Engineering Economics
Engineering economics compares the costs and benefits of alternatives across time so that engineers can justify decisions on financial grounds. The organizing principle is the time value of money: a dollar today is worth more than a dollar later. The FE leans on a small set of interest factors and the discipline to move every cash flow to a common point in time.
Simple versus compound interest
Simple interest accrues only on the original principal: total owed = P·(1 + i·n). A $5,000 loan at 8% simple for 3 years owes 5,000·(1 + 0.08·3) = $6,200. Compound interest accrues on principal plus accumulated interest, which grows faster over time. Almost all engineering-economy problems assume compounding; simple interest appears mainly as a contrast. Reading the problem carefully to see which is specified prevents a systematic error.
Single-payment time value of money
The single-payment compound-amount factor moves a present sum forward: F = P·(1 + i)ⁿ. $1,000 for 5 years at 6% grows to 1,000·(1.06)⁵ ≈ $1,338. The inverse, the present-worth factor, discounts a future sum back: P = F/(1 + i)ⁿ. $5,000 received in 10 years at 8% is worth 5,000/(1.08)¹⁰ ≈ $2,316 today, and $10,000 in 5 years at 7% is worth 10,000/(1.07)⁵ ≈ $7,130. Every fair comparison requires cash flows be brought to the same instant first.
Uniform series (annuities)
A uniform series is an equal end-of-period payment A. Its future worth is F = A·[((1 + i)ⁿ − 1)/i], so $1,000 deposited annually for 5 years at (say) 6% accumulates the series total. Its present worth is P = A·[((1 + i)ⁿ − 1)/(i·(1 + i)ⁿ)]. The capital-recovery factor (A/P) converts a present amount into equal payments — the basis of loan and mortgage calculations — and the sinking-fund factor (A/F) finds the deposit needed to reach a future target. Identifying which factor a problem calls for is most of the work.
Nominal and effective interest rates
A nominal annual rate that compounds more than once a year has a higher effective annual rate: i_eff = (1 + r/m)^m − 1, where r is nominal and m the number of compounding periods. 12% nominal compounded monthly gives i_eff = (1 + 0.12/12)¹² − 1 ≈ 12.68%. More frequent compounding always raises the effective rate. Comparisons must be made on a consistent basis — either match the interest period to the payment period or convert to the effective rate first.
Comparing alternatives
Alternatives are ranked by present worth, equivalent uniform annual worth, rate of return, or benefit–cost ratio, each moving all cash flows to a common basis. Options with unequal service lives are compared over equal annual worth or a least-common-multiple study period so the comparison is fair. Break-even analysis finds the volume or time at which two options cost the same. A key principle: sunk costs — money already spent — are irrelevant to a current decision, because no choice now can recover them.
Depreciation and after-tax analysis
Depreciation spreads a capital asset's cost over its useful life for accounting and tax purposes. Straight-line depreciation is constant each year, D = (initial cost − salvage)/life. Accelerated methods such as declining balance and the tax-code MACRS take larger deductions early. Because depreciation is a non-cash expense that reduces taxable income, it shields cash flow, which after-tax economic analysis captures by adjusting for the tax rate. Salvage value and the timing of tax effects then feed into discounted-cash-flow comparisons of competing projects.
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