PV = FV / (1 + i)n
PV = Present Value
FV = Future Value
i = Discount rate
n = Number of periods
The present value of a lump sum formula shows what a cash lump sum received in the future is worth today.
The formula discounts the value of the lump sum received at the end of period n (future value), back to its value at the start of period 1 (present value).
The Excel PV function can be used instead of the present value of a lump sum formula, and has the syntax shown below.
PV(i, n, pmt, FV, type)
*The pmt and type arguments are not used when performing the present value calculation in Excel.
Present Value of a Lump Sum Formula Example
If a lump sum of 25,000 is received at the end of period 10, and the discount rate is 5%, then the value of the lump sum today is given by the present value of a lump sum formula as follows:
PV = FV /(1 + i)n PV = 25,000 /(1 + 5%)10 PV = 15,347.83
The same answer can be obtained using the Excel PV function as follows:
PV = -PV(i,n,,FV) PV = -PV(5%,10,,25000) PV = 15,347.83
The present value of a lump sum formula is one of many used in time value of money calculations, discover another at the link below.