# Internal rate of return method

Like net present value (NPV) method, **internal rate of return (IRR) method** also takes into account the time value of money. It analyzes an investment project by comparing the internal rate of return to the **minimum required rate of return** of the company.

The **internal rate of return** (sometimes known as **yield on project**) is the rate at which an investment project promises to generate a return during its useful life. It is the discount rate at which the present value of a project’s net cash inflows becomes equal to the present value of its net cash outflows. In other words, internal rate of return is the discount rate at which a project’s net present value becomes equal to zero.

The **minimum required rate of return** is set by management. Most of the time, it is the cost of capital of the company.

Under this method, If the internal rate of return promised by the investment project is greater than or equal to the minimum required rate of return, the project is considered acceptable otherwise the project is rejected. Internal rate of return method is also known as *time-adjusted rate of return method*.

To understand how computations are made and how a proposed investment is accepted or rejected under this method, consider the following example:

## Example:

The management of VGA Textile Company is considering to replace an old machine with a new one. The new machine will be capable of performing some tasks much faster than the old one. The installation of machine will cost $8,475 and will reduce the annual labor cost by $1,500. The useful life of the machine will be 10 years with no salvage value. The minimum required rate of return is 15%.

**Required:** Should VGA Textile Company purchase the machine? Use internal rate of return (IRR) method for your conclusion.

### Solution:

To conclude whether the proposal should be accepted or not, the internal rate of return promised by machine would be found out first and then compared to the company’s minimum required rate of return.

The first step in finding out the internal rate of return is to compute a discount factor called* internal rate of return factor*. It is computed by dividing the

*investment required for the project*by

*net annual cash inflow*to be generated by the project. The formula is given below:

#### Formula of internal rate of return factor:

In our example, the required investment is $8,475 and the net annual cost saving is $1,500. The cost saving is equivalent to revenue and would, therefore, be treated as net cash inflow. Using this information, the internal rate of return factor can be computed as follows:

Internal rate of return factor = $8,475 /$1,500

= 5.650

After computing the internal rate of return factor, the next step is to locate this discount factor in “present value of an annuity of $1 in arrears table“. Since the useful life of the machine is 10 years, the factor would be found in 10-period line or row. After finding this factor, see the rate of return written at the top of the column in which factor 5.650 is written. It is 12%. It means the internal rate of return promised by the project is 12%. The final step is to compare it with the minimum required rate of return of the VGA Textile Company. That is 15%.

#### Conclusion:

According to internal rate of return method, the proposal is not acceptable because the internal rate of return promised by the proposal (12%) is less than the minimum required rate of return (15%).

Notice that the internal rate of return promised by the proposal is a discount rate that equates the present value of cash inflows with the present value of cash out flows as proved by the following computation:

*Value from “present value of an annuity of $1 in arrears table“.

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