# Internal Rate of Return

## IRR

The internal rate of return or IRR is the return at which the company determines the project break even. As per the Knight's, IRR is commonly used by financial analysts along with the Net Present Value or NPV. Both the methods are quite similar but use different variables. With NPV, the analyst assumes the discount rate and then calculates the present value of the investment. However, with IRR, the analyst calculates the actual return provided by project cash flows, then compares the rate of return with the company's hurdle rate (expected rate of return). If the IRR return is higher, it is worthwhile to invest in the project.

### What is the Internal Rate of Return?

The internal rate of return is a method used to estimate the profitability of the potential investment. It is the discount rate that makes the net present value of an investment equals zero. The Internal rate of return method is widely used in discounting cash flow analysis, and also used for analyzing capital budgeting method.

While calculating the IRR, the present value of future cash flows equals the initial investment of the project, and thus makes the NPV = 0.

After calculating the IRR, it should be compared with the minimum required rate of return or cost of capital of the project. For example, If the calculated IRR is found greater than the minimum required rate of return, then the project should be accepted whereas If the calculated IRR is found lesser than the minimum required rate of return, then the project should be rejected.

### Internal Rate of Return Definition

The internal rate of return or IRR is a discounting cash flow method to determine the rate of return earned by the project excluding the external factor. By IRR definition, it is the discounting rate at which the present value of all future cash flows is equal to the initial investment, that is the rate at which the company investments break even.

### Internal Rate of Return Formula

IIRR is the interest rate that makes the net present value (NPV) of all cash flows equal to zero. The NPV is the difference between the present value of cash inflows (estimated profit) and the present value of cash outflow (estimated expenditure) over a period of time. When NPV sets to zero, then it equates the present value of inflows and outflows, and this makes the IRR calculation more simple. When NPV sets to zero, then it equates the present value of inflows and outflows, and this makes the IRR calculation more simple.

The internal rate of return formula is given as:

$0 = CF_{0} + \frac{CF_{1}}{(1 + IRR)^{1}} + \frac{CF_{2}}{(1 + IRR)^{2}} + \frac{CF_{3}}{(1 + IRR)^{3}} + \frac{CF_{4}}{(1 + IRR)^{4}} + \frac{CF_{5}}{(1 + IRR)^{5}} + . . . . . + \frac{CF_{n}}{(1 + IRR)^{n}}$

Or

Internal Rate of Formula is also given as:

$0 = NPV = \sum_{n=0}^{N} \frac{CF_{n}}{1 + IRR)^{n}} - CF_{0}$

In the above rate of return formula,

CF0 - Initial investment

CF1, CF2, CF3, CF4 ….CFnk are cash inflows

NPV - Net Present Value

IRR - The internal Rate of Return

N = Total Number of periods

n - The number of periods

Let us now understand how to calculate the internal rate of return or IRR.

### How to Calculate Internal Rate of Return?

For the calculation of the internal rate of return, we use a similar formula as NPV. To calculate IRR, analysts have to depend on trial and error methods and cannot use analytical methods. Analysts also calculate IRR using different software like Microsoft Excel. In MS-Excel, there is a financial function that calculates IRR using cash flows at regular intervals. The formula uses to calculate IRR is:

$IRR = \frac{\text{Cash Flows}}{1 + r)_{n}} - \text{Initial Cost of the Project}$

The rate at which the cost of investment and the present value of cash flow matches will be considered an ideal rate of return. A project that can achieve this rate is considered a profitable project. In other words, the rate at which cash outflows and the present value of cash inflow equate makes the project attractive.

IRR Calculator

The internal rate of return calculator is used to determine the actual rate of return of the investment. You can use these returns to calculate these returns to compare two or more different investment options.  You can also compare these returns with the returns you can earn in risk-free investment to determine the worth of investment.

To use the IRR calculator, simply enter your initial investment amount, cash flow frequency, and cash flow figures. Cash flow does not have to be annual, it can be at any regular internal such as only, quarterly, or semi-annually.

### Internal Rate of Return Example

Let us understand IRR through internal rate of return example given below:

The management of Raymond clothing company is planning to replace old machinery with new machinery as new machinery will help them to complete their important task much faster than the older one. The installation cost of new machinery is $\$8475 and will reduce the labour cost by $\$1500. The useful life of new machinery will be 10 years with no salvage value. The minimum required rate of return is 15%. Should the company purchase new machinery? Use the internal rate of return method to derive the conclusion.

Solution:

To know whether new machinery should be purchased or not, we will first calculate the internal rate of return and then compare this return with the company's hurdle rate (the minimum required rate of return).

The internal rate of return will be calculated by dividing the investment required for the project (i.e., Net initial investment) to net annual cash flow. The rate of return formula is:

$\text{Internal Rate of Return } - \frac{\text{Net Initial Investment}}{\text{Net Annual Cash Flow}}$

In this internal rate of return example, the investment required is 8475, and the net annual cost saving is 1500. This saving is equal to revenue and therefore considered as the net annual cash flow. Using this information, we can calculate the IRR.

$\text{Internal Rate of Return } = \frac{\ 8475}{\ 1500} = 5.650$

After calculating the IRR, the next step is to locate this discount factory in the present value annuity table given below.

As the useful life of a machine is 10 years, the discount factor would be found in 10 - period line or row. In the present value of the annuity of \$ 1 table, we can see that the discount factor 5.650 is mentioned in the 12% column of the 10th row. Hence, the actual rate of return or IRR of the project is 12%. The final step is to compare this IRR with the project minimum required rate of return and i.e. is 15%.

### What are the Limitations of the IRR Method?

• IRR may not provide accurate estimate cost as while calculating IRR, the cost of capital is not considered in the equation. The cost of capital is the required rate of return also known as hurdle rate is required returns to fund the project.

• When using IRR to compare multiple projects, it does not look at the size or scope of the project for comparison, it only compares the cash flows to the amount of capital being injected to generate those cash flows.

• The aim of the IRR method is to determine the projected cash flow form the capital injected. It does not consider the potential costs such as fuel and maintenance cost, that are variable over time. This may affect the profit in future.

• The biggest limitation of IRR is that it makes assumptions that future cash flows can be invested at the same internal rate of return. In reality, the numbers obtained by IRR can be quite high.

• It required calculations that are quite long and tedious.

### Conclusion:

According to the internal rate of return, the proposal of purchasing new machinery should not be accepted as the IRR 12% is less than the minimum required rate of return (15%).

Q1. What are the Uses of the Internal Rate of Return Method?

Ans: Companies use the IRR method to determine if an investment project or expenditure is beneficial. Calculating the IRR will help the companies to decide either the project is acceptable or not. The IRR method is the easiest method to determine the profitability of an investment and to compare one investment to another.  If the calculated IRR is found greater than the cost of capital, then it is worthwhile to invest in the project.

Hence, the companies use the IRR method to calculate expected or projected IRR While analyzing one or more projects. If choosing between multiple investments the project with the highest IRR should be selected assuming all the projects require the same amount of upfront investment.

Q2. What is the Difference Between IRR or NPV?

Ans:

 Differences NPV IRR Results It gives results in a dollar value that a project will generate. It gives results in the percentage return that the project is expected to generate. Focuses It focuses on project surpluses. It focuses on the breakeven cash flow of a project. Decision The NPV helps companies to make the investment decision easily as it obtains results in dollar value. The IRR method does not help in making the feasible decision as the percentage return does not tell how much money will be made. Rate of Return While using the NPV method, the expected rate of return for the investment of intermediate cash flow is the cost of capital. While using the IRR method, the presumed rate of return for the investment of intermediate cash flow is IRR. Difficulty The NPV method required the use of discount rate, which is difficult to derive as management might want to adjust returns based on the perceived risk level. The IRR method does not have this issue as the rate of return is simply derived from the underlying cash flow.

Q3. What is the Cost of Capital?

Ans: Cost of capital, also known as the hurdle rate, is the minimum rate of return that a business expects to earn from its investment to increase the value of the firm in the market. It is used to evaluate and decide new projects, as well as the minimum return investor expects from the invested capital.