Engineering Economy Fundamentals and Cash-Flow Diagrams

Learning Objectives

  • Frame an engineering decision in terms of feasible alternatives, required service, and economic objective.
  • Draw cash-flow diagrams with time zero, period boundaries, signed inflows and outflows.
  • Represent end-of-period uniform series and uneven cash-flow streams without shifting their dates.
  • Distinguish sunk, opportunity, fixed, variable, and incremental costs.
  • Use MARR and a common study period, money basis, and focal date to compare alternatives.
  • Make a conditional recommendation and identify non-economic constraints and sensitivity checks.

Engineering Economy

Engineering economy is the systematic comparison of monetary consequences of technically feasible engineering alternatives over time. An economic result supports, but does not replace, compliance, safety, reliability, environmental, and service decisions.

Define the Decision Before the Formula

For each candidate option, state the engineering service to be delivered, the decision-maker viewpoint, the study period, the cash-flow estimates and dates, and the criterion for choosing. Mutually exclusive alternatives require a common service basis and a consistent economic horizon. Document different lifetimes, replacement assumptions, and residual values rather than comparing dissimilar services directly.

Cash Flow and Sign Convention

A cash flow CFtCF_t is a receipt or expenditure at a specified time tt. From the project-owner viewpoint used here, money received is positive (++, upward arrow) and money paid is negative (−-, downward arrow). A lender or seller may see opposite signs. The sign must be stated, not inferred from color.

Time Zero and Period Boundaries

Time 00 is the specified present/decision date. For annual end-of-period accounting, the interval from t=0t=0 to t=1t=1 is the first year, and a year-1 payment occurs at the end of that interval, not at t=0t=0. An amount on a tick belongs to that date. Cash-flow arrows show discrete amounts; they are not a continuous income curve.

Signed owner-view cash-flow timelineTime axis 0 through 3 years. Outflow minus 1000 thousand PHP at time zero, inflow plus 200 thousand at year one, outflow minus 100 thousand at year two, and inflow plus 250 thousand at year three. All values illustrative.time (years)0123-1,000+200-100+250Amounts in PHP 1,000; illustrative owner viewpoint

Read the Signed Timeline

Every arrow ends or starts at a specific tick. For this illustrative stream, CF0=−1,000,000CF_0=-1{,}000{,}000 PHP, CF1=+200,000CF_1=+200{,}000 PHP, CF2=−100,000CF_2=-100{,}000 PHP, and CF3=+250,000CF_3=+250{,}000 PHP. Its labels identify values; its arrow lengths are not a proportional monetary scale.

Interactive Cash-Flow Modeling

Use the timeline simulations to change purchase, maintenance, revenue, and salvage events. Compare the dates and signs of arrows rather than assuming every yearly payment begins at time zero.

Engineering Cost-Behavior Laboratory

Concept and model scope

Separate fixed and variable cost, then see how activity level changes total cost and the operating break-even threshold within the stated relevant range.

Activity quantity500 units
Contribution margin
₱1,300
Unit revenue or benefit minus unit variable cost.
Total cost at selected quantity
₱1,250,000
₱500,000 fixed + ₱750,000 variable.
Net operating result
₱150,000
Revenue/benefit equals or exceeds modeled operating cost at this quantity.
Break-even quantity
385 units
Linear-model threshold where total revenue equals total cost.
Cost composition at selected quantity
Fixed portionVariable portion

The linear break-even relation is valid only while fixed cost, unit variable cost, and unit revenue remain approximately constant over the relevant range.

Cash-Flow Timeline Laboratory

Concept and model scope

Edit cash-flow dates and signed amounts, then observe how the diagram and present worth respond at a stated MARR.

MARR per period10.00%
Cash flows

This teaching diagram limits the editable horizon to 50 periods so very large accidental inputs cannot create an unbounded SVG/tick workload.

Net present worth
₱185,605
Net PW is nonnegative at the selected MARR.
012345-₱1,000,000₱280,000₱280,000₱280,000₱280,000₱480,000

Positive arrows are inflows and negative arrows are outflows from the defined viewpoint. A zero cash flow is shown as a point on the axis, not as an arrow. If two entries share a period, the calculation combines them before discounting.

Uniform Versus Uneven Streams

A uniform series has equal amounts at equally spaced dates. The ordinary annual series AA here occurs at t=1,2,…,nt=1,2,\ldots,n (end-of-year), with no implied payment at t=0t=0. An uneven stream consists of distinct dated amounts, CFtCF_t, and is discounted one payment at a time. Do not use a uniform-series factor for an uneven stream unless it has first been correctly transformed.

Uniform and uneven annual outflow streamsTop panel: no payment at year zero and four minus 90 thousand PHP payments at the ends of years one through four. Bottom: uneven payments at years one through four of minus 40, minus 110, minus 60, and minus 130 thousand PHP.Uniform end-of-year seriesUneven dated stream0123401234-90-90-90-90-40-110-60-130Amounts in PHP 1,000; all payment dates are at year-end.

