## **Learning Outcomes**

After reading this article, you will be able to perform NPV and profitability index calculations, explain how these tools are used to assess and rank investment projects, and apply these methods to make project selection decisions, including under capital rationing. You will also understand the advantages, limitations, and exam pitfalls associated with each approach and their relevance to maximising shareholder wealth.

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

For ACCA Financial Management (FM), you are required to understand and apply investment appraisal techniques that enable the selection and ranking of projects. In particular, you should focus on:

- Calculating net present value (NPV) and understanding its use in project appraisal
- Calculating and interpreting the profitability index (PI, also called NPV index)
- Ranking projects using NPV and PI where there are capital constraints
- Distinguishing between divisible and indivisible projects in capital rationing scenarios
- Discussing the advantages and limitations of NPV and PI methods
- Applying project selection techniques to maximise shareholder wealth

## **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 a project based on its profitability index (PI)?
2. Which method—NPV or PI—should be used to rank projects when capital is limited and projects may be partially undertaken?
3. True or false? The PI is calculated as the present value of project inflows divided by the present value of project outflows.
4. Briefly explain how project selection differs between divisible and indivisible investment projects under a single-period capital constraint.

## **Introduction**

Project appraisal is a fundamental part of financial management. Net present value (NPV) and the profitability index (PI) are key tools for evaluating investment proposals. Both methods use discounted cash flows but have specific uses when ranking projects, especially under capital rationing. Understanding these techniques is essential for making decisions that increase shareholder wealth.

> **Key Term: net present value (NPV)**
> The sum of the present values of all cash inflows and outflows associated with a project, calculated using the required rate of return. A positive NPV indicates a project is expected to add value.
>
> **Key Term: profitability index (PI)**
> The ratio of the present value of future cash inflows to the present value of cash outflows for a project. Also called the NPV index.

## NPV—THE PRIMARY APPRAISAL TECHNIQUE

NPV involves discounting all project cash inflows and outflows to their present values using the organisation’s required rate of return (cost of capital). Projects with a positive NPV are financially viable as they are forecast to generate more value than they cost.

### Decision Rule

- Accept projects with NPV > 0
- If projects are mutually exclusive, select the one with the highest NPV
- In capital rationing, NPV alone may not always determine the best allocation (see PI below)

### **Worked Example 1.1**

**A business is considering installing equipment costing \$120,000. It expects to generate cash inflows of \$50,000 annually for three years. The cost of capital is 8%. Should the project be accepted?**

> **Answer:**
> Step 1: Calculate PV of inflows.
> PV = \$50,000 × [PV factor for 3 years at 8%] = \$50,000 × 2.577 = \$128,850
>
> Step 2: Calculate NPV.
> NPV = \$128,850 − \$120,000 = \$8,850
>
> Since NPV is positive, the project should be accepted.

## PROFITABILITY INDEX—RANKING UNDER CAPITAL RATIONING

The profitability index (PI) (also known as the NPV index) is used when available funds are insufficient to undertake all positive NPV projects. PI ranks projects based on the value created per unit of investment.

> **Key Term: capital rationing**
> A situation where the funds available for investment are insufficient to undertake all available positive NPV projects.

### Calculating PI

PI = Present value of project inflows / Present value of investment outflows

- PI > 1: Project is viable
- Higher PI = more value created per \$1 invested

### **Worked Example 1.2**

**A company has \$200,000 to invest. Project A costs \$100,000 (NPV \$20,000). Project B costs \$100,000 (NPV \$30,000). Both are divisible. How should funds be allocated?**

> **Answer:**
> Step 1: Calculate PI for both projects.
> A: PI = (\$100,000 + \$20,000)/\$100,000 = 1.20  
> B: PI = (\$100,000 + \$30,000)/\$100,000 = 1.30
>
> Step 2: Rank and allocate.
> Invest first in B (higher PI), then A with remaining funds. Invest \$100,000 in B (NPV \$30,000), \$100,000 in A (NPV \$20,000). All funds used, maximum total NPV = \$50,000.

### Using PI with Divisible vs Indivisible Projects

- **Divisible projects:** Projects can be partially undertaken; use PI to allocate funds in order of highest PI until funds are exhausted.
- **Indivisible projects:** Projects can only be taken as a whole; use trial and error to find the combination of projects with the highest total NPV within the budget.

### **Worked Example 1.3**

**Assume the same company (\$200,000 funding), but Project A and B are indivisible, and Project C is available at \$200,000 (NPV \$25,000, PI 1.125). Which projects should be selected?**

> **Answer:**
> Test combinations:
>
> - A + B not possible (\$100,000 + \$100,000 = \$200,000, NPV \$50,000)
> - C alone (\$200,000, NPV \$25,000)
>
> Selecting A and B provides higher total NPV (\$50,000). Choose A and B.

## ADVANTAGES AND LIMITATIONS

### NPV—Strengths

- Considers time value of money
- Measures absolute value added
- Directly relates to shareholder wealth

### PI—Strengths

- Useful where capital is restricted
- Prioritises value per dollar invested
- Allows rational allocation with divisible projects

### Limitations

- PI may not give the best combination with indivisible projects
- NPV may not fully address capital constraints without PI
- Both methods require accurate cash flow forecasts and discount rates

### **Exam Warning**

> The PI method is only appropriate for ranking and allocating funds if projects are perfectly divisible. If projects are indivisible, you must consider all feasible combinations to maximise total NPV.

## **Summary**

NPV is the preferred technique for assessing project viability and ranking mutually exclusive investments. The profitability index is essential for optimising project selection under single-period capital rationing when projects are divisible. Use trial-and-error for indivisible projects. Both methods aim to maximise the value created for shareholders.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Calculate and interpret NPV for project appraisal
- Define and calculate the profitability index (PI)
- Use PI to rank projects under capital constraints with divisible projects
- Apply trial-and-error for ranking indivisible projects
- Understand decision rules for NPV and PI
- Discuss advantages and limitations of each technique

## **Key Terms and Concepts**

- net present value (NPV)
- profitability index (PI)
- capital rationing

Appraisal techniques and rankings - NPV and profitability index