## **Learning Outcomes**

This article explains how capital budgeting decisions are adapted when capital is rationed and project risk differs from the firm’s average risk. It clarifies the distinction between hard and soft capital rationing, highlights their implications for project acceptance or rejection, and shows how funding limits alter the simple NPV decision rule. The article explains how to rank and select projects using the profitability index and other value-based criteria when funds are constrained across single or multiple periods. It details how firms estimate and apply risk-adjusted hurdle rates, including the use of project betas, pure-play comparables, and risk premiums to align discount rates with project-specific risk. The discussion covers how inappropriate use of a single company-wide cost of capital can bias investment choices and distort firm value. The article also examines the role of real options—such as deferral, expansion, contraction, and abandonment—in enhancing project value, influencing capital allocation under constraints, and guiding exam-style judgments about which projects should be prioritised when capital is scarce.

## **CFA Level 2 Syllabus**

For the CFA Level 2 exam, you are expected to understand how capital rationing and risk-adjusted hurdle rates affect practical investment decisions and firm value, with a focus on the following syllabus points:

- Differentiating types of capital rationing and their impact on capital budgeting processes
- Describing and applying methods for estimating risk-adjusted hurdle rates for projects with varying risk profiles
- Evaluating the effect of capital rationing on the selection and ranking of investment projects
- Incorporating real options into project evaluation under capital 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. What is the fundamental difference between hard and soft capital rationing?
2. If a firm applies one company-wide cost of capital, what issue arises when evaluating high-risk and low-risk projects?
3. True or false? Capital rationing always leads to optimal value creation for shareholders.
4. Briefly explain how a project-specific risk-adjusted discount rate might be determined in practice.

## **Introduction**

Efficient capital budgeting ensures that a firm's funds are allocated to projects delivering the highest possible value while considering risk. However, in reality, firms may face capital rationing, meaning they cannot fund all value-adding investments. In these cases, firms must prioritize which projects to undertake, often adjusting the required rate of return according to project risk. This article details how capital rationing can constrain investment selection and how risk-adjusted hurdle rates help ensure the correct evaluation of projects under uncertainty, including the influence of real options.

## TYPES OF CAPITAL RATIONING

Capital rationing restricts the amount available to invest in projects, either because of market limitations or management choices.

> **Key Term: capital rationing**
> The situation where a firm cannot fund all projects with positive net present value, requiring the selection of a subset based on ranking and available funds.
>
> **Key Term: hard capital rationing**
> A constraint on investment imposed externally, such as limits from capital markets or lending restrictions, making it impossible to raise sufficient capital.
>
> **Key Term: soft capital rationing**
> A self-imposed limitation set by management, often due to internal policy, risk concerns, or a desire to control growth, rather than absolute market constraints.

### Hard Capital Rationing

This occurs when a firm is unable to obtain sufficient external finance needed to fund all attractive projects, perhaps due to poor credit standing or adverse market conditions. In such cases, investment is strictly limited by available capital.

### Soft Capital Rationing

Here, management deliberately limits the annual investment budget, possibly to avoid excessive debt or to ensure manageable growth. It is possible for these policies to be relaxed if compelling opportunities arise.

## PROJECT SELECTION UNDER CAPITAL RATIONING

In perfect markets without rationing, all projects with positive net present value (NPV) would be accepted. With capital rationing, however, only those project combinations that maximize value within the funding limit should be chosen. This typically requires:

- Ranking projects by profitability index (PI) or benefit-cost ratio.
- Selecting projects in order of PI until available funds are exhausted.
- Recognizing that strict rationing may cause some value-adding projects to be rejected.

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

### **Worked Example 1.1**

A company has \$2 million to invest and faces three independent projects:

- Project A: NPV = \$240,000; Outlay = \$1,000,000
- Project B: NPV = \$180,000; Outlay = \$800,000
- Project C: NPV = \$60,000; Outlay = \$500,000

Which projects should be selected under hard capital rationing?

