 # NPV vs IRR Method By Yuriy Smirnov Ph.D.

## Problem

The net present value (NPV) and internal rate of return (IRR) methods are based on the same discounted cash flows technique, hence they take into account the time value of money concept. Furthermore, both of them are frequently used in capital budgeting decisions. In most cases, they provide the same appraisal, but conflict can sometimes occur.

The problem arises in case of mutually exclusive projects when a company should try to select the best one among others. It can happen that one project has a higher NPV but lower IRR, and the other one has a higher IRR but lower NPV. Shown below is an example of how to solve this conflict.

## Example

A company is considering two mutually exclusive projects that are equally risky. Detailed information about cash flows is presented in the table below.

 Initial Cost, CF0 Cash flows at the end of relevant year, CFt IRR 0 1 2 3 4 5 Project Y -\$11,000,000 \$3,000,000 \$3,700,000 \$4,000,000 \$4,500,000 \$3,500,000 19.85% Project Z -\$11,000,000 \$4,000,000 \$5,000,000 \$3,750,000 \$3,000,000 \$2,000,000 21.04%

The internal rate of return of Project Y is 19.85% and 21.04% for Project Z. If IRR is the only screening criterion, Project Z looks more attractive and should be accepted.

But let’s look further if the cost of capital raised for both projects is 11%. In this instance, the NPV of Project Y is \$2,407,063 and Project Z \$2,312,414. If the NPV is the only screening criterion, Project Y must be accepted.

Now we can see a typical “NPV vs. IRR problem” when those criteria are producing conflicting conclusions. To solve that problem, let’s calculate the NPV at a number of different discount rates to create the graph below. The cost of capital of 13.0918% is the break-even point because both projects have equal NPV of \$1,727,845. If the discount rate is below 13.0918%, Project Y will have a higher net present value than Project Z. For any discount rate higher than 13.0918%, Project Z will have a higher net present value than Project Y.

Such conflict between NPV and IRR is the reason why net present value is considered a better screening criterion than the internal rate of return. The background is that NPV reflects the additional shareholders’ value created by a project.

## Reasons for conflict

Two basic reasons lead the NPV profile to cross and why conflict occurs.

1. Difference in project scale. If two projects have different initial costs, the cross of the NPV profile may occur.
2. Difference in cash flows timing. This conflict can happen when most of the cash flows from one project come in earlier years and most of the cash flows from the other project come in later years, as in the example discussed above.

We recommend reliance on the net present value as a screening criterion in case of such conflict between mutually exclusive projects. The background of such a recommendation is that the reinvestment rate plays the key role. The basic assumption of the NPV method is that future cash flows are reinvested at a discount rate (cost of capital rate), and the IRR method assumes that future cash flows are reinvested at an internal rate of return. The reinvestment rate equal to the cost of capital is a more realistic assumption, especially in the long run.