# Incremental IRR Calculator

## What is Internal Rate of Return?

Internal Rate of Return (IRR) is a financial metric used to measure the profitability of an investment. It is the interest rate at which the net present value (NPV) of an investment's future cash flows is equal to zero. In other words, it is the rate at which an investment's benefits (cash inflows) are equal to its costs (cash outflows).

IRR is a widely used metric in finance and is often used to compare the profitability of different investments. However, it is important to note that IRR is not always the best metric to use. For example, if an investment has uneven cash flows or if it is not an independent project, then IRR may not be an appropriate metric to use.

Incremental IRR is a variant of IRR that is used to evaluate the profitability of a specific project or investment compared to its next best alternative. It is calculated by taking the difference in the IRRs of two projects and comparing the results. This metric is especially useful when evaluating projects with different lifetimes or when considering the impact of a specific project on the overall profitability of a company.

## Incremental IRR Formula

To calculate incremental IRR, the first step is to calculate the IRR for each project individually. This can be done by using the IRR formula, which is:

NPV = -C0 + (C1/(1+r)^1) + (C2/(1+r)^2) + ... + (Cn/(1+r)^n)

Where C0 is the initial investment, C1, C2, ..., Cn are the cash inflows at the end of each period, and r is the IRR. The value of r that makes NPV equal to zero is the IRR.

## Incremental IRR Example

Once the IRR has been calculated for each project, the incremental IRR can be calculated by taking the difference between the IRRs. For example, if project A has an IRR of 20% and project B has an IRR of 30%, then the incremental IRR for project B compared to project A is 10%. This means that project B is expected to be 10% more profitable than project A, all else being equal.

It is important to note that when comparing two projects, the incremental IRR is only meaningful if the projects are mutually exclusive. Mutually exclusive projects are projects that cannot be undertaken at the same time. If the projects are not mutually exclusive, then IRR may not be an appropriate metric to use.

Additionally, when comparing two projects with different lifetimes, it is important to take into account the time value of money. The time value of money states that a dollar today is worth more than a dollar in the future because of the potential to earn interest on that dollar. Therefore, projects with shorter lifetimes may have higher IRRs than those with longer lifetimes, even if the latter projects have higher net present values.

Incremental IRR is a useful tool for evaluating the profitability of specific projects, particularly when comparing mutually exclusive projects with different lifetimes. However, it is important to use this metric in conjunction with other financial metrics, such as net present value, to get a comprehensive understanding of the potential profitability of an investment.

Another important thing to consider when using IRR as a metric is whether a project is dependent on another one. In most cases, IRR assumes that each project is an independent one and its cash flows are not affected by other projects. But in reality some projects are dependent on another and its outcome could affect the future cash flows of the first one. In this case, IRR will not be an appropriate metric to use, instead, a different one like modified IRR should be used