Sources and References

Primary texts — Park, C. S. Contemporary Engineering Economics, 6th ed. Pearson, 2016. Newnan, D. G., Eschenbach, T. G., and Lavelle, J. P. Engineering Economic Analysis, 13th ed. Oxford University Press, 2017.

Supplementary texts — Blank, L. and Tarquin, A. Engineering Economy, 8th ed. McGraw-Hill, 2018. Fuller, S. K. and Petersen, S. R. Life-Cycle Costing Manual for the Federal Energy Management Program. NIST Handbook 135. National Institute of Standards and Technology, 1995.

Online resources — MIT OpenCourseWare 15.401 Finance Theory lecture notes; NIST Building Life-Cycle Cost (BLCC) software documentation; American Society of Civil Engineers Civil Engineering Economics open materials; Treasury Board of Canada cost-benefit analysis guide; OECD Environmental Project Appraisal handbooks.

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Chapter 1: Time Value of Money

1.1 The Fundamental Principle

A dollar today is not the same as a dollar next year. Three forces drive this: productive opportunity (the dollar could be invested), inflation (purchasing power erodes), and risk (a future dollar may not arrive). Engineering economics expresses all of these through an interest rate that translates cash flows across time.

1.2 Single Sum Formulas

With interest rate \(i\) per period and \(n\) periods:

\[ F = P(1+i)^n \qquad P = \frac{F}{(1+i)^n}. \]

The factor \((1+i)^n\) is denoted \((F/P, i, n)\); its reciprocal is \((P/F, i, n)\). Tabulated factors predate calculators and remain useful in practice for clarity.

1.3 Uniform Series

For a uniform end-of-period payment \(A\) over \(n\) periods at rate \(i\), the present worth is

\[ P = A\,\frac{(1+i)^n - 1}{i(1+i)^n} = A\,(P/A, i, n), \]

and the future worth is

\[ F = A\,\frac{(1+i)^n - 1}{i} = A\,(F/A, i, n). \]

These are the equations that underlie every mortgage, bond, and annuity.

1.4 Gradient Series

An arithmetic gradient \(G\) starting in period 2 has present worth

\[ P = G\left[\frac{(1+i)^n - 1}{i^2(1+i)^n} - \frac{n}{i(1+i)^n}\right], \]

and a geometric gradient with rate \(g\) per period has present worth

\[ P = \frac{A_1}{i - g}\left[1 - \left(\frac{1+g}{1+i}\right)^n\right]\quad (i \ne g). \]

These capture escalating operating costs and growing revenues typical of long-lived infrastructure.

Chapter 2: Evaluating Alternatives

2.1 Present Worth, Future Worth, Annual Worth

Three standard measures of worth rank mutually exclusive alternatives of equal service life. Present worth discounts all cash flows to time zero. Future worth compounds to the end of study. Annual worth converts to a uniform annual amount, useful when lives differ because lives cancel out in the reinvestment assumption. Decision rule: choose the alternative with the largest present worth (or largest annual worth, or smallest annual cost).

2.2 Internal Rate of Return

The internal rate of return (IRR) is the interest rate at which net present worth equals zero:

\[ \text{NPW}(i^*) = \sum_{t=0}^{n}\frac{A_t}{(1+i^*)^t} = 0. \]

Projects with IRR greater than the minimum attractive rate of return (MARR) are acceptable. Multiple sign changes in the cash flow may give multiple IRRs, requiring the modified IRR or direct present-worth comparison.

2.3 Benefit-Cost Ratio

Used in public project evaluation, the benefit-cost ratio is

\[ B/C = \frac{\text{PW of benefits}}{\text{PW of costs}}. \]

B/C greater than unity is acceptable; incremental B/C is used between alternatives. The treatment of disbenefits (as reduced benefits or added costs) affects the ratio but not the decision.

2.4 Payback Period

Simple payback is the time to recover the initial investment from net cash inflows ignoring time value. Discounted payback does not ignore it. Payback is intuitive and widely used but misses cash flows after the payback date; it should complement, not replace, present worth analysis.

