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.