## **Learning Outcomes**

This article explains how capital budgeting analysis should be structured for CFA Level 2, focusing on the identification, modeling, and interpretation of project cash flows in realistic decision settings. It clarifies how to distinguish operating, investing, and financing cash flows that are relevant for capital budgeting from sunk costs and other non-incremental items, and how to quantify incremental cash flows at both the project and firm level. It discusses how to model project interactions, including combined benefits, cannibalization effects, mutually exclusive projects, and sequenced or staged investments, and how these interdependencies alter stand‑alone NPV calculations. It examines how to incorporate opportunity costs, externalities, and resource constraints into cash flow forecasts so that overall project value is measured correctly. It introduces the main categories of real options—abandonment, expansion, delay, and flexibility—and shows how option-like features change the risk profile and economic value of capital projects. It also highlights common exam traps in cash flow specification, emphasizing precise terminology, internally consistent assumptions, and disciplined exclusion of irrelevant cash flows.

## **CFA Level 2 Syllabus**

For the CFA Level 2 exam, you are expected to understand how capital budgeting incorporates realistic project cash flow modeling and the treatment of interdependent projects and real options, with a focus on the following syllabus points:

- Identifying and quantifying relevant cash flows for capital investment decisions
- Recognizing project interdependencies and modeling cash flow interactions
- Adjusting capital budgeting analysis for real options and optionality
- Assessing how abandonment, expansion, timing, and other real options affect project value
- Understanding incremental versus total cash flows
- Incorporating combined benefits, opportunity costs, and cannibalization into project appraisals

## **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 of the following is considered an incremental cash flow for capital budgeting analysis?
   a) Overhead costs already incurred
   b) Additional sales generated by the project
   c) Sunk costs from previous project evaluation
   d) Historic R&D expenditures

2. When a company launches a new product that reduces sales of its current offerings, the negative cash flow effect is best described as:
   a) Opportunity cost
   b) Combined benefit
   c) Cannibalization
   d) Shadow pricing

3. What is the primary impact on project NPV of including a real option to abandon the project if market conditions deteriorate?

4. Explain how project interdependencies can affect overall capital budgeting decisions.

## **Introduction**

Capital budgeting requires meticulous modeling of project cash flows to ensure investment decisions are based on realistic value estimates. Effective analysis separates incremental cash flows from irrelevant amounts and incorporates the complex effects of multiple, possibly interacting projects, as well as the value of managerial flexibility through real options. This article details the modeling of project cash flows, the impact of interactions and interdependencies, and the incorporation of real options into project assessment frameworks.

> **Key Term: incremental cash flow**
> The change in a firm's future cash flows directly attributable to a proposed project, reflecting only those cash flows that will occur if the project proceeds.
>
> **Key Term: real option**
> A right, but not an obligation, for managers to alter project decisions based on future circumstances, such as abandonment or expansion, which adds option value to traditional project NPV calculations.

## Fundamentals of Project Cash Flow Modeling

Capital budgeting decisions must distinguish between relevant and irrelevant cash flows.

- Only **incremental cash flows**—those arising solely as a result of undertaking the project—are included in the analysis.
- Sunk costs, which are already incurred and cannot be recovered, should be excluded.
- Opportunity costs (the value of foregone alternatives due to pursuing the project) must be reflected as incremental outflows.
- Externalities such as cannibalization (new project sales reducing existing sales) or positive combined benefits require cash flow adjustment.

> **Key Term: sunk cost**
> An expense already incurred and irrevocable, which must not be included as an incremental cost in project appraisal.
>
> **Key Term: opportunity cost**
> The value of the next best alternative that is sacrificed when a particular investment is chosen.
>
> **Key Term: combined benefit**
> The combined effect of projects creating incremental cash flow greater than the sum of individual project cash flows alone.
>
> **Key Term: cannibalization**
> The reduction in existing product cash flows due to the introduction of a new project, considered a negative incremental cash flow.

## Modeling Project Interactions and Interdependencies

Projects may not be independent; sometimes investment in one alters the expected cash flows or opportunity set of others:

- **Mutually reinforcing projects** produce greater value together (combined benefit).
- **Substitute or mutually exclusive projects** compete for limited resources or market opportunity—select the one providing the highest risk-adjusted NPV.
- **Sequenced or staged investments** involve optional follow-on or expansion projects, where current decisions enable or block future investments.

