## **Learning Outcomes**

After reading this article, you will understand the application and limitations of discounted cash flow (DCF) techniques under capital rationing. You will be able to distinguish between hard and soft capital rationing, carry out project appraisal with resource constraints, and evaluate common decision rules including profitability index and linear programming. By the end, you will confidently apply these approaches to ACCA exam scenarios.

## **ACCA Advanced Performance Management (APM) Syllabus**

For ACCA Advanced Performance Management (APM), you are required to understand not only how to appraise investment projects using DCF but also how to deal with practical constraints such as limited capital. This article addresses:

- The application of DCF techniques (NPV, IRR) in project appraisal
- The nature and implications of capital rationing (hard and soft)
- Techniques for project selection under capital rationing, including the profitability index (PI) and linear programming basics
- The limitations of traditional DCF when resources are insufficient for all projects
- The importance of aligning project appraisal decisions with strategic objectives and resource constraints

## **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 best describes a 'hard' capital rationing scenario?  
   a) The company chooses not to use available funds  
   b) External finance is absolutely unavailable  
   c) Only one project can be accepted at a time  
   d) The board is unsure which projects to pursue

2. Why is the profitability index (PI) used in capital rationing situations?  
   a) It eliminates risk  
   b) It allows ranking of projects by NPV only  
   c) It maximizes return per unit of capital invested  
   d) It ranks projects by accounting rate of return

3. True or false? If capital is not restricted, all projects with a positive NPV should be accepted.

4. In a scenario where several projects are divisible, explain how you would allocate limited capital to maximize value.

5. Define soft capital rationing and provide an example.

## **Introduction**

Investment appraisal using discounted cash flow is a key management accounting technique. In practice, however, organisations rarely have enough capital to fund all projects that have a positive net present value (NPV). Capital rationing describes this challenge and introduces important complexities. In the ACCA exam, you must demonstrate not just mechanical calculation skills, but the ability to advise on optimal project selection when resources are limited.

> **Key Term: discounted cash flow (DCF)**  
> DCF is a method of valuing projects by calculating the present value of expected future cash flows using a specified discount rate.
>
> **Key Term: net present value (NPV)**  
> NPV is the sum of all cash inflows and outflows discounted at the required rate of return. A positive NPV indicates value creation.

## **DCF Techniques for Project Appraisal**

The main objective when using DCF techniques is to maximize shareholder wealth by selecting value-adding projects. Normally, all independent projects with a positive NPV would be selected. However, in capital rationing situations, constraints prevent this.

### Types of Capital Rationing

Projects may be rejected not because they are unprofitable, but due to a lack of available funds. There are two main forms:

> **Key Term: capital rationing**  
> Capital rationing is the situation where an organisation cannot undertake all investment projects with a positive NPV due to external or internal resource constraints.
>
> **Key Term: hard capital rationing**  
> Hard capital rationing arises when external finance is not available at any price, e.g. due to market conditions or restrictive lending.
>
> **Key Term: soft capital rationing**  
> Soft capital rationing occurs when restrictions are imposed internally (e.g. management setting a cap on investment) rather than by the market.

### **Worked Example 1.1**

A manufacturing business has funds of \$1,000,000 for investment. It has three projects:

- Project A: NPV = \$200,000; Initial outlay = \$600,000
- Project B: NPV = \$120,000; Initial outlay = \$400,000
- Project C: NPV = \$110,000; Initial outlay = \$500,000

The business cannot borrow more funds and projects are not divisible.

**Question:** Which projects should be selected to maximize NPV?

> **Answer:**  
> Projects A (\$600,000) and B (\$400,000) exhaust the available capital and produce a combined NPV of \$320,000. Choosing either A and C (\$1,100,000) or B and C (\$900,000) leaves capital unutilized or fails to maximize value. The optimal choice is Projects A and B.

### Project Divisibility and the Profitability Index

If projects can be undertaken in part (divisible), or when the budget constraint is rigid, the profitability index (PI) can assist in ranking projects. The PI is the ratio of present value of future cash flows to initial investment.

> **Key Term: profitability index (PI)**  
> PI is the present value of future cash flows divided by the initial investment. It is used to rank projects under capital rationing.

### **Worked Example 1.2**

A business can invest up to \$600,000 and has these divisible projects:

- Project D: NPV \$90,000; Outlay \$300,000; PI = 1.3
- Project E: NPV \$100,000; Outlay \$400,000; PI = 1.25

**Question:** How should the business allocate funds to maximize NPV?

> **Answer:**  
> PI shows Project D has greater value per $ invested. Allocate \$300,000 to D (full), leaving \$300,000. Next, invest as much as possible in E: \$300,000 of \$400,000. Pro-rata NPV for E: \$100,000 × (300/400) = \$75,000. Total achievable NPV = \$90,000 + \$75,000 = \$165,000.

### Constraints Beyond Capital

Sometimes, the constraint is not only capital, but also resources such as labour or materials in multiple periods. If so, project selection often requires linear programming or specialist optimisation techniques. For most ACCA exam scenarios, however, basic ranking and allocation using PI will suffice.

## **Complexities and Limitations**

The decision becomes more complex if:

- Projects are mutually exclusive (cannot both be taken)
- Projects are interdependent (require or exclude one another)
- Only a fixed fraction of a project can be taken up (divisible)
- Constraints exist in multiple periods, not just in the initial investment year

DCF hides some practical risks:

- Estimated cash flows are uncertain
- Capital markets may open or close suddenly
- Divisibility is unusual in real life—most projects are “all-or-nothing”

### **Exam Warning**

> Under time-limited conditions, ensure your recommendation is feasible with the resource limit given. Do not select combinations whose total capital outlay exceeds the constraint, even if individually they have superior NPV.

## **Summary**

In capital rationing, you must maximize total NPV by optimally allocating scarce resources. Use the PI to rank divisible projects by value created per $ invested. Where projects are indivisible, list all combinations possible under the budget. Complex, multi-period constraints may require more advanced methods. Always explain your selection logic clearly.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Explain the difference between hard and soft capital rationing
- Use DCF approaches for project appraisal
- Apply the profitability index to rank divisible projects
- Select projects under constrained capital to maximize total NPV
- Recognize when advanced methods (e.g., linear programming) are needed
- Identify and avoid common pitfalls on the exam, such as exceeding the capital limit

## **Key Terms and Concepts**

- discounted cash flow (DCF)
- net present value (NPV)
- capital rationing
- hard capital rationing
- soft capital rationing
- profitability index (PI)

DCF techniques and complexities - Project appraisal with capital rationing