Chapter 3: Depreciation, Taxes, and After-Tax Analysis

3.1 Depreciation Methods

Depreciation allocates the cost of a capital asset to the periods benefiting from its use. Straight-line gives constant annual charge \((B - S)/n\), where \(B\) is initial basis, \(S\) is salvage, and \(n\) is service life. Declining balance at rate \(d\) applies \(d\) to the book value each year. MACRS (US) and capital cost allowance (Canada) use prescribed class rates.

The half-year convention in Canada’s CCA assumes acquisition mid-year; in the first year only half the rate applies. For a class with CCA rate \(d\), the undepreciated capital cost at the end of year \(n\) with no additions or dispositions is

\[ \text{UCC}_n = B(1 - d/2)(1-d)^{n-1}. \]

3.2 Income Tax

Corporate income tax rate \(t\) is applied to taxable income = revenues − expenses − depreciation. Operating expenses and depreciation are deductible; capital expenditures are not. After-tax cash flow is

\[ \text{ATCF} = \text{Revenue} - \text{Expenses} - \text{Tax} \pm \text{Capital flows}. \]

The after-tax MARR is the hurdle rate applied to ATCF. If pre-tax MARR is \(i_p\), after-tax MARR is approximately \(i_a = i_p(1 - t)\).

3.3 Depreciation Tax Shield

Depreciation reduces taxable income and therefore reduces tax by \(t \times D\), where \(D\) is the depreciation. The present worth of this tax shield is a positive contribution to project value. For a straight-line asset of basis \(B\) over \(n\) years with tax rate \(t\) at after-tax rate \(i_a\),

\[ \text{PW(shield)} = \frac{tB}{n}(P/A, i_a, n). \]

Chapter 4: Inflation and Real versus Nominal Analysis

4.1 Definitions

Nominal (actual) dollars reflect the purchasing power at the time of the cash flow. Real (constant) dollars restate all cash flows to a single reference year’s purchasing power. The relationship involves the inflation rate \(f\):

\[ A_{real} = \frac{A_{nominal}}{(1+f)^n}. \]

Nominal MARR \(i\) and real MARR \(i_r\) are related by

\[ (1 + i) = (1 + i_r)(1 + f). \]

4.2 Consistent Analysis

The discipline is consistency: discount nominal cash flows at the nominal rate, real cash flows at the real rate. Mixing produces nonsense. Tax payments are typically nominal (computed on nominal income), so after-tax analysis often uses nominal dollars throughout.

Chapter 5: Life-Cycle Cost Analysis

5.1 Scope

Life-cycle cost (LCC) analysis captures all costs associated with an asset from acquisition to disposal: initial construction, financing, operations (energy, water, occupant productivity), maintenance, repair, replacement, deconstruction, and residual value. In infrastructure, life cycles of 30, 50, or 100 years are common.

5.2 Components

Typical LCC components for a commercial building are:

Component	Typical share of LCC
Initial design and construction	15–25%
Operations (energy, water)	35–50%
Maintenance and repair	15–25%
Replacement of systems	10–20%
End-of-life	1–5%

These shares demonstrate why the lowest-first-cost design is rarely the lowest life-cycle cost. Envelope investments that cost 5% more at construction can return 30% savings in operational energy.

5.3 Discount Rate Selection

LCC is highly sensitive to the discount rate. A 50-year future cost of $1M at 3% real rate has present worth $228,000; at 7% real rate, $34,000. Public-sector analyses typically use real discount rates of 3 to 5%. Private-sector analyses use the firm’s weighted average cost of capital, often 6 to 10% real. Lower rates weight future operational costs more heavily, favouring durable, energy-efficient designs.

5.4 Incremental Analysis

When choosing between alternatives, analyze the difference: incremental cost versus incremental benefit. If alternative B costs $100,000 more than A and saves $12,000 per year for 20 years at 5% real, incremental PW = \(-100{,}000 + 12{,}000\times(P/A,5\%,20) = -100{,}000 + 12{,}000 \times 12.462 = 49{,}540\). B is preferred.

