Engineering Economy and Cost Analysis
Engineering economy compares alternatives on a time-value-of-money basis. Candidates must know the factor notation and formulas: single-payment (F/P, P/F), uniform series (F/A, A/F, P/A, A/P), and gradient factors. Core relations: F = P(1+i)ⁿ; P = F(1+i)⁻ⁿ; the uniform series present worth P = A[(1+i)ⁿ − 1]/[i(1+i)ⁿ]; and A = P[i(1+i)ⁿ]/[(1+i)ⁿ − 1].
Decision methods include present worth (PW), annual worth (AW), future worth (FW), rate of return (ROR), payback, and benefit-cost. Use PW for equal lives; for unequal lives, use AW or a common study period. Incremental analysis is required for ROR comparisons among mutually exclusive alternatives-compare in order of increasing cost and accept an increment only if its incremental ROR exceeds the MARR. Traps: comparing alternatives with unequal lives by PW without adjustment; using average ROR instead of incremental; and forgetting salvage value (a receipt) or that depreciation is not a cash flow but affects taxes.
Depreciation: straight-line D = (B − S)/n; MACRS uses declining-balance with the half-year convention and ignores salvage. Taxes use taxable income = revenue − expenses − depreciation; after-tax cash flow = net income + depreciation. Inflation: real versus nominal rates via (1 + i_nominal) = (1 + i_real)(1 + f). Break-even: Q = FC/(price − variable cost).
Worked example
A machine costs $50,000, saves $18,000/yr for 4 years, MARR = 10%. P/A factor for 10%, 4 yr = 3.170. PW of savings = 18,000 × 3.170 = $57,060. PW net = 57,060 − 50,000 = +$7,060 → acceptable.