Economic Analysis Methods
Key Takeaways
- Present Worth Analysis compares alternatives by converting all cash flows to present values — choose the highest PW.
- Annual Worth Analysis converts all cash flows to equivalent annual amounts — useful for comparing alternatives with different lifespans.
- Rate of Return (ROR) is the interest rate that makes the present worth of all cash flows equal to zero.
- Benefit-Cost Ratio (B/C) compares present worth of benefits to costs; B/C > 1 means economically justified.
- Break-even analysis finds the point where revenue equals costs (or two alternatives have equal cost).
- For mutually exclusive alternatives, use incremental analysis to evaluate whether the additional investment is justified.
Economic Analysis Methods
Present Worth (PW) Analysis
Convert ALL cash flows to their present value at a given interest rate (MARR — Minimum Attractive Rate of Return).
Decision Rule:
- Single project: Accept if PW ≥ 0
- Multiple alternatives: Choose the alternative with the highest PW
Important: When comparing alternatives with different lifespans, use the Least Common Multiple (LCM) of the lifespans or convert to Annual Worth instead.
Annual Worth (AW) Analysis
Convert all cash flows to an equivalent uniform annual series.
Advantages:
- Automatically handles different lifespans (no LCM needed)
- Easy to understand — "This project costs $X per year"
Decision Rule: Choose the alternative with the highest AW.
Rate of Return (ROR) Analysis
The ROR (also called Internal Rate of Return, IRR) is the interest rate i* that makes PW = 0:
Decision Rule:
- Accept if ROR ≥ MARR
- For mutually exclusive alternatives, use incremental ROR analysis
Incremental Analysis
When comparing two alternatives A and B (where B costs more):
- Calculate the incremental cash flows (B - A)
- Find the ROR of the increment
- If incremental ROR ≥ MARR, choose the more expensive alternative (B)
- Otherwise, choose the less expensive alternative (A)
Benefit-Cost (B/C) Analysis
Commonly used for public sector projects:
| B/C Value | Decision |
|---|---|
| B/C > 1 | Project is economically justified |
| B/C = 1 | Break-even point |
| B/C < 1 | Project is NOT economically justified |
Break-Even Analysis
Find the value of a variable (production quantity, usage hours, etc.) where two alternatives have equal cost, or where revenue equals cost.
Example: Machine A costs $10,000 and has variable costs of $5/unit. Machine B costs $20,000 with variable costs of $3/unit. Break-even quantity:
10,000 + 5Q = 20,000 + 3Q → 2Q = 10,000 → Q = 5,000 units
Below 5,000 units: choose Machine A. Above 5,000 units: choose Machine B.
Cost Terminology
| Term | Definition |
|---|---|
| Sunk Cost | Already spent; should NOT influence future decisions |
| Opportunity Cost | Value of the next best alternative forgone |
| Fixed Cost | Does not vary with production volume (rent, insurance) |
| Variable Cost | Varies with production volume (materials, labor) |
| Marginal Cost | Cost of producing one additional unit |
| Life-Cycle Cost | Total cost from acquisition through disposal |
Depreciation
Depreciation allocates the cost of an asset over its useful life for tax purposes.
Straight-Line Depreciation
MACRS (Modified Accelerated Cost Recovery System)
- The most common depreciation method for tax purposes in the U.S.
- Uses prescribed percentages for each year based on recovery period
- Does NOT use salvage value
- The FE Reference Handbook contains MACRS depreciation tables
Book Value
A project has an initial cost of $50,000 and annual benefits of $12,000 for 6 years. At MARR = 10%, the B/C ratio is approximately:
Sunk costs should be treated how in an engineering economic analysis?
An asset costs $40,000 and has a salvage value of $4,000 after a 6-year useful life. What is the annual straight-line depreciation?
When comparing two mutually exclusive alternatives with different service lives using Present Worth analysis, you should: