Capital Budgeting - Handbook

Type: BIP (Binary Integer Programming)

This handbook explains the Capital Budgeting sample problem in the LP Black Box platform.

This is a classic investment selection problem where you must choose which projects to fund.

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The Problem

Scenario

A company has $100 million to invest in 5 potential projects. Each project requires a certain investment and provides a certain return.

Project	Investment ($M)	Return ($M)	NPV Value ($M)
Project A	30	45	15
Project B	25	35	10
Project C	40	60	20
Project D	15	22	7
Project E	50	70	20

Budget: $100 million

Your Goal

Maximize total NPV (Net Present Value) while staying within budget.

The Key: Binary Variables

Each project is either:

• Funded (1) - invest in this project
• Not funded (0) - skip this project

This is why we use Binary variable type - you can only choose 0 or 1, not partial investments.

The Variables

Variable	Type	Meaning
projA	Binary (0 or 1)	Is Project A funded?
projB	Binary (0 or 1)	Is Project B funded?
projC	Binary (0 or 1)	Is Project C funded?
projD	Binary (0 or 1)	Is Project D funded?
projE	Binary (0 or 1)	Is Project E funded?

The Constraints

1. Budget: Total investment cannot exceed $100M

   Formula: 30×projA + 25×projB + 40×projC + 15×projD + 50×projE ≤ 100

2. Minimum Projects: Must fund at least 3 projects

   Formula: projA + projB + projC + projD + projE ≥ 3

3. Mutual Exclusion: Cannot fund both Project C and Project E together

   Formula: projC + projE ≤ 1

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How to Use

Step 1: Load the Sample

Select Capital Budgeting from the dropdown.

Step 2: Solve

The solver determines which projects to fund for maximum NPV within budget.

Step 3: Interpret Results

The solution will show:

• projA = 1 means Project A is funded
• projC = 0 means Project C is not funded

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Try It Yourself

• Change the budget to $80M
• Add a constraint that Project A and B must both be selected or both not selected
• Remove the mutual exclusion constraint

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Real-World Applications

• IT Project Selection: Choose which software projects to implement
• Real Estate Development: Select which properties to develop
• R&D Portfolio: Decide which research projects to fund
• Equipment Purchase: Choose which equipment to buy

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This demonstrates how Binary Integer Programming solves selection problems where you must choose discrete "yes/no" options.