present value

Present 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.

Calculation

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 for years at a rate of interest of % (where interest of "5 percent" is expressed fully as 0.05) compounded annually, the present value of the receipt of , years in the future, is:

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.

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.

Choice of interest rate

The interest rate used is the risk-free interest rate. 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.

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.

A cash flow stream with a limited number (n) of periodic payments (C), receivable at times 1 through n, is an annuity. Future payments are discounted by the periodic rate of interest (i).The present value of this annuity is determined with this formula:

A periodic amount receivable indefinitely is called a perpetuity, although few such instruments exist. The present value of a perpetuity can be calculated by taking the limit of the above formula as n approaches infinity. The bracketed term reduces to one leaving:

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.

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:
number of periods
interest rate in the period
present value at time 0
future value at time n

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

The time value of money is based on the premise that an investor prefers to receive a payment of a fixed amount of money today, rather than an equal amount in the future, all else being equal.
worldwide view of the subject.

On ground of assurance of the return, there are two kinds of Investments - Riskless and Risky.
Compound interest is the concept of adding accumulated interest back to the principal, so that interest is earned on interest from that moment on. The act of declaring interest to be principal is called compounding (i.e. interest is compounded).
Investment or investing[1] is a term with several closely-related meanings in business management, finance and economics, related to saving or deferring consumption.
In mathematics, a percentage is a way of expressing a number as a fraction of 100 (per cent meaning "per hundred"). It is often denoted using the percent sign, "%". For example, 45 % (read as "forty-five percent") is equal to 45 / 100, or 0.45.
A year (from Old English gēr) is the time between two recurrences of an event related to the orbit of the Earth around the Sun. By extension, this can be applied to any planet: for example, a "Martian year" is the time in which Mars completes its own orbit.
In a linear conception of time, the future is the portion of the time line that has yet to occur, i.e. the place in space-time where lie all events that still will or may occur.
• Additive inverse, an arithmetic concept
• Additive rhythm, a larger period of time constructed from smaller ones
• Additive synthesis, an audio synthesis technique

Cash flow is a term that refers to the amount of cash being received and spent by a business during a defined period of time, sometimes tied to a specific project. Measurement of cash flow can be used
• to evaluate the state or performance of a business or project.

In the branch of mathematics called functional analysis, the Laplace transform, , is a linear operator on a function f(t) (original ) with a real argument t (t ≥ 0) that transforms it to a function F(s) (
The risk-free interest rate is the interest rate that it is assumed can be obtained by investing in financial instruments with no default risk. However, the financial instrument can carry other types of risk, e.g.
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.

Example

bond is a debt security, in which the authorized 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. All material things can be lent but this article focuses exclusively on monetary loans. Like all debt instruments, a loan entails the redistribution of financial assets over time, between the and the .
lease or tenancy is the right to use or occupy personal property or real property given by a to another person (usually called the or tenant) for a fixed or indefinite period of time, whereby the lessee obtains exclusive possession of the property in return for paying the

An annuity contract is a financial product, typically offered by a financial institution, that may accumulate value and take a current value and pay it out over a period of years.
Depreciation is a term used in accounting, economics and finance with reference to the fact that assets with finite lives lose value over time. (There is also a separate use in international finance to refer to a reduction in the exchange rate of a currency - see Depreciation
Summation is the addition of a set of numbers; the result is their sum. The "numbers" to be summed may be natural numbers, complex numbers, matrices, or still more complicated objects. An infinite sum is a subtle procedure known as a series.
geometric series is a series with a constant ratio between successive terms. For example, the series

is geometric, because each term is equal to half of the previous term.

Simple Description

A perpetuity is an annuity that has no definite end, or a stream of cash payments that continues forever. There are few actual perpetuities in existence (although the British government has issued them in the past, and they are known and still trade as
Inflation is measured as the growth of the money supply in an economy, without a commensurate increase in the supply of goods and services. This results in a rise in the general price level as measured against a standard level of purchasing power.
Credit risk is the risk of loss due to a debtor's non-payment of a loan or other line of credit (either the principal or interest (coupon) or both).

Faced by lenders to consumers

Main article: Consumer credit risk