# Present value

**Present value**is the value on a given date of a future payment or series of future payments, discounted to reflect thetime value of money and other factors such asinvestment 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 can lend or borrow for $,t,$ years at an interest rate $,i,$ per year (where interest of "5percent " is expressed fully as 0.05), the present value of the receiving $,C,$ monetary units $,t,$year s in thefuture is::$C\_t\; =\; C(1\; +\; i)^\{-t\},\; =\; frac\{C\}\{(1+i)^t\}\; ,$

This is also found from the formula for the future value with negative time.

The

purchasing power in today's money of an amount "C" of money, "t" years into the future, can be computed with the same formula, where in this case "i" is an assumed futureinflation rate .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 of:

:$mathrm\{PV\}\; =\; frac\{C\}\{(1+i\_1)(1+i\_2)\}\; ,$

**Technical details**Present value is

additive . The present value of a bundle ofcash flow s 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 arisk 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

loan s,lease s, salaries, membership dues, annuities, straight-linedepreciation charges) stipulate structured payment schedules, which is to say payment of the same amount at regular time intervals. The term "annuity" is often used to refer to any such arrangement when discussing calculation of present value. The expressions for the present value of such payments aresummation s ofgeometric 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 ordinary annuity is determined with this formula: [*cite web |url=http://www.college-cram.com/study/finance/presentations/1116|title=Annuities: Present and Future Value|accessdate=2008-07-10*]:$PV\; ,=,frac\{C\}\{i\}cdot\; [1-frac\{1\}\{left(1+i\; ight)^n\}]$

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::$PV,=,frac\{C\}\{i\}$

The first formula is found from subtracting from the latter result the present value of a perpetuity delayed n periods.

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 thedefault risk is incorporated into the interest rate.See

time value of money for further discussion.**References****ee also***

Capital budgeting

*Lifetime value

*Net present value

*Future value

*Time value of money

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2010.*

### Look at other dictionaries:

**Present value**— Pres ent value or Present worth Pres ent worth (of money payable at a future date). The principal which, drawing interest at a given rate, will amount to the given sum at the date on which this is to be paid; thus, interest being at 6%, the… … The Collaborative International Dictionary of English**present value**— The amount of cash today that is equivalent in value to a payment, or to a stream of payments, to be received in the future. To determine the present value, each future cash flow is multiplied by a present value factor. For example, if the… … Financial and business terms**Present value**— The amount of cash today that is equivalent in value to a payment, or to a stream of payments, to be received in the future. The New York Times Financial Glossary * * * present value present value also present discounted value ➔ value1 * * *… … Financial and business terms**Present Value - PV**— The current worth of a future sum of money or stream of cash flows given a specified rate of return. Future cash flows are discounted at the discount rate, and the higher the discount rate, the lower the present value of the future cash flows.… … Investment dictionary**present value**— The value at the present time of future *cash flows. The *time value of money implies that units of *money are worth more at present than in the future, owing to the erosion of monetary value caused by inflation. Present values are thereby… … Auditor's dictionary**present value**— /ˌprez(ə)nt vælju:/ noun 1. the value something has now ● In 1984 the pound was worth five times its present value. 2. the value now of a specified sum of money to be received in the future, if invested at current interest rates. Abbreviation PV… … Dictionary of banking and finance**present value**— noun also present worth : the principal of a sum of money payable at a future date that drawing interest at a given rate will amount to the given sum at the date on which this sum is to be paid at 65 interest the present value of $106 due one… … Useful english dictionary**Present Value**— Der Barwert (z. T. Gegenwartswert oder aus dem Englischen: present value) ist ein Begriff aus der Finanzmathematik . Der Barwert, ist der Wert, den zukünftige Zahlungen in der Gegenwart besitzen. Er wird durch Abzinsung der zukünftigen Zahlungen… … Deutsch Wikipedia**present value**— dabartinė vertė statusas T sritis turto vertinimas apibrėžtis Būsimos mokamos sumos ar kelių sumų vertė, diskontuota iki esamos arba kito laikotarpio pradžios dienos. atitikmenys: angl. present value šaltinis Tarptautiniai vertinimo standartai… … Lithuanian dictionary (lietuvių žodynas)**present value**— present worth (of a sum payable in the future) calculated by deducting interest that will accrue between the present and future date … English contemporary dictionary