# Internal rate of return (IRR)

## Definition

It is the discount rate of the project on which the Net Present Value (NPV) of the project is zero. It is the actual rate of return of the Project.

## IRR Decision Rule

• If IRR > Cost of Capital, accept the project.
• If IRR < Cost of Capital, reject the project.

Formula – IRR

## Explanation

To clear the concept of IRR, let us take a simple example. A business has a surplus of \$100,000 and they want to invest in a project. They are considering a project which has a life of just one year. After one year, the project will be completed, and the business will realize all the cash received from the project. The business expected that after the end of the project, they will get \$108,000 from it. Based on this information, one can easily think that this project should be accepted by the business because it will yield 8% on their investment. But it is not true. Just having profits is not enough for the business. The business generates funds from the shareholders and the banks. They need to pay them back in the form of dividends or interest. So, management must make sure that the project gets enough return to pay the providers of finance.

Let’s say, the business has taken \$100,000 from the bank to fund the investment and it needs to pay 10% interest on it. Now if you compare this with the project with an 8% return, you can conclude that the project is not worthwhile and viable for the business because it is not going to cover their cost of capital. Management calculates the cost of capital which then forms a basis of comparison for IRR. The cost of capital is the minimum required rate of return any project must generate to cover its cost of investment. Any project is suitable if it generates a return greater than the cost of capital. So, in this case, if the cost of capital is 10% and the project generates a rate of 8%, then this project is not viable. But if this project yields a return of 15%, then management should invest in that project.

## Calculation of IRR

The example considered above was very simple but in reality, most projects have a life greater than 1 year. So, how can we calculate its IRR? There are two steps to calculate the IRR of a project:

1. Calculate the NPV of the project using two different discount rates. Ideally, the two rates chosen are those on which the NPV is positive at one rate and negative at the other.

2. Calculate the IRR using the IRR formula.

## Example – IRR

The management of a company is evaluating a project. Management has provided you with the following information:

• IRR takes into account the Time Value of Money (TVM). Future cash flows are discounted using appropriate discount rates before NPV and IRR are calculated.

• It is simple to understand for managers because it is a percentage return. Although management may not understand the detail of the IRR, they still can understand what this percentage means and it can be used for decision making.

• The whole life of the project is considered in IRR including later cash flows, which are ignored in the payback period.

• If a decision is taken on the fact that IRR is greater than the company’s cost of capital, shareholders’ wealth is increased.