Documentation/How Tos/Calc: PV function

PV

Returns the present value of a stream of future payments.

Syntax:

PV(rate; numperiods; payment; futurevalue; type)

rate: the (fixed) interest rate per period.

numperiods: the total number of payment periods in the term.

payment: the payment made each period. If futurevalue is given, this may omitted (defaults to 0).

futurevalue: the cash balance you wish to attain at the end of the term (optional - defaults to 0). With a loan, this would normally be 0.

type: when payments are made (optional - defaults to 0):

0 - at the end of each period.

1 - at the start of each period (including a payment at the start of the term).

The value of money is time-dependent; for example, $100 today would be worth $110 in a year if invested at a 10% interest rate.

PV returns the value today, of a payment being made each period for numperiods periods, with fixed rate interest being compounded each period. Often, the interest used is that which applies to minimum risk investments, for example those issued by a government.

The examples below clarify how the function may be used.

See Derivation of Financial Formulas for the underlying formula.

Example:

PV(5%; 15; 1000; 0; 0)

returns -10,379.66 in currency units. You have the opportunity to buy an annuity, which would pay you 1000 at the end of each year for 15 years. You assume a constant interest rate of 5%. On this basis, the annuity is worth 10,379.66 today; if it is priced higher than this you might not wish to buy it. The result is negative, because you must pay for the annuity.

PV(5%/12; 3*12; -100; 0; 0)

returns 3,336.57 in currency units. You are considering a loan of 3,500, which would mean you paying back 100 at the end of each month for 3 years. You assume a constant interest rate of 5%. On this basis, the loan is only worth 3,336.57, so might be a poor deal. The monthly payment is negative because you pay it, and the result positive because the loan is paid to you.

See also:

IPMT, PMT, PPMT, NPV, IRR, FV, NPER

Derivation of Financial Formulas

Financial functions

Issues:

• Take care that you understand how this function compounds the interest each period.