Present Value of a Lump Sum Formula

Formula

PV = FV / (1 + i)n
Variables used in the formula
PV = Present Value
FV = Future Value
i = Discount rate
n = Number of periods

Use

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).

Excel Function

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.

Last modified July 16th, 2019 by Michael Brown

About the Author

Chartered accountant Michael Brown is the founder and CEO of Double Entry Bookkeeping. He has worked as an accountant and consultant for more than 25 years in all types of industries. He has been the CFO or controller of both small and medium sized companies and has run small businesses of his own. He has been a manager and an auditor with Deloitte, a big 4 accountancy firm, and holds a BSc from Loughborough University.

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