Capital budgeting models must adjust for shared overhead, resource constraints, or market effects, ensuring the combined cash flows correctly represent the firm's net incremental benefit.

### **Worked Example 1.1**

A company is considering developing two products, X and Y. If launched independently, X and Y produce NPVs of \$1 million and \$0.6 million. Launched together, cross-selling increases combined revenue, and joint investment reduces fixed costs, increasing joint NPV to \$2.1 million. What is the value of the combined benefit?

> **Answer:**  
> Combined benefit value = Joint NPV − (NPV of X + NPV of Y) = \$2.1 million − (\$1.0 million + \$0.6 million) = \$0.5 million.

## Real Options in Capital Budgeting

Traditional NPV computations assume project decisions are fixed ex ante. However, managers can respond to uncertainties and new information by exercising **real options**, which may include:

- **Abandonment**: Option to exit and recover value if the project underperforms
- **Expansion**: Option to increase investment if the project outperforms
- **Delay (Timing)**: Option to wait for more favorable market conditions before investing
- **Flexibility**: Option to change input mix, product, or operations in response to evolving environments

The presence of real options can increase the value of a project, making the adjusted NPV greater than if only passive cash flows are considered.

> **Key Term: abandonment option**
> A real option allowing the firm to cease a project early and recover residual value, thus capping downside risk.
>
> **Key Term: expansion option**
> A real option providing the right to increase investment in a project if outcomes are favorable, enabling upside potential capture.
>
> **Key Term: timing option**
> The firm's choice to wait and invest at a later date, leveraging improved information and reducing risk.

### **Worked Example 1.2**

A manufacturing project initially has an NPV of \$200,000. If there is an embedded abandonment option to recover \$300,000 (book value) if future market prices drop below a threshold in Year 2, the project’s risk-adjusted cash flows can improve. How does an abandonment option affect risk and NPV?

> **Answer:**  
> The abandonment option limits downside, reducing risk and increasing expected project value. NPV should be calculated as the base NPV plus the option value provided by early exit flexibility, yielding total value > \$200,000.

### **Exam Warning**

> Failing to adjust for project interdependencies, or wrongly including sunk costs, are common exam pitfalls. Always isolate only incremental effects and carefully model interactions, combined benefits, and option values.

## Application: Stepwise Project Cash Flow Analysis

An effective capital budgeting analysis includes these steps:

1. Identify all project-related revenues and costs, adjusting for cannibalization and opportunity costs.
2. Exclude all sunk costs.
3. Examine possible project interdependencies—adjust base cash flows for combined benefits and negative interactions.
4. Assess and value relevant real options (abandonment, expansion, delay), and add the option value to the passive project NPV.
5. Use scenario analysis to model variability and optimize decisions using the flexibility provided by options.

### **Worked Example 1.3**

Suppose Project A requires licensing an asset that could otherwise be leased to another firm for \$50,000 annually. What is the correct approach to incorporating this fact into Project A’s cash flow model?

> **Answer:**  
> The forgone lease income is an opportunity cost and should be treated as an incremental outflow, reducing Project A’s annual net cash inflows by \$50,000.

## **Summary**

Project cash flow modeling is a critical aspect of capital budgeting and must focus on incremental cash flows, proper adjustment for project interactions, and the incorporation of real options into project assessment frameworks. Flexibility to respond to market changes increases project value, and ignoring interdependencies or option value can lead to inaccurate assessments. For the CFA exam, emphasize clarity in identifying, modeling, and interpreting these effects.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Define and identify incremental cash flows for capital budgeting
- Exclude sunk costs and include opportunity costs in project cash flow analysis
- Adjust for cannibalization and project interdependencies, including combined benefits and mutual exclusivity
- Recognize and model the impact of real options on project value (abandonment, expansion, delay)
- Apply scenario analysis and stepwise evaluation for interacting or staged projects

## **Key Terms and Concepts**

- incremental cash flow
- real option
- sunk cost
- opportunity cost
- combined benefit
- cannibalization
- abandonment option
- expansion option
- timing option

Capital budgeting and real options - Project cash flow modeling and interactions