Formula and Use
The present value of a lump sum formula shows what a 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).
In the formula the terms have the following meanings.
- PV = present value of the future cash flow
- FV = future value of the cash flow
- i = period discount rate or interest rate
- n = number of periods until the cash flow is received
Excel Function
The Excel PV function can be used instead of the PV of a lump sum formula. The syntax of the function is 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 Examples
Example 1
To illustrate suppose a lump sum of 25,000 is received at the end of period 10. Additionally the discount rate is 5%. In this case the value of the lump sum today is given by the present value of a lump sum formula as follows.
FV = 25,000 n = 10 periods i = 5% PV = FV /(1 + i)n PV = 25,000 /(1 + 5%)10 PV = 15,347.83
In this case at a discount rate of 5%, the value today of 25,000 received in 10 periods time is 15,347.83.
The same answer can be obtained using the Excel PV function as follows:
FV = 25,000 n = 10 periods i = 5% PV = -PV(i,n,,FV) PV = -PV(5%,10,,25000) PV = 15,347.83
Example 2
To further illustrate suppose a lump sum of 10,000 is received at the end of year 5. Additionally the discount rate is 4%. In this case the value of the lump sum today is given by the PV of a lump sum formula as follows.
FV = 10,000 n = 5 years i = 4% PV = FV /(1 + i)n PV = 10,000 /(1 + 4%)5 PV = 8,219.27
In this case at a discount rate of 4%, the value today of 10,000 received in 5 periods time is 8,219.27.
Again the same answer can be obtained using the Excel PV function as follows:
FV = 10,000 n = 5 years i = 4% PV = -PV(i,n,,FV) PV = -PV(4%,5,,10000) PV = 8,219.27
The PVof a lump sum formula is one of many used in time value of money calculations, discover another at the link below.
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 and has built financial models for 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 degree from Loughborough University.