## What is Net Present Value?

Net present value is the most important concept of finance. It is used to evaluate the investment and financing decisions that involve cash flows occurring over multiple periods. The difference between the present value of cash inflow and cash outflow is termed as net present value (NPV). It is used for capital budgeting and investment planning. It is also used to compare similar investment alternatives.

The current total value of the future payments is calculated by discounting the future payments. It helps in analysing the projected return on investment.

## Features of Net Present Value

Net present value is the summation of the present value of all cash flows which can be positive as well as negative.

Inflation affects the value of money in the present time and at the future time. The future value of money is more than the present value.

Net present value (NPV) helps to calculate the future value of investments and select the one which can give better returns.

Net present value helps the managers of the firm to compare the projects and choose the one which can give better results in the future.

For example: Money earned in the future would not be as worthy as earned in present.

How to calculate NPV: The formula for calculating Net present value (NPV) is as follows

NPV = C / [ (1 + r) ^{n}]

where, PV = Present Value,

C = Future payment (cash flow),

r = Discount rate,

n = number of periods based on future cash flows.

Practical problem:

Calculate NPV of a specific project of the following cash flow stream:

Year | Cash Flow ($) |

0 | $ 1,00,000 |

1 | 200,000 |

2 | 200,000 |

3 | 300,000 |

4 | 300,000 |

5 | 350,000 |

The cost of capital (r) is 10%

NPV = 200,000/1.10+200,000+1.10+300,000/1.10/300,000/1.10+350,000/1.10 â€“ 1,000,000 = -5,272

### Properties of NPV rule

The value of the firm can be expressed as the sum of the present value of a project as well as the net present value of the prospective projects.

**Value of a firm =sum of the present value of a firm + sum of the net present value of the expected future project.**

When a firm dismisses a present project, which has a negative Net present value based on its expected future cash flows, the value of the firm increases by that amount.

When a firm divests itself of an existing project, the price at which the project is devested affects the value of the firm. Present value of the anticipated cash flow of the investment increases or decreases with the increase or decrease in the price.

If the value of NPV is negative, the project is estimated to give a negative return in the future. And when the result is positive the investment can give a better return.

## Cash Flows Capitalized at the Cost of Capital

The NPV rule assumes that the intermediate cash flows of a project that is, cash flow that occurs between the initiation and the termination of the project are reinvested at a rate of return that is equal to the cost of capital.

NPV calculation permits time-varying discount rate: NPV can be calculated using a time varying discount rate.

The formula is

$\text{NPV}={\displaystyle \underset{}{\overset{}{\xe2\u02c6\u2018}}\frac{\text{CFn}}{\text{(1+i)}}}\text{-Initial}\text{\xe2\u20ac\u2030}\text{Investment}$

C is the cash flow at the end of the year t

Rt = discount rate for the year which is denoted as t

Example: assuming a five-year project of software development. The technological uncertainty associated with the industry leads to a higher discount rate in future

Discount rate | 14% | 15% | 16% | 18% | 20% |

Cash flows | 4,000 | 5,000 | 7,000 | 6,000 | 5,000 |

Investment | 12,000 |

The present value of the cash flow:

Present value of C1 = 4,000/1.14 = 3,509

PV of C2 = 5,000/ (1.14 Ã— 1.15) = 3,814

PV of C3 = 7,000/ (1.14 Ã— 1.15 Ã— 1.16) = 4,603

PV of C4 = 6,000/ (1.14 Ã— 1.15 Ã— 1.16 Ã— 1.18) = 3,314

PV of C5 = 5,000/ (1.14 Ã— 1.15 Ã— 1.16 Ã— 1.18 Ã— 1.20) = 2,322

Hence NPV of the project = 3,509+3,814+4,603+3,344+2,322-12,000 = $5,592

## What is Internal Rate of Return?

Internal rate of return (IRR) is the discount rate of a project which makes its NPV=0. It is a discount rate that equates the present value of future cash flows with the initial investments. It helps to determine nominal cash flows.

**Formula**

Investment= $\text{Investment}={\displaystyle \underset{}{\overset{}{\xe2\u02c6\u2018}}\frac{\text{Ct}}{\text{(1+i)t}}}$ t

Where C= cash flow at the end of the year t

R is the internal rate of return

N is the life of the project

**Difference between NPV and IRR: **NPV is relatively similar to IRR. Internal rate of return generates the percentage value that a project is expected to produce whereas Net present value results in a dollar value of a project.

Internal Rate of return focuses on the breakdown cash flow level of a project whereas net present value emphasizes project surplus.

IRR doesnâ€™t help the investor in making the decision on where to invest as the future return is not known. Net present value helps to estimate the return on investment and hence helps in decision making.

Under the IRR method, the rate of return is derived from the underlying asset and hence it is easy to calculate whereas in the NPV method discount rate of the return is used to reach the result. Hence it is difficult and based on apparent risk levels.

NPV method is used more frequently as compared to the IRR method.

## Limitations of NPV

Net present value does not take into consideration the life of the project. Hence for long-term projects, the NPV rule is not relevant.

A 100% accuracy difficult to estimate as it is based on future cash flows and discounted rates.

There is always an opportunity cost that is involved in every investment which is not considered while calculating NPV.

## Context and Applications

This topic is significant in the professional exams for both undergraduate and graduate courses, especially for

- Bachelor of Commerce
- Master of Commerce
- MBA

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