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Encyclopedia > Present value

The present value of a single or multiple future payments (known as cash flows) is the nominal amounts of money to change hands at some future date, discounted to account for the time value of money, and other factors such as investment risk. A given amount of money is always more valuable sooner than later since this enables one to take advantage of investment opportunities. Present values are therefore smaller than corresponding future values. Various denominations of currency, one form of money Money is any good or tokens that functions as a medium of exchange that is socially and legally accepted in payment for goods and services and in settlement of debts. ... The time value of money (TVM) is a way of calculating the value of a sum of money, at any time in the present or future. ... Future value measures what money is worth at a specified time in the future assuming a certain interest rate. ...

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.

## Contents

The most commonly applied model of the time value of money is compound interest. To someone who has the opportunity to invest an amount of money C for t years at a rate of interest of i% (where interest of "5 percent" is expressed fully as 0.05) compounded annually, the present value of the receipt of C, t years in the future, is: Compound interest refers to the fact that whenever interest is calculated, it is based not only on the original principal, but also on any unpaid interest that has been added to the principal. ... Invest redirects here. ... A percentage is a way of expressing a proportion, a ratio or a fraction as a whole number, by using 100 as the denominator. ... A year (from Old English gÄ“r) is the time between two recurrences of an event related to the orbit of the Earth around the Sun. ... Look up Future in Wiktionary, the free dictionary. ...

The expression (1 + i)t enters almost all calculations of present value. Where the interest rate is expected to be different over the term of the investment, different values for i may be included; an investment over a two year period would then have PV (Present Value) of:

Present value is additive. The present value of a bundle of cash flows is the sum of each one's present value. Look up Additive in Wiktionary, the free dictionary When used as a noun, additive refers to something that is introduced to a larger quantity of something else, usually to alter characteristics of the larger quantity. ... This article does not cite any references or sources. ...

In fact, the present value of a cashflow at a constant interest rate is mathematically the same as the Laplace transform of that cashflow evaluated with the transform variable (usually denoted "s") equal to the interest rate. For discrete time, where payments are separated by large time periods, the transform reduces to a sum, but when payments are ongoing on an almost continual basis, the mathematics of continuous functions can be used as an approximation. In mathematics, the Laplace transform is a technique for analyzing linear time-invariant systems such as electrical circuits, harmonic oscillators, optical devices, and mechanical systems. ...

## Choice of interest rate

The interest rate used is the risk free interest rate (for example the yield on US treasury bonds). If there are no risks involved in the project, the expected 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. A risk premium is the minimum difference between the expected value of an uncertain bet that a person is willing to take and the certain value that he is indifferent to. ...

## Annuities, perpetuities and other common forms

Many financial arrangements (including bonds, other loans, leases, salaries, membership dues, annuities, straight-line depreciation charges) stipulate structured payment schedules, which is to say payment of the same amount at regular time intervals. The term annuity is often used in to refer to any such arrangement when discussing calculation of present value. The expressions for the present value of such payments are summations of geometric series. In finance, a bond is a debt security, in which the issuer owes the holders a debt and is obliged to repay the principal and interest (the coupon) at a later date, termed maturity. ... A loan is a type of debt. ... This article or section should include material from Tenancy agreement A lease is a contract conveying from one person (the lessor) to another person (the lessee) the right to use and control some article of property for a specified period of time (the term), without conveying ownership, in exchange for... Annuity contracts are offered by organizations and individuals that may accumulate value and take a current value and pay it out over a period of years. ... Declining-balance depreciation of a \$50,000 asset with \$6,500 salvage value over 20 years. ... For evaluation of sums in closed form see evaluating sums. ... In mathematics, a geometric progression is a sequence of numbers such that the quotient of any two successive members of the sequence is a constant called the common ratio of the sequence. ...

A periodic amount receivable indefinitely is called a perpetuity, although few such instruments exist. A perpetuity is an infinite geometric series which reduces to PV = C / i, where C is the periodic cash flow and i the periodic rate of interest. A perpetuity is an annuity in which the periodic payments begin on a fixed date and continue indefinitely. ...

A cash flow stream with a limited number (n) of periodic payments ("C"), receivable at times 1 through n, is an annuity. The value of this annuity is determined with this formula:

These calculations must be applied carefully, as there are underlying assumptions:

• That it is not necessary to account for price inflation, or alternatively, that the cost of inflation is incorporated into the interest rate.
• That the likelihood of receiving the payments is high - or, alternatively, that the default risk is incorporated into the interest rate.

See time value of money for further discussion. Credit risk is the risk of loss due to a counterparty defaulting on a contract, or more generally the risk of loss due to some credit event. Traditionally this applied to bonds where debt holders were concerned that the counterparty to whom theyve made a loan might default on... The time value of money (TVM) is a way of calculating the value of a sum of money, at any time in the present or future. ...

## Present value formula

One hundred units 1 year from now at 5% interest rate is today worth:

So the present value of 100 units 1 year from now at 5% is 95.23 units.

The above is in regard to a single lump sum amount. There is a separate formula to calculate PV of annuities. For present value of annuities, use this formula:

Often, the present value formula is written in a simplified formula (for example, in textbooks on finance) as:

Similarly, the annuity formula is often simplified and written as follows:

where:
n = number of periods
r = interest rate in the period
PV = present value at time 0
FV = future value at time n

This simplified form is easier to present, and well-adapted to using financial tables, financial calculators and computer spreadsheets.

It has been suggested that this article or section be merged with Discounted cash flow. ... In marketing, the Lifetime Value (LTV) of a customer is the present value (usually expressed in currency) of future profits that can be derived from a customer based on the profits that have been received from that customer in the past. ... The process of determining which potential long-term projects are worth undertaking, by comparing their expected discounted cash flows with their internal rates of return. ... The time value of money (TVM) is a way of calculating the value of a sum of money, at any time in the present or future. ...

Results from FactBites:

 PlanetMath: present value (308 words) By calculating the present values of these options, one may be able to compare the “present” values of these payments and figure out which is the preferable option. Net present values are commonly used when one is interested in comparing car loans or home mortgages. This is version 5 of present value, born on 2007-02-09, modified 2007-02-11.
 Present value - Wikipedia, the free encyclopedia (780 words) The present value of a future cash flow is the nominal amount of money to change hands at some future date, discounted to account for the time value of money. Because of this present values are smaller than corresponding future values. The present value of a bundle of cash flows is the sum of each one's present value.
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