## **Learning Outcomes**

By the end of this article, you will be able to apply and critically evaluate discounted cash flow (DCF) investment appraisal techniques: Net Present Value (NPV), Internal Rate of Return (IRR), and Modified Internal Rate of Return (MIRR). You will understand their advantages and limitations, identify ranking conflicts between these methods, and resolve common pitfalls when comparing projects, particularly in the ACCA AFM exam context.

## **ACCA Advanced Financial Management (AFM) Syllabus**

For ACCA Advanced Financial Management (AFM), you are required to understand and apply DCF techniques in investment appraisal, and to identify practical complications that affect decision-making. In your revision, focus on:

- Evaluating project viability using NPV, IRR, and MIRR methods
- Recognising why these methods may give conflicting project rankings
- Calculating and interpreting MIRR and discussing its application
- Dealing with special scenarios: non-conventional cash flows and non-standard projects
- Resolving issues arising in project selection and ranking conflicts

## **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. Which DCF method is theoretically superior for investment appraisal: NPV, IRR, or MIRR? Briefly explain why.
2. What is a project ranking conflict, and why can it arise between the NPV and IRR methods?
3. True or false? The IRR for a project always exists and is unique.
4. Calculate the MIRR for a project with an initial outlay of \$10,000 and cash inflows of \$5,000 for each of years 1–3, assuming a cost of capital of 8%.

## **Introduction**

DCF techniques are central to advanced investment appraisal in the ACCA AFM exam. They aid in evaluating whether capital projects should proceed, based on the present value of future cash flows. The main DCF methods are NPV, IRR, and MIRR. While all methods aim to assess project value, they sometimes give conflicting recommendations, especially in ranking mutually exclusive projects. Understanding these methods, their assumptions, strengths, and limitations is essential for sound financial decision-making and ACCA exam success.

## **CORE DCF TECHNIQUES**

### Net Present Value (NPV)

**NPV** is calculated by discounting estimated future cash flows to their present value using an appropriate discount rate (usually the project’s cost of capital), then subtracting the initial investment.

> **Key Term: Net Present Value (NPV)**
> The sum of all project cash flows discounted to present value at the cost of capital, less the initial outlay. NPV > 0 indicates increased shareholder wealth.

NPV provides a direct measure of value added and aligns with the primary objective of shareholder wealth maximisation. Projects with a positive NPV should be accepted.

### Internal Rate of Return (IRR)

**IRR** is the discount rate that makes the NPV of a project zero.

> **Key Term: Internal Rate of Return (IRR)**
> The discount rate at which the present value of future cash inflows equals the initial investment—i.e. NPV equals zero.

A project is acceptable if its IRR exceeds the cost of capital. IRR reflects the project’s return as a percentage, which is often easier to interpret.

### Modified Internal Rate of Return (MIRR)

MIRR addresses some limitations of the IRR approach by adopting more realistic reinvestment and finance rate assumptions.

> **Key Term: Modified Internal Rate of Return (MIRR)**
> The discount rate that equates the present value of investment outflows to the future value of inflows, assuming reinvestment at the cost of capital.

MIRR is generally unique for a given project and is viewed as a more reliable indicator for mutually exclusive projects.

### **Worked Example 1.1**

**A project costs \$12,000 and generates net cash flows of \$5,000 per year for three years. The cost of capital is 10%. Calculate the NPV, IRR (by interpolation), and MIRR.**

> **Answer:**
>
> - NPV: \$5,000 × 2.487 (3-year annuity factor at 10%) = \$12,435; NPV = \$12,435 - \$12,000 = \$435.
> - IRR: Try 12% (\$5,000 × 2.402 = \$12,010, NPV = \$10). By interpolation, IRR ≈ 12%.
> - MIRR: FV of inflows = \$5,000 × (1.10² + 1.10¹ + 1) = \$5,000 × (1.21 + 1.10 + 1) = \$5,000 × 3.31 = \$16,550. MIRR = (\$16,550/\$12,000)^(1/3) – 1 ≈ 11.3%.

