## NPV vs IRR

**NPV vs IRR**

**Definition:**

Analysis of a project requires financial evaluation using Capital Budgeting and Investment Planning techniques. Two essential tools for any such financial analyst are NPV and IRR.

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**NPV** or **Net Present Value** is the value of annual free cash flows from an investment less than the investment outlay in today’s terms. This means that you take all the future cash flows from the project, discount them back to present value, and then subtract the initial investment manually to arrive at NPV.

**IRR** or **Internal Rate of Return** is the discount rate that equates the present value of projects free cash flows with the project’s initial cash outlay. Essentially, the metric works as a discounting rate that equates the NPV of cash flows to zero.

**Formulas Used:**

__An essential graph: __

In the graph above, we have a Discount rate on the x-axis and the NPV on the y-axis. The discount rate at which NPV becomes zero is called the IRR rate.

**Differences between NPV and IRR:**

Based on definitions and formulas, we arrive at a number of differences between NPV and IRR:

**Metric**: NPV method shows the__dollar value amount__that will produce, while IRR generates the__percentage-based return__that the project is expected to create.**Purpose**: NPV focuses on__Project Surpluses__and IRR focuses on the__breakeven cash flow__of a project.**The Reinvestment Rate**: Presumed rate of return for the reinvestment of intermediate cash flows is the firm’s__cost of capital__when NPV is used, while it is the__internal rate of return__under the IRR method.

When two mutually exclusive projects are being ranked, NPV and IRR would most likely conflict when the project’s investments are of different scale and/or the timing of cash flows may differ.

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**Example (NPV vs IRR):**

Consider Project 1 and Period 2, one requiring an initial investment of **₹**100 for a payoff of **₹**120 in 3^{rd} period, and the other requiring **₹**50 in period 1, **₹**52.5 in period for the same payoff in period 3. The discount rate is 5%.

Project 1 |
Project 2 |

-100 | -50 |

0 | -52.5 |

+120 | +120 |

In this case, the NPV of both the projects is going to be the same. But the IRR of project 1 would be 9.54% and the IRR of project 2 would be 11.07%. Using the NPV method, one would be indifferent between both the projects. IRR on the other hand clearly shows that Project 2 should be preferred over Project 1. This difference is there because NPV assumes that investor reinvests at the discount rate while the assumption with IRR is that investor reinvests at the IRR rate.

Similarly, we might have cases where the scale of investment is different.

Project A needs $10 million investment and generates $10 million each in year 1 and year 2. It has an NPV of $7.4 million at a discount rate of 10% and an IRR of 61.8%.

Project B needs $1 million investment and generates $2 million in Year 1 and $1 million in Year 2. Its NPV at a discount rate of 10% and IRR turns out to be $1.6 million and 141.4% respectively. Based on NPV, Project A would be better, but IRR suggests a contradictory view.

**Final Words (NPV vs IRR):**

The NPV provides a foundation for an investment decision since it gives out results in the form of how much money you’re going to make on a project taking into consideration the time value of money. IRR on the other hand provides a percentage-based return. Therefore, IRR is mostly used as a subordinate or a complementary calculation, whereas NPV is a widely used metric that also provides sufficient information to work with on its own.

**Author: Aman Aggarwal**

**About the Author:** Aman is an Economics and Finance graduate with a budding interest in Strategic Management and Investment. An avid reader of all things Behavioral and Data Science –I strongly believe in solving problems with solutions backed up by quantitative rigor.

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