> For the complete documentation index, see [llms.txt](https://help.modelreef.io/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://help.modelreef.io/help/financial-outputs-and-valuation/irr-calculation.md).

# IRR Calculation

This article explains how **internal rate of return (IRR)** is calculated in Model Reef.

You will learn:

* The difference between project IRR and equity IRR.
* How IRR is computed from model cashflows.
* How entry price or initial investment is handled.

IRR is the discount rate that makes the NPV of a series of cashflows equal to zero.

{% stepper %}
{% step %}

### Cashflows used for IRR

Model Reef can compute IRR on two main cashflow sets:

* **Project IRR**
  * Uses FCFF and any initial project investment.
  * Measures return to the full capital structure.
* **Equity IRR**
  * Uses FCFE and equity entries and exits.
  * Measures return to equity holders only.

You can configure which cashflows are used for each IRR calculation in the valuation settings.
{% endstep %}

{% step %}

### Role of purchase price or initial investment

To compute IRR, you usually need an initial negative cashflow that represents:

* The price paid to acquire a business.
* The equity invested at the start of a project.
* The net initial funding requirement.

In Model Reef you can:

* Enter a **purchase price** or initial equity investment as an input.
* Combine this with future FCFF or FCFE cashflows.

The IRR is then the rate r that solves:

{% code title="NPV equation" %}

```
NPV
= Sum of (Cashflow in period ÷ (1 + r) ^ t)
= 0
```

{% endcode %}

Where the first major cashflow is negative and later cashflows are positive in a typical investment case.
{% endstep %}

{% step %}

### Numerical method and behaviour

The valuation engine uses numerical root finding similar to Excel's XIRR:

* It handles uneven cashflow timing.
* It works with varying period lengths.
* It returns the rate that sets NPV to zero, if a solution exists.

In cases where cashflows change sign multiple times there may be multiple IRRs or none. In practice, most planning and transaction models use patterns with a single sign change, which produce a single economically meaningful IRR.
{% endstep %}

{% step %}

### Interpreting IRR in scenarios

You can use IRR across scenarios to:

* Compare Base, Downside and Upside equity returns.
* See the impact of different capital structures or purchase prices.
* Evaluate whether IRR meets internal or investor hurdles.

IRR should be interpreted together with NPV, money multiple and risk assumptions rather than in isolation.
{% endstep %}
{% endstepper %}

## Related articles

* [Warehouse Capacity & Logistics Model](/use-cases/wholesale-distribution-and-b2b-trade/warehouse-capacity-and-logistics-model.md)
* [Build an Annual Planning Pack](/how-tos/scenarios-and-planning/build-an-annual-planning-pack.md)
* [Multi Entity Setup](/help/building-your-model/multi-entity-setup.md)
* [Formula Editor Layout](/syntax/formula-syntax/formula-editor-layout.md)