Net Present Value Formula
The net present value formula calculates NPV, which is the difference between the present value of cash inflows and the present value of cash outflows, over a period of time. Net present value (NPV) determines the total current value of all cash flows generated, including the initial capital investment, by a project. Let us study the net present value formula using solved examples.
What Is Net Present Value Formula?
The net present value formula finds application in estimating which projects are likely to generate great profits. This Formula can be expressed as:
\( NPV = \sum_{n = 1}^N \frac{ C_n }{ (1 + r)^n } \)
 N = Total number of time periods
 n = Time period
 \(C_n\) = Net cash flow at time period
 r = Internal rate of return
OR
NPV can also be calculated by finding the difference between the Present Value(PV) after the competition of time duration of investment and the initial amount invested where the Present Value "PV" after time "t" for a rate of return "r" can be calculated as:
Present value, PV = \(\frac{ \text {cash value at time period }}{ (1 + \text {rate of return})^{ \text {time period}}}\)
Let us see the applications of the net present value formula in the following section.

Example 1: An investor made an investment of $500 in property and gets back $570 the next year. If the rate of return is 10%. Calculate the net present value.
Solution:
To find: Net present value on investment
Given:
Amount invested = $500
Money received after a year = $570
Rate of return = 10% = 0.1
Using net present value formula,
Present value, PV = \(\frac{ \text {cash value at time period }}{ (1 + \text {rate of return})^{ \text {time period}}}\)
PV = \(\frac{ \$ 570}{ (1 + 0.1 )^1}\)
PV = $570/1.1
PV = $518.18
Net Present Value = $518.18 − $500.00 = $18.18
Answer: For 10% rate of return, investment has NPV = $18.18.

Example 2: Sam bought a house for $750,000 and sells it a year later for $990,000, after deducting any realtor's fees and taxes. Calculate net present value, if the rate of return is 5%.
Solution:
To find: Net present value on the deal
Given:
Investment on buying the house = $750,000
Monet received from sale a year later = $990,000
Rate of return = 5% = 0.05
Using net present value formula,
Present value, PV = \(\frac{ \text {cash value at time period }}{ (1 + \text {rate of return})^{ \text {time period}}}\)
PV = \(\frac{ \$ 990,000}{ (1 + 0.05 )^1}\)
PV = $990,000/1.05
PV = $942,857.143
Net Present Value = $942,857.143 − $750,000 = $192,857.143
Answer: For 5% rate of return, investment has NPV = $192,857.143