Engineering Economics for the FE Exam
Engineering economics appears on every FE exam discipline and typically accounts for 5 to 10 percent of the exam. The good news is that economics problems follow predictable patterns and can be solved systematically using formulas and tables from the reference handbook. With focused study, this section can become one of your strongest areas.
Core Concept: Time Value of Money
The foundation of engineering economics is the time value of money: a dollar today is worth more than a dollar in the future because today's dollar can be invested and earn interest. All economic analysis formulas are built on this concept.
The Six Basic Factors
Engineering economics uses six fundamental factors to convert between present, future, and annual values:
- P/F (Present Worth Factor): Converts a single future amount to its present value. Use when you know a future cost or revenue and need its present equivalent.
- F/P (Future Worth Factor): Converts a single present amount to its future value. Use when you need to find what a current investment will be worth later.
- P/A (Present Worth of Annuity): Converts a series of equal annual payments to a single present value. Use for comparing recurring costs or revenues.
- A/P (Capital Recovery Factor): Converts a present amount to equivalent annual payments. Use for loan payments and equipment cost recovery.
- F/A (Future Worth of Annuity): Converts a series of equal annual payments to a single future value. Use for savings account and sinking fund calculations.
- A/F (Sinking Fund Factor): Determines the annual payment needed to accumulate a target future amount. Use when planning for future expenses.
Using the Interest Tables
The NCEES Reference Handbook contains compound interest tables for various interest rates. Each table lists the six factors for different numbers of periods. To use the tables:
- Identify the interest rate per period
- Identify the number of periods
- Look up the appropriate factor
- Multiply the factor by the dollar amount
Practice using these tables during your study sessions so you can locate the right table and factor quickly during the exam.
Present Worth Analysis
Present worth analysis converts all cash flows (costs and revenues) to their equivalent present values at a given interest rate. The alternative with the highest present worth (for revenue projects) or lowest present worth of costs (for cost projects) is the preferred choice.
Steps for present worth analysis:
- Draw a cash flow diagram showing all costs and revenues at their respective time periods
- Convert all cash flows to present values using the appropriate factors
- Sum all present values (revenues are positive, costs are negative)
- Compare alternatives and choose the one with the best present worth
Annual Worth Analysis
Annual worth analysis converts all cash flows to equivalent annual amounts. This is particularly useful when comparing alternatives with different useful lives, because annualized costs automatically account for different time horizons.
Rate of Return Analysis
The rate of return (ROR) is the interest rate that makes the present worth of all cash flows equal to zero. An investment is acceptable if its ROR exceeds the minimum attractive rate of return (MARR). On the FE exam, you may need to find the ROR by interpolation between interest rates in the tables.
Benefit-Cost Analysis
Benefit-cost ratio (B/C) analysis is used primarily for public projects. The B/C ratio equals the present worth of benefits divided by the present worth of costs. A project is acceptable if B/C is greater than or equal to 1.0.
Depreciation Methods
The FE exam tests several depreciation methods:
- Straight-line depreciation: Equal depreciation each year. Annual depreciation = (Initial cost minus salvage value) divided by useful life.
- Declining balance (DB): Depreciation is a fixed percentage of the book value each year. Higher depreciation in early years.
- Modified Accelerated Cost Recovery System (MACRS): The depreciation method used for tax purposes in the U.S. Uses predetermined recovery periods and rates.
Common Economics Problem Types on the FE Exam
- Comparing two or more investment alternatives using present worth or annual worth
- Finding the breakeven point between two options
- Calculating loan payments or lease costs
- Computing depreciation and book value at a given year
- Determining whether a project meets the MARR
Tips for Economics Problems
- Always draw a cash flow diagram. This visual representation prevents errors in identifying when cash flows occur.
- Watch the timing. Are payments at the beginning or end of each period? The standard formulas assume end-of-period payments.
- Match your interest rate to your period. If payments are monthly, use a monthly interest rate, not an annual one.
- Check your answer's reasonableness. If a present worth calculation gives a result larger than the sum of all future cash flows, something is wrong.
Engineering economics is one of the most formulaic sections of the FE exam. Once you learn the patterns and practice with the reference handbook tables, these problems become routine and reliable points.