FE Exam: Engineering Economics

Engineering economics on the FE exam is about one thing: making defensible decisions with money over time. You are not expected to be a finance professional, but you are expected to compare alternatives, handle cash flows correctly, and choose the method that fits the question. The core tools revolve around the time value of money, depreciation, project evaluation metrics, and benefit-cost analysis.

What “engineering economics” means on the FE

Engineers routinely choose between options that differ in cost, timing, and performance: buy vs. lease equipment, replace an asset now or later, select between two processes with different operating costs, or justify a capital project. Engineering economics provides standardized methods to compare those alternatives on a consistent basis.

On the FE exam, questions usually present:

• A set of cash flows (costs, revenues, savings) over time
• An interest rate (sometimes called MARR, i, or discount rate)
• A decision rule (pick the better alternative, compute a value, or determine break-even)

The challenge is less about advanced math and more about setting up the timeline correctly and applying the right factor or formula.

Time value of money (TVM): the foundation

The time value of money says a dollar today is worth more than a dollar tomorrow because today’s dollar can earn interest. Most FE economics problems reduce to converting cash flows between:

• Present value (P)
• Future value (F)
• Uniform annual series (A)
• Sometimes a gradient series (increasing or decreasing by a constant amount each year)

Compounding and discounting

If you invest a present amount $P$ at interest rate $i$ for $n$ periods, the future value is:

$$F=P(1+i{)}^n$$

Discounting reverses the process:

$$P=\frac{F}{(1+i{)}^n}$$

Common FE pitfalls include mixing nominal and effective rates (if compounding frequency is given) and putting cash flows at the wrong time. Unless stated otherwise, cash flows typically occur at the end of each period.

Annuities and uniform series

A uniform annual series is a constant payment each year (or each period). Converting between $P$ and $A$ is central:

$$P=A\left(\frac{1-(1+i{)}^{-n}}{i}\right)$$

and

$$A=P\left(\frac{i(1+i{)}^n}{(1+i{)}^n-1}\right)$$

On the FE, this shows up in loan payments, equivalent annual cost comparisons, and annualized savings.

Practical timeline discipline

Before touching a calculator, sketch a quick timeline:

• Mark year 0 as “today” (present)
• Place each cash flow at the correct year
• Identify whether values are costs (negative) or benefits (positive)
• Decide what you are solving for: present worth, annual worth, future worth, or a rate

A clean timeline prevents sign mistakes, which are among the most common reasons candidates miss otherwise straightforward problems.

Depreciation: understanding cost recovery and book value

Depreciation in engineering economics is an accounting method for allocating an asset’s cost over its useful life. On the FE, depreciation is often tied to:

• Book value after a certain number of years
• Depreciation expense in a given year
• Comparing replacement options where salvage value matters

Two concepts are essential:

• First cost: purchase and installation cost (capitalized cost)
• Salvage value: expected resale value at the end of life (or at the time of disposal)

Book value is generally:

$$\text{Book Value}=\text{First Cost}-\text{Accumulated Depreciation}$$

Common depreciation methods

You may see straight-line depreciation because it is simple and commonly tested:

• Depreciable base = First cost − Salvage value
• Annual depreciation (straight-line) = Depreciable base / useful life

Declining balance methods (like double-declining) may appear in some curricula, but FE questions typically focus on applying the given method correctly rather than choosing a method. If the problem statement provides the depreciation approach, follow it exactly and track the book value year by year.

Why depreciation matters in project decisions

Even when taxes are not explicitly tested in depth, depreciation affects accounting cost and can influence decisions when book value and salvage value are involved. For example, if an asset is sold, comparing sale price to book value can matter in after-tax analyses (if those are included). If taxes are not mentioned, keep the analysis to the cash flows provided: purchase, operating costs, maintenance, and salvage.

Project evaluation methods: choosing between alternatives

Project evaluation is the heart of engineering economics. The FE exam uses several standard metrics. The correct metric depends on what the question asks and the cash-flow pattern.

