**NPV = –C _{0} + [ C_{1 }÷ (1 + r) ] + [ C_{2} ÷ (1 + r)^{2} ] + … + [ C_{r} (1 + r)^{r} ]**

–C_{0} = Initial investment

C = cash flow

r = discount rate

T = time

Net present value or NPV is basically a formula which is used by investors and financial analysts to figure out the present value of all cash flows from an investment discounted at suitable rate. The formula can be rewritten for discount sum of all cash flows as;

NPV = –C_{0} + { ∑^{T}_{i=1} [ C_{i }÷ (1 + r)^{i} ] }

While making decisions to invest in which project it is very important to measure the profitability of each investment or project. Therefore, to calculate the profitability a number of techniques and approaches are available for different purposes one of such methods is NPV. In the formula above **–C _{0}** is the initial investment which an individual will invest in the project it is represented as negative as it is cash outflow. With this approach the cash outflow will be automatically subtracted from the discounted sum of all cash inflows and the final result will show only the profit/loss value.

## Net present value of illustration

Let’s suppose an illustration where Jason T-shirts is a company looking to invest in an investment project. Jason T-shirt is expecting to invest around $700,000 for making a new department for their product. It is estimated that the cash outflow for 1^{st} year will be $500,000 for the 2^{nd} year it will be $300,000 for the 3^{rd} year it will be 100,000 and in 4^{th} year it will be $20,000. The discount rate for expected return is estimated as 10%.

Year |
Cash Flow |
Discount rate |
Present Value |

0 | -700,000 | -700,000 | |

1 | 500,000 | 0.9091 | 454,550 |

2 | 300,000 | 0.8265 | 247,950 |

3 | 100,000 | 0.7513 | 75,130 |

4 | 20,000 | 0.683 | 13,660 |

**With this calculation the net present value is = $91,290*

If we use the formula of net present value as it is available above then;

NPV = –$700,000 + [$500,000 ÷ 1.10] + [$300,000 ÷ 1.10^{2}] + [$100,000 ÷ 1.10^{3}] + [$20,000 ÷ 1.10^{4}]

When solving for the above equation, the new investment for Jason T-shirt is a profitable venture with a positive NPV of $91,271.09