## **Learning Outcomes**

After reading this article, you will be able to distinguish between hard and soft capital rationing, apply the profitability index for project selection, explain single- and multi-period capital rationing, and evaluate optimal project combinations under resource constraints. You will also understand key exam approaches to risk, divisible and indivisible projects, and how to rank investments under capital rationing.

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

For ACCA Financial Management (FM), you are required to understand project selection under limited capital conditions. In particular, you should revise:

- The main concepts and reasoning behind capital rationing
- The differences between hard (external) and soft (internal) capital rationing
- Application of profitability index (PI) for ranking divisible and indivisible projects under single-period capital constraints
- Identification and impact of mutually exclusive projects
- Selection of the optimal portfolio of projects given funding restrictions
- The treatment of risk and uncertainty in capital budgeting decisions

## **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 primary difference between hard and soft capital rationing?
2. How is the profitability index (PI) calculated, and why is it important in capital rationing?
3. Which method should be used to select projects if they are indivisible and subject to a single-period investment constraint?
4. True or false? Capital rationing always leads to the maximisation of shareholder wealth.

## **Introduction**

Businesses aim to invest in all projects with a positive net present value (NPV) to maximise shareholder wealth. However, in practice, capital is often limited, so managers must choose between competing projects. This situation—where not all desirable investments can be funded due to shortage of finance—is called capital rationing. Understanding risk, allocation methods, and the use of relevant decision metrics is essential for effective project selection when capital is restricted.

> **Key Term: capital rationing**
> The situation where a business cannot fund all available projects with positive NPVs due to limited capital, requiring selection among competing investments.

## Types of Capital Rationing

Capital rationing can arise from internal management decisions or from factors outside the business.

### Hard (External) Capital Rationing

This occurs when external financial markets or lenders restrict the availability of funds. Examples include poor credit ratings, economic downturns, or specific industry factors that make raising finance impossible or extremely expensive.

> **Key Term: hard capital rationing**
> An absolute limit on investment funds imposed by external parties, such as banks or investors, preventing the business from raising more capital regardless of potential returns.
>
> **Key Term: soft capital rationing**
> A self-imposed internal restriction by management, such as budget limits, policy decisions, or risk aversion, even though additional capital could be raised if desired.

### Soft (Internal) Capital Rationing

Soft capital rationing results from internal policy decisions, such as strict budgeting, concern about overtrading, or reserving funds to manage perceived risks. While not imposed by the market, these limits are set by the managers of the business themselves.

## Single-Period Capital Rationing

The most common exam scenario involves single-period capital rationing: the business can invest up to a fixed amount in projects, all of which require an initial outlay at time zero.

Projects may be:

- **Divisible:** the business can invest in a fraction of the project and receive a proportional share of the returns.
- **Indivisible:** the business can only accept or reject the entire project.

The objective is always to select the combination of projects that maximises total NPV within the available capital.

### Profitability Index (PI) and Divisible Projects

When projects are divisible, ranking by the profitability index (PI) ensures the optimal allocation of funds.

> **Key Term: profitability index (PI)**
> The ratio of a project’s NPV to its initial investment. PI = NPV / Initial Investment. Used to rank projects under capital rationing.

Projects are ranked in order of highest PI. Funds are allocated first to the project with the highest PI, then to the next, and so on until the capital is used up. If projects are perfectly divisible, the ‘cut-off’ project is funded in part, and the returns are proportional.

### Indivisible Projects

If projects are not divisible, trial and error or enumeration is required. All combinations of projects that do not exceed the capital constraint are considered, and the mix yielding the highest total NPV is chosen. Where mutually exclusive projects exist, only one from the group can be selected.

### **Worked Example 1.1**

A company has \$120,000 to invest and the following three projects:

| Project | Initial Outlay ($) | NPV ($) |
| ------- | ------------------ | ------- |
| A       | 50,000             | 25,000  |
| B       | 60,000             | 32,000  |
| C       | 80,000             | 38,000  |

All projects are divisible.

**Which projects should be selected and in what proportion to maximise total NPV?**

> **Answer:**
>
> - Calculate PI for each:
>   - A: 25,000 / 50,000 = 0.50
>   - B: 32,000 / 60,000 = 0.53
>   - C: 38,000 / 80,000 = 0.48
> - Rank: B (0.53), A (0.50), C (0.48)
> - Fully invest in B (\$60k, \$32k NPV) and A (\$50k, \$25k NPV) = \$110k, \$57k NPV.
> - \$10k left for C: \$10k / \$80k = 12.5% of project → \$38k × 12.5% = \$4.75k NPV.
> - Total NPV: \$57k + \$4.75k = \$61.75k.

### **Worked Example 1.2**

Using the same data, if projects are indivisible and only full projects can be selected, what is the optimal project selection?

> **Answer:**
>
> - Possible combinations:
>   - B + A: \$60k + \$50k = \$110k (within \$120k), NPV = \$32k + \$25k = \$57k.
>   - C + A: \$80k + \$50k = \$130k (exceeds \$120k).
>   - C + B: \$80k + \$60k = \$140k (exceeds \$120k).
>   - C alone: \$80k (NPV \$38k).
>   - B alone: \$60k (NPV \$32k).
>   - A alone: \$50k (NPV \$25k).
> - Best: B + A (\$57k NPV). All other valid combinations yield lower NPV.

## Multi-Period Capital Rationing

Multi-period capital rationing involves investment limits across several periods (e.g., two years in a row). This is more complex and may require mathematical programming (beyond syllabus needs for FM) to find the optimal solution. For exam purposes, focus is on single-period scenarios or explaining the additional complexity of multi-period situations.

## Mutually Exclusive Projects

Sometimes, certain projects cannot both be chosen (e.g., they use the same equipment or serve the same market). In these cases, treat them as mutually exclusive—only one from the group may be selected. When ranking, ensure you do not combine mutually exclusive projects in your options.

## Risk and Capital Rationing

Managers should recognise that capital rationing means not all positive NPV projects can be accepted, so total shareholder wealth is not maximised. Capital rationing is sometimes unavoidable (hard), but soft capital rationing should be justified with sound reasoning (e.g., to limit overtrading). It is important to identify and communicate the potential impact of rejecting profitable investments due to capital constraints.

### **Exam Warning**

> Projects with the highest NPV do not always have the highest PI. Always rank by PI (not NPV) when projects are divisible under a capital constraint.

## **Summary**

Capital rationing forces managers to make choices between competing investments due to limited capital. The optimal selection of projects under one-period rationing depends on whether projects are divisible (rank and allocate by PI) or indivisible (find the highest-NPV combination that does not exceed the constraint). Recognising the type of rationing and correctly applying selection methods is essential for the exam.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Define capital rationing, hard and soft types
- Explain how single-period capital rationing is addressed
- Calculate and use the profitability index (PI) for project selection
- Differentiate between divisible and indivisible project methods
- Identify and handle mutually exclusive projects
- Understand risk and the effect of capital rationing on shareholder wealth

## **Key Terms and Concepts**

- capital rationing
- hard capital rationing
- soft capital rationing
- profitability index (PI)

Risk analysis and project selection - Capital rationing single and multi-period