Net present value or NPV is a very prominent technique for analysis in the arena of finance. Net present value is equal to the present value of all the future cash flows of a project less the initial outlay of the project. It is very important and useful in arriving at the decisions related to investment in projects, plants, or machinery.

## Definition and Meaning of NPV

Net present value is the present value/today’s value of all the cashflows to be generated by an asset in the future. In other words, it is the value that can be derived using an asset. Alternatively, it is the discounted value based on some discount rate. It is also widely used by banks, financial institutions, investment bankers, venture capitalists, etc. to assess an asset or even a business for arriving at its valuation.

## How to Calculate Net Present Value (NPV)?

Calculation of net present value requires three things viz. stream of future cash flows (inflows or outflows), a discounting rate, and the initial investment amount. All we need to do is to discount the future cash flows to present value using the appropriate discount rate and deduct the initial investment from the total of all the present values arrived after discounting.

**The formula for Net Present Value (NPV):**

Net Present Value (NPV) | C_{1} | C_{2} | C_{3} | C_{n} | |||||||

= | — | + | — | + | — | …….. | — | – | Initial Investment | ||

(1+r)^{1} | (1+r)^{2} | (1+r)^{3} | (1+r)^{n} |

Where C_{n} = Cash Flow at time n.

*Future Cash Flows: *Future cash flows are the expected cash flow to be received by the investor on the proposed investment.*Discount Rate:* It is the highest rate of return which the investor can earn by investing the same money in some other investment alternative. In other words, a discount rate is the opportunity cost of capital which means the cost of compromising the other opportunity.*Initial Investment:* It is the cash outflow at the beginning of the project like the cost of machinery etc.

## Net Present Value (NPV) Example

Let’s understand NPV with an example. Suppose, you bought machinery worth 2 Million Dollars and it will fetch 0.5 Million Dollars every year for 6 Years and there will be no scrap value for the machine. What should you do? Invest or Not? Apparently, somebody may say you are investing 2 million but getting 3 million so you should go for it. Let’s say you have another opportunity to invest the same money @ 14% per annum. The following example explains how the opportunity is not worth investing in if your opportunity cost or discounting rate is 14%. Cash flows are discounted by 14% and we find that their present value is 1.94 Million. If you are offered 1.94 Million in exchange for 2 Million today, would you enter into the deal? Obviously, a rational person would not entertain that.

Cash Flow | Year | Amt | Discount Factor: (1/1+14%)n | Present Value |

C1 | 1 | 5,00,000 | 1.14 | 4,38,596 |

C2 | 2 | 5,00,000 | 1.3 | 3,84,734 |

C3 | 3 | 5,00,000 | 1.48 | 3,37,486 |

C4 | 4 | 5,00,000 | 1.69 | 2,96,040 |

C5 | 5 | 5,00,000 | 1.93 | 2,59,684 |

C6 | 6 | 5,00,000 | 2.19 | 2,27,793 |

Present Value of Future Cash Flows | 19,44,334 | |||

Initial Investment | 20,00,000 | |||

Project Not Worth | -55,666 |

## Method and Analysis

The net present value method is used to determine whether a project/investment is worth doing by comparing two things: initial investment and the total value of future cash flows. Net present value analysis simply concludes about a project to be worth doing when it finds the present value of future cash flows greater than the initial investment and vice versa. Put simply, it brings the complicated stream of cash flows into a simple weighing scale situation where you can easily know which is heavier. In our context, we just have to see which is higher the present value of future cash flows or the initial investment.

## Calculation of Net present value (NPV) and NPV tables

The calculation of net present value is little complicated due to the presence of power over the numeric values. To make it simple, there are pre-calculated tables of a combination of different discount rates and periods. NPV tables are used for the sake of simplicity of calculations. Nowadays, all such applications are available in excel and are widely used. Not just a formula is available but specific tools are also available.

Net present value has a close relation with capital budgeting. Capital budgeting requires extensive use of the NPV technique. NPV method is one of the chief methods used in capital budgeting.

We cannot deny that NPV is one of the very good techniques for analyzing projects but the final decision about the project cannot be made just based on this. It is always advisable to look at all the sides of the dice. There are many other metrics that are consulted such as return on investment, profit margin, cash flows, return on assets, tax implications, different kinds of risks, etc.

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Year Outlay (Investment cost in USD) Cash flow (in USD)

0 6,000 200

1 500 3500

2 0 2000

3 0 1000

4 150 800

If the interest rate is 10%; calculate the discounted payback period.please help bay giving answer