Internal Rate of Return (IRR) is a discount rate that is used to identify potential/future investments that may be profitable. The IRR is used to make the net present value (NPV) of cash flows from a project/investment equal to zero.

In simpler terms, the IRR is used to determine what percentage return of an investment is necessary for it to break even when adjusted for the value of time and money involved. This is often considered the minimum acceptable return on investment, as most companies want to do more than just break even.

Internal Rate of Return is also sometimes referred to as the “discounted cash flow rate of return” or the “economic rate of return”. The “internal” part of the name refers to the fact that external factors such as inflation or the cost of capital are not included in the calculation.

## IRR Formula

$$NPV = \dfrac{CF_{0}}{(1 + r)^{0}} + \dfrac{CF_{1}}{(1 + r)^{1}} + \dfrac{CF_{2}}{(1 + r)^{2}} + \dfrac{CF_{n}}{(1 + r)^{n}} - Initial\: Investment = 0$$

- NPV = Net present value
- CF = Cash flow per period
- r = Internal rate of return

Put simply, the IRR is determined by experimenting to find the rate which cause the NPV of a series of payments to equal $0. The above formula is a derived version of the NPV formula:

$$NPV = \displaystyle\sum_{t=1}^{T} \dfrac{Ct}{(1+r)^{t}}$$

If the payments for each cash flow are expected to be the same, you can also use the simpler NPV formula:

$$NPV = CF \times \dfrac{1-(1+r)^{-n}}{r} - Initial\: Investment$$

From this point, the only variable that needs to be calculated is the IRR itself. This is done in Microsoft Excel in most instances but can be done manually if need be as shown below. It can take a bit of trial and error when calculated but is certainly possible.

## IRR Example

$$NPV = \dfrac{\$20{,}000}{(1 + 10\%)^{1}} + \dfrac{\$30{,}000}{(1 + 10\%)^{2}} + \dfrac{\$40{,}000}{(1 + 10\%)^{3}} + \dfrac{\$40{,}000}{(1 +10\%)^{4}} - \$100{,}000 = 0$$

The IRR is presented as a percentage. In this instance, the found IRR is 10%. Assuming that the business is lower than 10%, this would represent a good investment. If the ending NPV does not equal zero, the percentage must be adjusted accordingly until that goal is reached. The return rate, after properly calculated, can be compared to other investments to determine what is ultimately worth the money.

As mentioned above, finding the exact rate that balances to 0 can take a bit of trial and error, and programs such as Microsoft Excel are commonly used to make this task easier.

## IRR Analysis

The IRR can be used for just about any potential investment, including the stock market, equipment, and other capital investments. While the projected amount of future cash flow is not always accurate due to a variety of factors, the IRR is a great jumping off point when considering any sort of future investment.

The IRR is also commonly used when comparing if it will be more profitable to open a new branch of business within a company or expand the operations of an existing one. An example of this would be a paper company deciding whether to open a new mill or simply expand an existing one. Both would certainly add value to the company, but the IRR could give a good indication of which is the more profitable decision in the long term.

The IRR is also useful in helping corporations evaluate stock buyback programs. Similarly to the new mill vs expanding a current mill example used above, the IRR analysis must show that buying back the company’s own stock is ultimately a better investment than using that funding elsewhere.

One limitation of the IRR is that it can tend to favor smaller investments with shorter-term returns over larger ones with longer-term returns. Whereas a $600 investment that returns $1800 per year appears to have a more favorable IRR than a $15,000 investment that returns $30,000 per year, the larger investment ultimately brings much more value.

## IRR Conclusion

- Internal Rate of Return is a metric used to indicate the rate of growth a project can be expected to generate.
- The IRR is presented as a percentage.
- The IRR helps in deciding whether or not a project is worth investing in.
- The IRR is generally the minimum accepted return on a project or investment. The goal of a company is often to do more than break even.
- The IRR helps a company determine which investments would be profitable, including aiding in decisions of expansion of existing assets or the purchase of new equipment.
- IRR

## IRR Calculator

You can use the calculator below to calculate the IRR. You will need to experiment with the interest rate value to find the correct rate which discounts the Net Present Value back to 0.

So, for example, if your cash flow was one period, for $105, and the initial investment was $100, then to get an NPV of $0 you would need an interest/discount rate of 5%. That is your internal rate of return.