Present worth (PW) and future worth (FW)

Present worth compares alternatives by converting all cash flows to an equivalent value at time 0 using the discount rate $i$. The option with the higher present worth is better if values are net benefits; if you are comparing costs only, the lower present cost is better.

Future worth does the same but accumulates everything to a future time $n$. PW and FW rankings are consistent when using the same rate and time horizon, so the exam may use either.

Annual worth (AW) and equivalent annual cost (EAC)

Annual worth converts all cash flows into an equivalent uniform annual amount over the analysis period. This is especially useful when:

• Alternatives have different lifespans
• You want a “per year” comparison
• You are comparing machines with different purchase costs and operating costs

For cost-only problems, the equivalent annual cost (a form of AW) is common. The decision rule is to choose the alternative with the lower annual cost.

Rate of return (IRR) and MARR

The internal rate of return (IRR) is the interest rate that makes the present worth equal to zero, meaning it satisfies:

$$0=\sum _{t=0}^n\frac{C{F}_t}{(1+\text{IRR}{)}^t}$$

On the FE, IRR questions usually involve selecting whether the IRR meets a minimum attractive rate of return (MARR). If IRR ≥ MARR for an investment (benefits exceed costs over time), it is acceptable under that criterion.

Be cautious with sign changes in cash flows, which can lead to multiple IRRs in advanced cases. The FE generally keeps IRR setups straightforward: an initial cost followed by positive net benefits.

Payback period (simple vs. discounted)

Payback period asks how long it takes for cumulative benefits to recover the initial investment.

• Simple payback ignores the time value of money.
• Discounted payback accounts for discounting.

Because the FE emphasizes time value of money, if the problem provides a discount rate and asks for payback “considering interest,” discounted payback is implied. Otherwise, simple payback may be used. The method is procedural: add cash flows (discounted if required) until the cumulative total becomes zero or positive.

Benefit-cost analysis: common in public and infrastructure projects

Benefit-cost (B/C) analysis is often used for public-sector projects where benefits are not purely revenue but societal value (reduced travel time, fewer accidents, improved reliability). On the FE, the setup is typically simplified: you are given monetized benefits and costs and asked for a ratio or a decision.

A standard form is:

$$\text{B/C}=\frac{\text{Present Worth of Benefits}}{\text{Present Worth of Costs}}$$

Decision rule:

• If B/C > 1, benefits exceed costs (economically justified)
• If B/C < 1, not justified
• If B/C = 1, break-even

Be consistent about what counts as a cost. Initial construction, operations, and maintenance typically go in the denominator. Salvage value may be treated as a benefit (reducing net cost) depending on the convention used in the problem statement. The FE often signals the intended approach through wording like “include salvage value as a benefit” or by listing it under benefits.

Exam-focused habits that improve accuracy

Always identify the interest rate and the analysis period

Many errors come from using the wrong $n$ or discount rate. If the problem says “8% per year compounded annually,” then $i=0.08$ per year. If compounding is monthly, convert carefully or use an effective annual rate if the problem is annualized.

Separate cash flow categories

A reliable approach is to group:

• Initial cost at time 0
• Annual operating and maintenance costs (uniform series)
• Periodic costs (e.g., major overhaul every 5 years)
• Salvage value at the end of the period

Then convert each category to the requested basis (P, A, or F) and combine with the correct signs.

Choose the method that matches the question

If the prompt says “equivalent annual cost,” do AW/EAC. If it says “present worth,” do PW. If it says “is the project acceptable at MARR,” PW at MARR or IRR relative to MARR are likely.

Bringing it together: what you’re really being tested on

FE engineering economics is less about memorizing every factor and more about disciplined setup:

• Respect the time value of money
• Convert cash flows to a common basis
• Apply depreciation only as specified
• Use project evaluation and benefit-cost criteria consistently

When you treat each problem as a structured comparison rather than a math puzzle,