## **PRACTICAL COMPLICATIONS**

### Reinvestment Assumptions and Multiple IRRs

NPV assumes cash inflows can be reinvested at the cost of capital. IRR assumes reinvestment at the project’s own IRR, which may be unrealistic. Projects with unconventional cash flows (where signs change more than once) can have multiple or no IRRs, making the decision rule unclear.

> **Key Term: Non-conventional Cash Flows**  
> A pattern where project cash flows change sign (from positive to negative or vice versa) more than once, possibly leading to multiple IRRs.
>
> **Key Term: Project Ranking Conflict**  
> Occurs when NPV and IRR methods provide different orderings for two or more mutually exclusive projects.

### Ranking Conflicts: NPV vs IRR

Differences in project scale, timing of cash flows, or duration can lead to ranking conflicts. NPV generally gives the correct decision for shareholder value but IRR can be misleading.

### **Worked Example 1.2**

**Project X requires \$50,000 and returns \$90,000 in five years. Project Y requires \$50,000 and returns \$15,000 per year for five years. Which project is preferred if the cost of capital is 10%?**

> **Answer:**
>
> NPV(X) = \$90,000 / (1.10)^5 – \$50,000 ≈ \$55,917 – \$50,000 = \$5,917.  
> NPV(Y) = \$15,000 × 3.791 – \$50,000 = \$56,865 – \$50,000 = \$6,865.  
> IRR(X) = (Solve \$50,000 invested, \$90,000 received in five years) → IRR ≈ 12.5%.  
> IRR(Y) = IRR of \$50,000 out, \$15,000 p.a. for five years → IRR ≈ 18%.  
> IRR prefers Y; NPV slightly prefers Y as well. If NPVs conflicted, NPV would be chosen.

### **Exam Warning**

> For projects with non-conventional cash flows or mutually exclusive options, always use NPV for final selection. Do not rely solely on IRR if ranking conflicts arise or multiple IRRs exist.

## **APPLYING MIRR IN PRACTICE**

The MIRR is calculated by compounding positive inflows at the cost of capital (reinvestment rate) and discounting outflows at the finance rate. MIRR avoids the multiple IRR problem and assumes cash flows are reinvested at the more realistic cost of capital.

### **Worked Example 1.3**

**A project has outlays of \$25,000 (T0), inflows of \$10,000 (T1), \$12,000 (T2), and \$10,000 (T3). Cost of capital is 8%. Find MIRR.**

> **Answer:**
>
> FV of inflows = \$10,000 × (1.08)² + \$12,000 × (1.08)¹ + \$10,000 (no compounding)  
> = \$10,000 × 1.1664 + \$12,000 × 1.08 + \$10,000 = \$11,664 + \$12,960 + \$10,000 = \$34,624.  
> MIRR = (\$34,624/\$25,000)^(1/3) – 1 = 1.112 – 1 = 11.2%.

## **SPECIAL CASES AND PROJECT COMPARISON**

### Scale and Timing Issues

NPV and IRR may conflict when projects differ in size, duration, or timing of cash flows. NPV provides an absolute value measure, while IRR is a rate, leading to divergent choices.

### Capital Rationing and Profitability Index

When available capital is limited, projects are ranked using the profitability index (PI):

> **Key Term: Profitability Index (PI)**
> The ratio of the present value of cash inflows to the initial investment, used to rank projects under capital constraints.

## **Summary**

DCF techniques help in project appraisal, but each method has assumptions and drawbacks. NPV is preferred for maximising value and resolving ranking conflicts. IRR is easy to communicate but can be misleading due to reinvestment assumptions or multiple IRRs. MIRR gives a more reliable, unique solution. Be alert to cash flow patterns and project characteristics when choosing a method.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Explain how to calculate and interpret NPV, IRR, and MIRR
- Identify limitations of IRR, including multiple or nonexistent IRRs
- Recognise and resolve project ranking conflicts between NPV and IRR
- Apply MIRR to projects with non-conventional cash flows
- Use the profitability index when capital is rationed

## **Key Terms and Concepts**

- Net Present Value (NPV)
- Internal Rate of Return (IRR)
- Modified Internal Rate of Return (MIRR)
- Non-conventional Cash Flows
- Project Ranking Conflict
- Profitability Index (PI)


DCF techniques and practical complications - NPV, IRR, MIRR and ranking conflicts