## **Learning Outcomes**

After reading this article, you will be able to calculate and interpret the Internal Rate of Return (IRR) for investment appraisal, distinguish between IRR and Net Present Value (NPV) rankings, and explain the implications of multiple IRRs. You will also learn when IRR is appropriate and its limitations, an important area for exam scenarios requiring informed project selection.

## **ACCA Financial Management (FM) Syllabus**

For ACCA Financial Management (FM), you are required to understand the application, strengths, and limitations of IRR in project appraisal. This article covers:

- Calculation of IRR for investment projects
- Comparison of IRR and NPV as investment appraisal methods
- Identification and explanation of the multiple IRR problem
- Appropriate use and limitations of IRR in rankings and decision-making
- Recognition of circumstances where NPV is preferred over IRR

## **Test Your Knowledge**

_Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, remember to look more closely at that area during your revision._

1. What is the decision rule for accepting or rejecting a project using IRR?
2. Why can projects with "non-conventional" cash flows result in multiple IRRs?
3. Project A has an IRR of 13% and an NPV of \$3,000 at a 10% cost of capital. Project B has an IRR of 18% but an NPV of \$2,000 at the same cost of capital. Which should be selected and why?
4. Explain how IRR assumes reinvestment of interim project cash flows. Is this assumption always realistic?

## **Introduction**

The Internal Rate of Return (IRR) is a key discounted cash flow technique used to evaluate investment projects. While IRR provides a readily understandable percentage return, it is essential to recognise both its strengths and inherent limitations—especially its occasional failure to rank projects correctly or the occurrence of multiple IRRs in certain scenarios. Understanding these issues is fundamental for accurate appraisal and robust recommendations in your ACCA FM exam.

> **Key Term: Internal Rate of Return (IRR)**
> The discount rate at which the net present value (NPV) of a project's cash flows is zero; represents the breakeven return of an investment.

## IRR: Method and Decision Rule

The IRR for a project is the rate of return which equates the sum of the discounted future inflows and outflows to zero. It is typically calculated by linear interpolation between two discount rates that provide NPVs above and below zero.

**IRR Decision Rule:**

- Accept projects if IRR > cost of capital.
- Reject projects if IRR < cost of capital.

Unlike NPV, IRR expresses the project's financial return as a percentage—allowing comparison with the required rate.

### **Worked Example 1.1**

**A project requires an initial outlay of \$100,000. It yields \$42,000 at the end of Year 1, \$58,000 in Year 2, and a final inflow of \$20,000 in Year 3. If the company's cost of capital is 8%, what is the IRR and should the project be accepted?**

> **Answer:**
> First, calculate the NPV at two rates:
>
> - At 8%: NPV = –\$100,000 + \$42,000/(1.08) + \$58,000/(1.08²) + \$20,000/(1.08³) = \$7,081 (rounded)
> - At 15%: NPV = –\$100,000 + \$42,000/(1.15) + \$58,000/(1.15²) + \$20,000/(1.15³) = –\$2,208 (rounded)
>   IRR = 8% + [\$7,081 ÷ (\$7,081 – (–\$2,208))] × (15% – 8%) ≈ 8% + [7,081 ÷ 9,289] × 7% ≈ 13.3%
>   Accept, as IRR > cost of capital.

## IRR Versus NPV: Rankings and Contradictions

Projects are often ranked by either NPV (absolute value added) or IRR (percentage return). For "conventional" projects (single outflow followed by all inflows), both usually suggest the same choice. However, discrepancies can arise.

When two projects are mutually exclusive (choosing one rules out the other), the project with the higher NPV at the required cost of capital should be selected—not necessarily the one with the higher IRR.

> **Key Term: Mutually Exclusive Projects**
> Projects where acceptance of one prevents the undertaking of the other.

### **Worked Example 1.2**

**Project M: IRR 17%, NPV \$4,500 at 10%. Project N: IRR 23%, NPV \$2,800 at 10%. The firm's required return is 10%. Which project should be chosen?**

> **Answer:**
> Despite Project N’s higher IRR, Project M adds more value at the cost of capital. Project M should be selected.

### **Revision Tip**

For project selection, always check NPV at the firm's cost of capital—IRR alone can be misleading when ranking projects, particularly if their investment scale or timing of cash flows differs.

## Multiple IRRs: The Problem with Unconventional Cash Flows

A key limitation of IRR arises with projects where cash flows change sign more than once (e.g. an outflow, then inflow, then further outflow). Such "non-conventional" cash flows can yield more than one IRR—confusing interpretation and decision-making.

> **Key Term: Multiple IRRs**
> The existence of more than one discount rate at which a project's NPV equals zero, resulting from non-conventional cash flows.

This occurs because the NPV profile crosses the zero axis more than once, producing several mathematically valid IRRs. The IRR decision rule becomes unreliable in these cases, as it does not indicate which IRR is relevant.

### **Worked Example 1.3**

**A project requires \$50,000 investment at T0. At T1, an inflow of \$120,000 occurs, but at T2, a required outflow of \$76,000 is needed. How many IRRs might this project have?**

> **Answer:**
> The cash flows switch sign twice: outflow → inflow → outflow. Therefore, there may be two IRRs. Linear interpolation is not reliable here. Choosing a project using IRR is not appropriate.

### **Exam Warning**

Do not recommend IRR as the sole appraisal technique for projects with more than one change in cash flow sign. In these cases, always use NPV for reliable investment advice.

## Additional Limitations of IRR

- **Ranking Bias:** IRR may favour small projects with high percentage returns instead of those adding the most value.
- **Reinvestment Rate Assumption:** IRR assumes interim cash flows are reinvested at the IRR, which is rarely realistic. NPV assumes reinvestment at the cost of capital—a more defensible assumption.
- **Multiple or No IRRs:** Some cash flow patterns produce multiple IRRs or, less commonly, none at all.

> **Key Term: Reinvestment Assumption**
> The implied rate at which a project's interim cash inflows are presumed to be reinvested: IRR assumes reinvestment at the IRR; NPV assumes at the cost of capital.
>
> **Key Term: NPV Profile**
> A graphical representation of a project's NPV at various discount rates, demonstrating where NPV is zero and the number of IRRs.

## Summary

While IRR is a popular measure conveying return as a percentage, it is not always reliable—especially for ranking mutually exclusive projects or where cash flows are non-conventional. Multiple IRRs or conflicts between NPV and IRR rankings demand extra care. In such cases, NPV remains the superior guide for maximising shareholder value.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Define IRR and explain the IRR decision rule
- Calculate IRR using interpolation for conventional projects
- State situations that lead to multiple IRRs and explain why they arise
- Compare IRR and NPV for ranking projects, noting when NPV is preferred
- Recognise IRR limitations, including reinvestment rate assumption and ranking inconsistencies

## **Key Terms and Concepts**

- Internal Rate of Return (IRR)
- Mutually Exclusive Projects
- Multiple IRRs
- Reinvestment Assumption
- NPV Profile

Appraisal techniques and rankings - IRR and multiple IRR issues