# Incremental IRR

Incremental internal rate of return (IRR) is the discount rate at which the present value of periodic differential cash flows of two projects equals the difference between the initial investments needed for each project.

One of the drawbacks of the traditional internal rate of return approach of capital budgeting is that it ignores the size of projects and may offer misleading conclusions in case of mutually exclusive projects.

Let us consider a company whose cost of capital is 15% and it must choose between Project A and Project B. Project A requires an initial investment of $300 million and returns $150 at the end of the first year. Project B requires an initial investment of $100,000 and returns $120,000 next year. If we use the traditional IRR technique to decide about the projects, we would choose Project A because it has an IRR of 50% against Project B IRR of just 10%. However, this conclusion is flawed because Project B will create far more wealth for as evident by its higher net present value.

$$ {\text{NPV}} _ \text{A}=\frac{\text{\$150}}{\text{1}+\text{15%}}-\text{\$100}\ =\ \text{\$30.43} $$

$$ {\text{NPV}} _ \text{B}=\frac{\text{\$120,000}}{\text{1}+\text{15%}}-\text{\$100,000}\ =\text{\$4,347.83} $$

This illustrates why net present value is the preferred capital budgeting method.

However, we can tailor the IRR method to analyze mutually exclusive projects by using the following approach:

- Identify the project with higher initial investment (H) and lower initial investment (L).
- Subtract initial investment of L from H to find incremental initial investment.
- Subtract net cash flows of L from H to find annual/periodic incremental cash flows.
- Find the incremental IRR by equating the present value of the incremental cash flows to the incremental initial investment.

## Example

Let us consider the City of Qarth which must decide whether to host a football tournament (Project F) or hold an industrial expo (Project E). For Project F, it must invest $200 million in the renovation of stadiums and other facilities which will enable it to earn $300 million next year. Alternatively, it can invest $600 million in creating a commercial and industrial hub and earn $500 million in each of the next two years.

If the city’s WACC is 10%, find out which project makes sense.

### Solution

You can verify that the individual IRRs of Project F and Project E are 50% and 42% respectively, which shows that hosting the football tournament is the preferred option. But since we know that IRR ignores the project size, we need to do further analysis. One way is to calculate the net present values of both projects.

Another approach is to calculate incremental IRR as follows:

- Incremental initial investment of Project E over Project F is $400 million ($600 million minus $200 million).
- Incremental Cash Flows in Year 1 are $200 million ($500 million minus $300 million).
- Incremental Cash Flows in Year 2 are $500 million because Project E has cash flows of $500 million and Project F has zero cash flows in Year 2.

The following equation can be set up to work out incremental IRR:

$$ \text{0}\ =\ -\text{\$400M}\ +\ \frac{\text{\$200M}}{{(\text{1}+\text{IRR})}^\text{1}}+\frac{\text{\$500M}}{{(\text{1}+\text{IRR})}^\text{2}} $$

Solving the above equation using trial and error method or MS Excel IRR function gives us a value of 40%. Since this is higher than the cost of capital of 10%, Project E is the preferred investment despite its lower individual IRR.

Written by Obaidullah Jan, ACA, CFA and last modified on