## **Learning Outcomes**

After reading this article, you will be able to explain and calculate Net Present Value (NPV) and Internal Rate of Return (IRR), understand how to use discounting techniques, and describe decision rules for accepting or rejecting capital projects. You will also be able to evaluate investment decisions using these methods to improve exam performance.

## **ACCA Foundations in Financial Management (FFM) Syllabus**

For ACCA Foundations in Financial Management (FFM), you are required to understand how discounting investment appraisal techniques are used to assess capital projects. For the exam, you should focus on:

- Explaining the meaning and importance of NPV and IRR in project appraisal
- Calculating NPV and IRR for given project data and using discount rate tables
- Applying and interpreting NPV and IRR decision rules
- Identifying the strengths and weaknesses of NPV and IRR as selection methods
- Understanding the impact of cost of capital on project appraisal

## **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 capital investment appraisal method measures the present value of all expected cash inflows and outflows using a discount rate?
   a) Payback period
   b) Net Present Value (NPV)
   c) Internal Rate of Return (IRR)
   d) Accounting rate of return

2. True or false? If a project’s NPV is positive at the firm’s required rate of return, the project should be accepted.

3. Which of the following best describes the IRR of a project?
   a) The rate at which payback period is maximized
   b) The discount rate at which NPV equals zero
   c) The average return on investment
   d) The required cost of capital

4. What is a key limitation of the IRR method when used to compare mutually exclusive projects?

## **Introduction**

Selecting the best projects for long-term investment is one of the most significant financial decisions a business will make. Investment appraisal methods support managers in making decisions that increase shareholder value. The Net Present Value (NPV) and Internal Rate of Return (IRR) are the primary discounted cash flow techniques used to evaluate such investments, as they consider the time value of money.

This article explains NPV and IRR principles, provides step-by-step calculations, and sets out clear decision rules, using simple examples to support understanding.

> **Key Term: Net Present Value (NPV)**
> The sum of the present values of all cash inflows and outflows associated with a project, discounted at the required rate of return.

## NPV: THE CORE OF DISCOUNTED CASH FLOW ANALYSIS

NPV estimates how much value a project will add to the business in today’s terms.

### Why is NPV important?

NPV accounts for both the size and timing of a project’s cash flows. Because money has a time value (cash received sooner is worth more), future cash flows are discounted using the business’s required rate of return—also called the cost of capital.

> **Key Term: Discount rate**
> The rate of return used to convert future cash flows into present value, reflecting the minimum return required by investors.
>
> **Key Term: Cost of capital**
> The required rate of return by providers of long-term finance, commonly used as the discount rate in NPV calculations.

### NPV Calculation Steps

1. Identify all relevant future cash inflows and outflows for the project.
2. Discount each cash flow to present value using the discount rate.
3. Sum all present values: NPV = Total PV of inflows − Total PV of outflows (including initial investment).

A positive NPV means the project is expected to add value above the cost of capital; a negative NPV indicates value will, on balance, be lost.

### **Worked Example 1.1**

A company is considering investing \$50,000 in a project. The expected net cash inflows are \$22,000 per year for three years. The required rate of return (discount rate) is 10%. Should the project be accepted?

> **Answer:**
>
> 1. Discount factors at 10%:
>    - Year 1: 0.909
>    - Year 2: 0.826
>    - Year 3: 0.751
> 2. Present value of inflows:
>    - Year 1: \$22,000 × 0.909 = \$19,998
>    - Year 2: \$22,000 × 0.826 = \$18,172
>    - Year 3: \$22,000 × 0.751 = \$16,522
>    - Total = \$54,692
> 3. NPV = \$54,692 − \$50,000 = \$4,692
>
> Since the NPV is positive, the project should be accepted.

### NPV Decision Rule

- **Accept** the project if NPV > 0
- **Reject** the project if NPV < 0

NPV directly measures how much shareholder value will rise or fall if the project proceeds.

### **Revision Tip**

Always include all incremental (extra) cash flows and use after-tax cash flows where required by exam questions.

## INTERNAL RATE OF RETURN (IRR): THE DISCOUNT RATE IN PRACTICE

> **Key Term: Internal Rate of Return (IRR)**
> The discount rate that makes the NPV of a project exactly zero.

IRR represents the break-even rate of return for an investment—the maximum cost of capital at which the project is acceptable.

### IRR Calculation

1. Use the NPV formula to calculate NPV at two different discount rates (one giving a positive NPV, one negative).
2. Interpolate between the rates to estimate the IRR.

### **Worked Example 1.2**

An initial investment of \$10,000 produces returns of \$6,000 per year for two years. Calculate the IRR to the nearest percent.

> **Answer:**
>
> First, estimate at two rates:
>
> - At 10%: PV inflows = \$6,000 × 0.909 + \$6,000 × 0.826 = \$5,454 + \$4,956 = \$10,410; NPV = \$410
> - At 15%: PV inflows = \$6,000 × 0.870 + \$6,000 × 0.756 = \$5,220 + \$4,536 = \$9,756; NPV = −\$244
>
> IRR ≈ 10% + [(\$410 / (\$410 + \$244)) × (15% − 10%)]
> IRR ≈ 10% + [(\$410 / \$654) × 5%] ≈ 10% + 3% = 13%
>
> The IRR is approximately 13%.

### IRR Decision Rule

- **Accept** the project if IRR > cost of capital
- **Reject** if IRR < cost of capital

If the IRR is higher than the minimum required return, the project is worthwhile.

## COMPARISON AND LIMITATIONS

### NPV vs. IRR

- NPV measures the absolute increase in value.
- IRR gives a percentage return for comparison.
- If projects are independent, both methods should provide the same accept/reject decision.
- When mutually exclusive projects compete, NPV is preferred as it maximises total shareholder wealth.

### **Worked Example 1.3**

Project A: NPV \$7,000, IRR 16%
Project B: NPV \$8,000, IRR 14%
Cost of capital: 12%. Which project should be chosen?

> **Answer:**
> Both projects are viable, but as only one can be selected, Project B is preferred for its higher NPV, despite having a lower IRR.

### **Exam Warning**

In exams, do not select a project solely based on the highest IRR when comparing mutually exclusive projects. NPV should decide.

## ADVANTAGES AND WEAKNESSES

> **Key Term: Discounted cash flow techniques**
> Methods that consider the time value of money, including NPV and IRR, for project appraisal.
>
> **Key Term: Mutually exclusive projects**
> Investment choices where selection of one project excludes the others.

### Advantages

- NPV: Reflects all cash flows, time value, and directly shows value added.
- IRR: Communicates return as an easily compared rate.

### Limitations

- IRR may give conflicting results with NPV for multiple or non-conventional cash flows.
- IRR assumes interim cash flows are reinvested at IRR, while NPV assumes reinvestment at the cost of capital.

## **Summary**

NPV and IRR are the main discounted cash flow methods for appraising investments, both using future cash flows and discounting them to present value. Decision rules are simple: accept projects with positive NPV or IRR above the cost of capital. When methods disagree, use NPV for selection.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Explain the calculation and meaning of NPV and IRR
- Apply the decision rules for NPV and IRR to investment projects
- Calculate NPV and IRR from provided cash flows and discount rates
- Describe when to prefer NPV over IRR, especially for mutually exclusive projects
- Recognise the strengths and weaknesses of discounted cash flow techniques

## **Key Terms and Concepts**

- Net Present Value (NPV)
- Discount rate
- Cost of capital
- Internal Rate of Return (IRR)
- Discounted cash flow techniques
- Mutually exclusive projects

Capital investment appraisal - NPV and IRR fundamentals and decision rules