Cheatsheet: Cost-benefit Analysis

1. Cost-Benefit Analysis Fundamentals

1.1 Core Definitions

1.2 Key Components

• Direct Costs: Explicit monetary expenditures (materials, labor, equipment)
• Indirect Costs: Overhead, administrative expenses, maintenance
• Tangible Benefits: Quantifiable monetary gains (revenue, cost savings)
• Intangible Benefits: Non-monetary advantages (reputation, employee morale, safety)
• External Costs/Benefits: Impacts on third parties not directly involved in the transaction

2. Time Value of Money

2.1 Present Value and Future Value

2.2 Annuity Formulas

2.3 Gradient Formulas

3. Economic Decision Criteria

3.1 Net Present Value (NPV)

3.2 Internal Rate of Return (IRR)

3.3 Benefit-Cost Ratio (BCR)

3.4 Payback Period

3.5 Annual Equivalent Worth (AEW)

4. Comparing Alternatives

4.1 Mutually Exclusive Alternatives

4.2 Unequal Service Lives

4.3 Incremental Analysis Decision Rule

• Order alternatives by increasing initial cost
• Start with lowest cost alternative as defender
• Compare defender to next higher cost challenger using incremental cash flows
• If ΔIRR > MARR (or ΔNPV > 0), challenger becomes new defender
• If ΔIRR < marr="" (or="" δnpv="">< 0),="" retain="">
• Continue until all alternatives evaluated

5. Depreciation and Taxes

5.1 Depreciation Methods

5.2 MACRS Depreciation

• 3-year property: Special tools, tractor units
• 5-year property: Automobiles, computers, office equipment
• 7-year property: Office furniture, most machinery and equipment
• Half-year convention: Asset placed in service at midpoint of first year
• No salvage value: MACRS depreciates to zero book value

5.3 After-Tax Cash Flow Analysis

5.4 Capital Gains and Losses

6. Inflation and Cost Estimation

6.1 Inflation Concepts

6.2 Inflation Formulas

6.3 Cost Estimation Methods

6.4 Common Cost Indexes

• Consumer Price Index (CPI): Measures changes in price level of consumer goods and services
• Producer Price Index (PPI): Measures changes in selling prices received by domestic producers
• Chemical Engineering Plant Cost Index (CEPCI): Tracks capital cost trends in chemical industry
• Marshall & Swift Equipment Cost Index: Process industry equipment costs

7. Risk and Uncertainty Analysis

7.1 Decision Analysis Under Uncertainty

7.2 Risk Measures

7.3 Sensitivity Analysis

• Purpose: Determine how changes in input variables affect output measure (NPV, IRR)
• One-at-a-time: Vary one parameter while holding others constant
• Breakeven Analysis: Find value where NPV = 0 or two alternatives are equivalent
• Spider Diagram: Plot multiple variables' effects on single output
• Tornado Diagram: Rank variables by impact magnitude

7.4 Decision Trees

• Decision nodes (squares): Points where decision maker chooses between alternatives
• Chance nodes (circles): Points where probabilistic outcomes occur
• Calculate expected values by working backward from terminal nodes
• Select path with highest expected monetary value at each decision node
• Expected Value of Perfect Information (EVPI) = EV with perfect info - EV without perfect info

7.5 Scenario Analysis

8. Replacement Analysis

8.1 Replacement Terminology

8.2 Replacement Analysis Procedure

• Sunk costs are irrelevant; use current market value as defender's initial cost
• Calculate economic life and minimum EAC for both defender and challenger
• Compare defender's marginal cost for next year with challenger's minimum EAC
• Replace when defender's marginal cost exceeds challenger's minimum EAC
• If asset serves different periods, use annual worth method

8.3 Economic Life Calculation

8.4 Replacement Decision Rules

9. Public Sector and Social Projects

9.1 Public vs. Private Projects

9.2 Social Discount Rate

• Social Rate of Time Preference: Rate at which society values present vs. future consumption
• Social Opportunity Cost: Return on displaced private investment
• Federal OMB guidance: 7% real discount rate for cost-benefit analyses
• Intergenerational Projects: Lower rates (2-3%) for long-term environmental projects

9.3 Benefit Classification

9.4 Cost Allocation

• Separable Costs: Costs attributable to single purpose in multi-purpose project
• Joint Costs: Costs common to multiple purposes; require allocation
• Proportional Use: Allocate based on relative usage or capacity
• Benefit-Based: Allocate in proportion to benefits received
• Incremental Cost Method: Allocate based on cost increases from adding each purpose

9.5 Public Project Evaluation

10. Break-Even and Make-or-Buy Analysis

10.1 Break-Even Analysis Fundamentals

10.2 Break-Even Between Alternatives

• Set total cost equations equal: TC1 = TC2
• Solve for the activity level (units, hours, volume) where costs are equal
• Select alternative with lower cost beyond break-even point
• Multiple alternatives: compare pairwise to identify relevant ranges

10.3 Make-or-Buy Decisions

10.4 Lease-or-Buy Analysis

11. Key Decision-Making Principles

11.1 Core Principles

• Only differences matter: Ignore costs and benefits common to all alternatives
• Ignore sunk costs: Past expenditures that cannot be recovered are irrelevant
• Include opportunity costs: Value of foregone alternatives must be considered
• Consider time value of money: Cash flows at different times are not directly comparable
• Use marginal analysis: Compare incremental benefits with incremental costs
• Separate financing from investment: Evaluate project viability independent of financing method

11.2 Common Pitfalls

11.3 Consistency Requirements