Engineering Economics on the FE Exam
Engineering economics appears on every FE exam discipline, typically accounting for 3 to 11% of the questions depending on your discipline. While the weight may seem small, these questions are often among the most straightforward on the exam if you know the formulas and methods. This makes engineering economics a high-value study area where preparation directly translates to correct answers.
Time Value of Money
The foundational concept in engineering economics is the time value of money: a dollar today is worth more than a dollar in the future because it can be invested to earn interest. This principle drives all economic analysis methods.
You need to master six time value of money factors:
- Single Payment Compound Amount (F/P): Given present value, find future value
- Single Payment Present Worth (P/F): Given future value, find present value
- Uniform Series Compound Amount (F/A): Given annuity, find future value
- Uniform Series Sinking Fund (A/F): Given future value, find required annuity
- Uniform Series Present Worth (P/A): Given annuity, find present value
- Uniform Series Capital Recovery (A/P): Given present value, find annuity
These factors are tabulated in the FE Reference Handbook for various interest rates. Practice reading and applying these tables quickly.
Present Worth Analysis
Present worth (PW) analysis converts all cash flows to their equivalent value at time zero using a given interest rate. To compare alternatives with equal lives, calculate the present worth of each alternative and select the one with the highest PW (for revenue alternatives) or least negative PW (for cost alternatives).
For alternatives with unequal lives, use the least common multiple of service lives approach, or convert to annual worth for comparison.
Annual Worth Analysis
Annual worth (AW) analysis converts all cash flows to an equivalent uniform annual amount. This method is especially convenient when comparing alternatives with different service lives, since the annual worth calculated over one life cycle is the same as the annual worth over any number of life cycles at the same interest rate.
Rate of Return Analysis
The rate of return (ROR) is the interest rate at which the present worth of all cash flows equals zero. To find the ROR, set up the present worth equation, set it equal to zero, and solve for the interest rate. This often requires trial and error or interpolation between tabulated values.
When comparing mutually exclusive alternatives by ROR, you must perform an incremental analysis: calculate the ROR on the incremental investment between alternatives and compare it to the minimum attractive rate of return (MARR).
Benefit-Cost Analysis
Benefit-cost (B/C) ratio analysis is used primarily for public sector projects. The B/C ratio equals the present worth of benefits divided by the present worth of costs. A project is acceptable if the B/C ratio is greater than or equal to 1.0. When comparing alternatives, use incremental B/C analysis similar to incremental ROR analysis.
Depreciation
Depreciation represents the loss in value of an asset over time. The FE exam tests several depreciation methods:
- Straight-Line: Equal depreciation each year. Annual depreciation equals (initial cost minus salvage value) divided by useful life.
- Declining Balance: A fixed percentage of the book value is depreciated each year. Double declining balance (DDB) uses a rate of 2 divided by the useful life.
- MACRS: Modified Accelerated Cost Recovery System, used for tax purposes. MACRS percentages are provided in the FE Reference Handbook.
Inflation and Taxes
Know the difference between actual (inflated) dollars and constant (real) dollars. The real interest rate adjusts the market interest rate for inflation. For after-tax analysis, taxable income equals revenue minus expenses minus depreciation, and income tax equals the tax rate times taxable income.
Study Strategy
Engineering economics problems are formulaic and predictable. Once you know which formula to apply, the calculation is usually straightforward. Spend your study time practicing problem identification: given a word problem, can you quickly determine which economic analysis method and which time value of money factors to use? Master this skill and engineering economics becomes one of the easiest sections on the exam.