# Internal rate of return method for investment appraisal

The Internal Rate of Return (IRR) is one of the most common methods for investment appraisal. IRR is also known as the Internal Capitalization Rate.

It is one of the more straightforward methods for valuing an investment and is easily derived from the net present value (NPV) method and discounted cash flow (DCF) models.

It is called internal as it doesn’t consider ‘external’ factors such as inflation, cost of capital, and the risk-free rate. Another name for IRR is discounted cash flow rate of return.

## Where is the Internal Rate of Return method used?

The IRR method is usually used in appraisal studies of the economic feasibility of projects. For example, the IRR may be calculated to determine how much each new store would have to be sold to generate a break-even profit (or to what price it should be sold at to generate a return equal to the original investment in the store).

IRR is also used in valuing businesses and other investments. Many investors believe that the fair value of an investment is the IRR. For example, one investor may purchase an investment for $10,000,000. When the investor wants to sell the investment, the investment has to generate $10,000,000 of cash or revenue. The investor would not like to have to pay for the investment if it would not pay off. So the investment has a fair market value for the revenue it will generate. Of course, it will also have a fair market value in the form of capital cost.

IRR is also calculated in appraisals of the economic value of an opportunity to build, purchase, lease, or establish a business or development. In such cases, the IRR is used to determine what it would cost to invest and the return.

## Difference between IRR and NPV

The IRR method differs from the NPV method in two ways. First, in the NPV method, the discount rate is often an externally determined value that the appraiser feels should be applied to the project.

In the IRR method, the internal rate of return is typically a function of the discount rate, which the appraiser calculates.

The second difference is that the IRR method is usually used to determine the economic feasibility of a project. In NPV, the IRR method is usually used to value a company.

## How to find IRR?

Use the following process to calculate the internal rate of return on a project:

- Use two discount rates. One should give a positive net present value and the other should give a negative net present value.
- Calculate the net present values using each of these discount rates.
- Apply this formula to find the IRR:

(Lower rate + (percentage difference between the rates x NPV using the lower rate))/Difference between the NPVs calculated using the 2 rates

The formula is quite complicated so let’s understand it using an example. But before that, let’s clarify some terms:

**Discount rate:**This is the rate that determines the present value of future cash flows. This is different from the cost of capital, which is the minimum rate of return necessary to make an investment worthwhile.**Net present value (NPV):**This is the total present value of all the future cash flows. To calculate it, you apply the discount rate to the net cash flow during each year and sum them all up.

Here’s an example where IRR is used. Say a company uses two discount rates: 10% and 36%. At 10%, the NPV is $44,915 and at 36%, the NPV is negative $4820. Using the formula, the IRR would be:

(10% + (26% x 44,915))/49,735 = 33.48%

This figure can then be compared to the cost of capital to decide whether or not to go forward with the investment. The investment is worth making only if the cost of capital is lower than the internal rate of return.

## Limitations of the IRR Method

Due to the fact that we are computing a rate of return, IRR is more challenging to compute manually than NPV. Our spreadsheets or calculators “search” for the interest rate. Iterations of trying one interest rate, determining if it is too high or too low, and then trying again would be required for us to calculate.

Unique cash flows might result in unusual, and perhaps many, outcomes. Unfortunately, most calculators won’t warn the user of this issue, thus, caution is required. IRR also does not appropriately rate mutually exclusive initiatives. Due to these factors, NPV is frequently used as the preferable criterion, or at the very least, to “double check” that IRR isn’t failing for one of these uncommon reasons.

## Conclusion

Internal rate of return (IRR) is a popular capital budgeting technique; it may be thought of as the return we will earn on our investment during its lifetime. The discount rate at which the NPV equals 0 is used to compute it. To put it another way, we set NPV to $0 and then find r. This is the rate at which the original investment and the present value of the cash flows are equal. Unfortunately, there is no simple way to determine this rate for some projects without resorting to the “guess and verify” technique; luckily, computers are fairly rapid at doing this.