# Internal Rate of Return (IRR)

Some firms calculate the net present value NPV of a project for knowing its work and few firms prefer to calculate the internal rate of return (IRR) to know whether project’s return is lower or greater than the opportunity cost of given project’s capital. For example, take a real estate sector, a firm wants to build a house and is planning to invest amount of \$600,000 in this project to calculate a cash flow of C1= 700,000 after one year. Therefore the firm forecasts a profit of \$100,000 on the project (700,000-600,000=100,000). This is a one period investment in which it is easy to find out the IRR. Internal rate of return for various periods will be calculated as follows:

IRR = PROFIT/INVESTMENT=C1-INVESTMENT/INVESTEMENT=700,000-600000/600,000

The investing in the alternative in a treasury note would just give a return of 8%, though the return on the real estate project is greater than the opportunity cost of invested capital. This gives two rules for deciding to go with real estate project:

1. NPV: You must go for a project that has positive net present value, when payoffs are discounted at the alternative opportunity cost of capital.
2. IRR: A firm should invest in a project which gives ROR that is greater than alternative opportunity cost of capital.
Both rates have the same cutoff point.

An investment with a net present value of zero will have a return that is same as the cost of capital. Suppose treasury notes have 16.7% of the return instead of 8%. Since real estate project also gives a return of 16.7%, the rule number two suggest that now a firm can invest in a project or treasury notes because both have same return.
The net present value shows that if the return rate is 16.7% then the project is also balanced with a zero NPV.
NPV= Co +C1/1+R= -600,000+700,000/1.167=0

This indicates that real estate investment would not make a firm poorer or richer; here worth is equal to the cost of a project. Thus both rules provide the same decisions about the project.

Rate of Return (ROR) Rule:

It is clear that if the real estate project is discounted at 8%, it has the net present value of 48,200. If project is discounted at 16.7%, than it has a net present value of zero. The two noticeable things about the Rate of Return are:

1. Rate of return in the project (16.7%) is also the discount rate that gave the zero NPV to the project. It means ROR is also the discount rate at which net present value is same as zero.
2. NPV of the project would be positive when opportunity cost of the project is less than the rate of return of the project. NPV of the project would be negative when opportunity cost of the project is higher than its rate of return. These both rules such as Net Present Value and Rate of Return are equivalent.

### 2 responses to Internal Rate of Return (IRR)

Navdeep Singh says:

awesome…!!!

Praveen R V says:

I wish to get project topics related with a public sector undertaking in finance to have analysis of profit,return etc