Engineering Economics: Time Value of Money

Core Concept

A dollar today is worth more than a dollar in the future because of earning potential. Engineering economics uses this principle to compare costs and benefits over time.

Key Formulas

Single Payment

Future Worth: F = P(1+i)ⁿ = P(F/P, i, n) Present Worth: P = F/(1+i)ⁿ = F(P/F, i, n)

• P = present value
• F = future value
• i = interest rate per period
• n = number of periods

Uniform Series (Annuity)

Future Worth: F = A[(1+i)ⁿ - 1]/i = A(F/A, i, n) Present Worth: P = A[(1+i)ⁿ - 1]/[i(1+i)ⁿ] = A(P/A, i, n) Capital Recovery: A = P × i(1+i)ⁿ/[(1+i)ⁿ-1] = P(A/P, i, n)

A = uniform end-of-period payment

Nominal vs. Effective Interest

Effective annual rate: i_eff = (1 + r/m)^m - 1

• r = nominal annual rate
• m = compounding periods per year

Example: 12% nominal, monthly compounding: i_eff = (1 + 0.12/12)^12 - 1 = 12.68%

Decision Methods

Net Present Value (NPV)

NPV = PW of benefits - PW of costs

• NPV > 0 → Economically viable

Benefit-Cost Ratio (BCR)

BCR = PW(Benefits) / PW(Costs)

• BCR > 1 → Accept project

Internal Rate of Return (IRR)

Interest rate at which NPV = 0

• Compare to MARR (Minimum Attractive Rate of Return)
• If IRR > MARR → Accept

Example

A pump costs $10,000, saves $2,500/year in operating costs, has a 10-year life, i = 8%.

P = $10,000
A = $2,500/year
n = 10 years
i = 8%

PW(savings) = 2500 × (P/A, 8%, 10) = 2500 × 6.710 = $16,775
NPW = 16,775 - 10,000 = $6,775 > 0 → ACCEPT

Summary

Always convert to a common point in time (present worth is most common). Use NPV for absolute decisions, BCR for comparing alternatives, IRR for rate-of-return analysis.