of money must take into account the potential opportunity costs and inflation rate.
This may be achieved quantitatively by means of the following mathematical formula:
Consider the following case:
An investor must choose between receiving an amount FV in n years’ time and a somewhat higher amount today.
The question is: How much, exactly, must it receive today to make the trade-off worthwhile?
Or, in other words: What is the present value of FV, n years from now, assuming a given rate of return on investment and inflation rate.
Here is the formula (where r = discount rate; and n = number time periods involved):
Present Value = Future Value / (1 + r)n
Let us take a concrete example.
Suppose that the future principal to be delivered in the future is $5,000; the discount rate (i.e., the rate of return in inflation-adjusted dollars) is five percent; and the number of time periods involved is two years.
Then,
Present Value = $5,000 / (1 + .05)2
Present Value = $5,000 / (1.1025)
Present Value = $4,535.15
Thus, the individual in question must receive at least $4,535.15 today if he is wait two years to receive a principal of $5,000 plus five-percent interest.
This calculation effectively showcases the idea of the time value of money. It also emphasizes the rationale for supplementary interest based on risk.
In summary, money held today holds greater significance than an identical amount in the future due to the passage of time.
The calculation of discounted or present value holds great significance in various financial evaluation contexts. Instances include net present value, bond yields, and pension commitments, all of which are based on present value assessments.