# NPV vs IRR

Net present value is an absolute measure i.e. it represents the dollar amount of value added or lost by undertaking a project. IRR on the other hand is a relative measure i.e. it is the rate of return a project offers over its lifespan.

NPV and IRR are two of the most widely used investment analysis and capital budgeting decision tools. Both are discounting models i.e. they take into account the time value of money phenomena. However, each method has its strengths and weaknesses and there are situations in which they do not agree on the ranking of acceptability of projects. For example, there might be a situation in which project A has higher NPV but lower IRR than project B. This NPV and IRR conflict depends on whether the projects are independent or mutually exclusive.

## Independent Projects

Independent projects are projects in which decision regarding acceptance of one project does not affect decision regarding others.

Since all independent projects can all be accepted if they add value, NPV and IRR conflict doesn’t arise. The company can accept all projects with positive NPV.

## Mutually Exclusive Projects

Mutually exclusive projects are projects in which acceptance of one project excludes the others from consideration. In such a scenario the best project is accepted. NPV and IRR conflict, which can sometimes arise in case of mutually exclusive projects, becomes critical. The conflict either arises due to the relative size of the project or due to the different cash flow distribution of the projects.

Since NPV is an absolute measure, it will rank a project adding more dollar value higher regardless of the original investment required. IRR is a relative measure, and it will rank projects offering best investment return higher regardless of the total value added.

## Examples

**Example 1:** Project A requires $10 million investments and generates $10 million each in year 1 and year 2. It has NPV of $7.4 million @ 10% discount rate and IRR of 61.8%. Project B requires $1 million investment and generates $2 million in Year 1 and $1 million in Year 2. Its NPV @ 10% and IRR turn out to be $1.6 million and 141.4%. Based on NPV one would conclude that Project A is better, but IRR offers a contradictory view. This conflict arose mainly due to the size of the project.

NPV vs IRR conflict also arises due to the different cash flow distribution. IRR inherently assumes that any cash flows can be reinvested at the IRR. This assumption is unrealistic because there is no guarantee that reinvestment at IRR can be achieved. NPV on the other hand assumes reinvestment at the cost of capital, which is conservative and realistic.

**Example 2:** Let’s consider two projects: A and B, both require $10 million investment each. Project A generates $15 million in Year 1 and $10 million in Year 2. Project B generates 0 in Year 1 and $30 million in Year 2. You can verify that Project A has NPV of $11.9 million at 10% discount rate and IRR of 100%. Project has NPV of $14.8 million and IRR of 73.2%. Despite both having the same initial investment, NPV is higher for Project B while IRR is higher for Project B. This is because in case of Project A more cash flows are in Year 1 resulting in longer reinvestment periods at higher reinvestment assumption and hence higher IRR. NPV is not affected by reinvestment assumption.

## Comparison of strengths and weaknesses

NPV is theoretically sound because it has realistic reinvestment assumption. It considers the cost of capital and provides a dollar value estimate of value added, which is easier to understand.

Another very important feature of NPV analysis is its ability to notch the discount rate up and down to allow for different risk level of projects.

However, NPV is dependent on the size of the project. Without careful analysis, an investor might select a high NPV project ignoring the fact that many smaller NPV projects could be completed with the same investment resulting in higher aggregate NPV. It requires careful analysis in capital rationing.

IRR is not affected by the size of the project. It will rank a project requiring initial investment of $1 million and generating $1 million each in Year 1 and Year 2 equal to a project generating $1 in Year 1 and Year 2 each with initial investment of $1. This feature makes it a good complement to NPV.

IRR is also easier to calculate because it doesn’t require estimation of cost of capital or hurdle rate. It just requires the initial investment and cash flows. However, this same convenience can become a disadvantage if projects are accepted without comparison to cost of capital.

However, IRR’s assumption of reinvestment at IRR is unrealistic and could result in inaccurate ranking of projects. Another, quite serious weakness is the multiple IRR problem. In case of non-normal cash flows, i.e. where a project has positive cash flows followed by negative cash flows, IRR has multiple values.

## Conclusion

Whenever there is a conflict in ranking of projects based on NPV and IRR, it is safer to always prefer the NPV ranking. This is due to the realistic assumption and theoretical soundness of the method.

However, IRR is a great complement to NPV. It helps see a more complete picture.

Written by Obaidullah Jan, ACA, CFAhire me at