Net Present Value (NPV) is a method of evaluation of economical effectiveness of investment. NPV is used to calculate the difference between the value of all present and future cash flows discounted to the present, both negative and positive, over the whole life of the investment.

The NPV illustrates an important concept – that money is not free and $1 today always worth more than$1 in the future. It costs money to borrow money and the interest rate devalues future cash. There are also opportunity costs that are not tangible, but they impact how the money is invested.

This is known as the Time Value of Money. The same amount of money available at the present time is worth more than the same amount in the future, because money available at the present time can be used to create more money.

Net Present Value allows you to compare various financial products such as investments, projects and loans. It considers all the revenues, expenses and timing of the investment.

### How to Calculate Net Present Value?

Net Present Value is calculated by summing Cash Flows in time divided by (1 + discount rate) time i. This number must be reduced by the initial investment price.

$NPV = \displaystyle\sum_{t=1}^N \frac{C_{t}}{(1 + i)^{t}} - C_{0}$

Where C0 = initial investment, N = total number of periods, i = the discount rate, t = the time of the Cash Flow, Ct = net cash inflow for the period t

Considering that the initial investment price is a negative Cash Flow, i.e. outgoing payment, the sum of incoming payments, i.e. positive Cash Flow from the investment should be greater than the purchase price, then NPV will be positive and the investment will be considered profitable.

### How to Interpret Net Present Value?

The value of the NPV can be interpreted as:

• the surplus of discounted net revenue over the initial investment price
• the surplus of net profit over a return from an alternative investment with an Internal Rate of Return equal to the discount rate
• increase of investor’s capital caused by implementing the investment project, taking into account changes in the value of money over time.

In this approach, NPV gives definite signals in terms of investment decisions. According to these premises, the investment is accepted when NPV ≥0 and not accepted when NPV <0.

There is a reverse but non-linear relationship between the discount rate and NPV: as the discount rate increases the value of the NPV for the given investment decreases (for standard cash flows), which affects the evaluation of the profitability of the investment and the potential decision on its implementation. Therefore, the following relationship between the IRR, discount rate and NPV occurs:

• if discount rate> IRR, then NPV <0
• if the discount rate = IRR, then NPV = 0
• if the discount rate <IRR, then NPV> 0.

### Example of Net Present Value Calculation

Let’s look at an example of how to calculate the Net Present Value of the investment on a new project. Company ABC considers investing $300,000 on their new project and expects that this project will provide benefits of$100,000 annually over the period of 5 years. The expected Return Rate is 10%.

 Year Undiscounted Cash Flow Calculation Present Value 0 -$300,000 -$300,000.00 1 $100,000 100000/1 + 0.10$90,909.09 2 $100,000 100000/(1 + 0.10)2$82,644.63 3 $100,000 100000/(1 + 0.10)3$75,131.48 4 $100,000 100000/(1 + 0.10)4$68,301.35 5 $100,000 100000/(1 + 0.10)5$62,092.13 Total $200,000$79,078.68

Net Present Value = \$79,078.68

That means the investment will not only be profitable, but the Expected Return Rate will be even higher than 10%. If the Return Rate of this investment was 10%, total discounted Net Present Value would be 0. The Net Present Value would need to be greater than or equal to 0 in order to be considered a valuable investment.