Chapter 6: Sensitivity, Scenario, and Risk Analysis

6.1 Sensitivity Analysis

Vary one input at a time around its base value and observe the effect on NPW or IRR. Tornado diagrams rank inputs by their influence. Typical sensitivities for a building project: discount rate, energy price, construction cost, service life, and occupancy rate. Inputs whose variation swings NPW most deserve the most effort to estimate accurately.

6.2 Scenario Analysis

Varying inputs together (best case, worst case, most likely) captures correlated uncertainty. Three scenarios are simple enough for executive presentation but miss the probability distribution of outcomes.

6.3 Monte Carlo Simulation

Assigning probability distributions to uncertain inputs and sampling thousands of times yields the full distribution of NPW. Percentiles (P10, P50, P90) communicate risk clearly. Correlations between inputs (energy prices and construction costs both rise with commodity inflation) must be modelled explicitly; assuming independence understates tail risk.

6.4 Expected Value and Decision Trees

For discrete scenarios with estimated probabilities \(p_k\) and outcomes \(V_k\), expected value is

\[ E[V] = \sum_k p_k V_k. \]

Decision trees extend this to sequential decisions. Real-options analysis values the flexibility to delay, abandon, or expand, often omitted by traditional DCF.

Chapter 7: Financing Infrastructure

7.1 Capital Sources

Public infrastructure is financed by government appropriation, general obligation bonds, revenue bonds, and increasingly by public-private partnerships. Private infrastructure uses equity, corporate bonds, and bank debt. The weighted average cost of capital (WACC) is

\[ \text{WACC} = \frac{E}{E+D}k_e + \frac{D}{E+D}k_d(1-t), \]

where \(E\) is market value of equity, \(D\) of debt, \(k_e\) is cost of equity, \(k_d\) is cost of debt, and \(t\) is tax rate.

7.2 Public-Private Partnerships

PPPs (P3s) transfer design, build, finance, operate, and maintain responsibilities to a private consortium over a long concession. Payments are performance-based (availability payments) or user-fee-based (tolls). Advocates cite risk transfer and life-cycle optimization; critics cite high private-sector capital cost and complex contracts. Whether a PPP outperforms conventional procurement depends on the balance between efficiency gains and financing-cost penalties.

7.3 Loan Amortization

A loan of principal \(P\) at interest rate \(i\) per period repaid by \(n\) equal payments has payment

\[ A = P\,\frac{i(1+i)^n}{(1+i)^n - 1}. \]

Each payment contains interest on the remaining balance plus principal repayment; early payments are mostly interest, later payments mostly principal. Amortization schedules are standard in construction loan administration.

Chapter 8: Business Plans for Engineering Projects

8.1 Contents

A business plan for an engineering project typically contains an executive summary, project description, market analysis, technical plan, management plan, financial projections (three to five years of income statement, balance sheet, cash flow statement), risk assessment, and funding request. The financial projections are the quantitative core; the narrative sections justify the assumptions behind them.

8.2 Break-Even Analysis

Break-even occurs when total revenue equals total cost. For a product with fixed cost \(F\), variable cost \(v\) per unit, and price \(p\) per unit,

\[ n^* = \frac{F}{p - v}. \]

The contribution margin \(p - v\) is the per-unit contribution to covering fixed cost. In infrastructure, break-even analysis applies to toll roads, parking facilities, and other facilities with high fixed cost and per-use revenue.

8.3 Quantitative Decision Making

Engineering economic analysis is a tool of decision making, not a guarantee of correctness. Good practice requires explicit assumptions, documented data sources, sensitivity analysis, and presentation of uncertainty to decision makers. The engineer who hides uncertainty behind a single-number NPW abdicates professional responsibility; the engineer who surfaces it earns the trust that leads to better decisions.