> **Answer:**
> Rank by profitability index:
>
> - A: $\text{PI} = 1.24$
> - B: $\text{PI} = 1.225$
> - C: $\text{PI} = 1.12$
>
> Invest in A and B: total outlay \$1.8 million (under \$2m), total NPV = \$420,000. Project C cannot be fully funded with remaining \$200,000.

## RISK-ADJUSTED HURDLE RATES

Not all projects carry the same risk as the firm’s existing assets. Using a single company-wide cost of capital can mislead decision makers, leading to underinvestment in low-risk projects and overinvestment in high-risk ones. Instead, each project should be discounted using a hurdle rate that reflects its own risk.

> **Key Term: risk-adjusted hurdle rate**
> The minimum required rate of return for a project, increased or decreased relative to the firm's standard cost of capital to reflect higher or lower risk.

### Estimating Project-Specific Hurdle Rates

A project-specific hurdle rate may be estimated by:

- Identifying comparable “pure play” firms and using their betas to adjust the project discount rate.
- Adding project-specific premiums to the firm’s base cost of capital for higher-risk projects or reducing it for safer projects.
- Considering qualitative factors, such as managerial judgement and scenario analysis, when precise quantitative measures are unavailable.

### **Worked Example 1.2**

A firm has a weighted average cost of capital (WACC) of 8%. A new software project is similar in risk to technology firms with an observed cost of capital of 11%. What hurdle rate should be applied?

> **Answer:**
> Use the “pure play” approach. Since the project's risk profile matches tech firms, apply a hurdle rate of 11% for discounting its expected cash flows.

### **Exam Warning**

> Using the firm's WACC for all projects ignores real differences in project risk. In the exam, always use risk-adjusted rates when project risk significantly diverges from the core business.

## THE ROLE OF REAL OPTIONS

Real options are embedded managerial choices—such as delaying, expanding, or abandoning a project—that can materially affect project value. These flexibilities may alter which projects are optimal under constrained capital and require consideration in hurdle rate setting and project assessment.

> **Key Term: real option**
> A right, but not an obligation, for managers to adjust or revise a capital project as new information becomes available.

### **Worked Example 1.3**

A firm can choose to expand a plant in year 2 if demand exceeds expectations. How does this real option affect the project's hurdle rate or capital rationing decision?

> **Answer:**
> The value of flexibility (the option to expand) raises the overall project value, which might justify a higher outlay or accepting the project with a lower NPV at the base case. If capital is tight, priority might be given to projects with valuable real options.

## EFFECTS AND LIMITATIONS OF CAPITAL RATIONING

- With capital rationing, the investment selection process deviates from the simple NPV rule, potentially sacrificing long-term value.
- Soft rationing may be relaxed for exceptionally attractive projects.
- Hard rationing may force otherwise profitable projects to be delayed or missed entirely.

### **Revision Tip**

> In real-world scenarios, always question whether capital constraints are genuine (hard) or set by policy (soft). This impacts both selection and negotiation in project evaluation.

## **Summary**

Capital rationing places practical limits on the investments a firm can make, requiring careful selection based on project profitability and risk. Applying risk-adjusted hurdle rates helps ensure that projects are evaluated on an appropriate, opportunity-cost basis—protecting against under- or over-investment. Incorporating real options can further refine project value, especially under funding constraints. Always distinguish between soft and hard capital rationing, and use risk-adjusted discount rates whenever possible.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Differentiate between hard and soft capital rationing and their effect on project selection
- Apply the profitability index to rank and choose projects under capital constraints
- Explain why risk-adjusted hurdle rates are used for projects of differing risk
- Outline methods for deriving project-specific hurdle rates, including use of “pure play” comparables
- Recognize the impact of real options on project valuation under capital rationing

## **Key Terms and Concepts**

- capital rationing
- hard capital rationing
- soft capital rationing
- profitability index (PI)
- risk-adjusted hurdle rate
- real option


Capital budgeting and real options - Capital rationing and risk-adjusted hurdle rates