Sequence Interpretation

Both panels are illustrative cost outflows from the owner viewpoint. The top can be denoted by annual A=−90,000A=-90{,}000 PHP for n=4n=4. The lower panel requires four explicitly dated payments. Neither contains a payment at time zero.

Opportunity Cost

Opportunity cost is the value of the best feasible alternative forgone when a resource is used. An owned machine's current net realizable sale proceeds may represent an opportunity cost of retaining it. Use a defensible, study-specific estimate, not historical purchase price by default.

Sunk Cost

A sunk cost is a past expenditure that the present decision cannot change. It should not be charged again when comparing current alternatives, although its lessons and any remaining recoverable value may affect the choice.

Minimum Attractive Rate of Return (MARR)

MARR is the decision maker's required return or hurdle rate used in the study. It is a chosen analysis input, not a universal or Philippine statutory percentage. State its source, effective period, nominal/real basis, and whether cash flows are before or after tax; the selected study assumptions control the numerical illustration.

Cost Classification and Incremental Choice

Fixed cost is unchanged over the activity range under study; variable cost changes with output; incremental cost is the change in future cost between alternatives. For a challenger-minus-defender analysis, ΔCFt=CFt,challenger−CFt,defender\Delta CF_t=CF_{t,\mathrm{challenger}}-CF_{t,\mathrm{defender}}. A category may change with viewpoint and relevant range. Compare mutually exclusive alternatives using a common objective, common service, and compatible timing assumptions.

Economic Equivalence

Two monetary patterns are equivalent at a stated discount rate when converted to the same focal date, or to the same equivalent annual basis on the same time and money assumptions.

General Present-Worth Equivalence

Discount each signed net cash flow to the chosen time-zero date using effective periodic rate i.

PW=∑t=0nCFt(1+i)tPW=\sum_{t=0}^{n}\frac{CF_t}{(1+i)^t}

Variables

SymbolDescriptionUnit
PWPWSigned present worth at time zero, in PHP-
CFtCF_tSigned net cash flow dated at period t, in PHP-
iiEffective discount rate per cash-flow period; use i greater than minus one-
ttCash-flow date measured in matching periods-
nnStudy horizon in those periods-

Match Period, Currency Basis, and Assumptions

Annual amounts require an annual effective discount rate, while monthly amounts require a monthly effective rate. If a nominal annual quote has mm compounding periods, the corresponding periodic rate is the stated nominal rate divided by mm only under that compounding convention. Never combine constant-PHP (real) flows with a market/nominal rate, or nominal flows with a real rate, without an explicit conversion. Align tax, inflation, cash-flow inclusion, and comparison horizon across alternatives.

Illustrative Pumping-Equipment Choice

Suppose options A and B deliver identical service for three years with all costs paid at the end of the stated year, zero inflation/taxes for this classroom example, and an assumed owner-chosen MARR of 10% effective annually. Option A costs PHP 500,000 today, has PHP 40,000 annual running costs, and returns PHP 100,000 salvage at year 3. Option B costs PHP 350,000 today, has PHP 100,000 annual running costs, and returns PHP 50,000 salvage at year 3. These are synthetic exercise values, not procurement quotes or mandated rates.

Comparison of two equal-service pumping optionsThree-year illustrative common timeline. Option A pays 500 thousand PHP at year zero, pays 40 thousand in years one and two, and has a net year-three inflow of 60 thousand after subtracting running costs from salvage. Option B pays 350 thousand at zero and 100 thousand in years one and two, with a net year-three outflow of 50 thousand. Rate is ten percent effective annually.A: higher first cost, lower operationB: lower first cost, higher operation01230123-500-40-40+60 net-350-100-100-50 netPHP 1,000; year-end arrows; MARR = 10% effective per year

Calculate, Compare, and Qualify the Choice

Using a positive present cost convention (outflows as costs and salvage subtracted), and d=(1.10)−1+(1.10)−2+(1.10)−3≈2.486852d=(1.10)^{-1}+(1.10)^{-2}+(1.10)^{-3}\approx2.486852:

PCA=500,000+40,000d−100,000(1.10)3≈PHP 524,343,PCB=350,000+100,000d−50,000(1.10)3≈PHP 561,119.\begin{aligned} PC_A&=500{,}000+40{,}000d-\frac{100{,}000}{(1.10)^3}\approx\text{PHP }524{,}343,\\ PC_B&=350{,}000+100{,}000d-\frac{50{,}000}{(1.10)^3}\approx\text{PHP }561{,}119. \end{aligned}

On the stated assumptions A has the lower present cost by about PHP 36,777. A different MARR, useful life, service capacity, price forecast, or salvage estimate could change the recommendation; non-economic requirements still apply.

Avoid Hidden Comparison Errors

Never omit time zero, shift year-end payments earlier, mix rate and cash-flow periods, double-count sunk costs, compare different service outputs, or treat an assumed classroom MARR as an issued project/Philippine policy rate.

Engineering Economy Problem Setup

  1. Define feasible alternatives and the common required service.
  2. Fix the study period, viewpoint, dated cash flows, units, and money basis.
  3. Record the source and period of MARR/discount-rate assumptions.
  4. Draw signed cash-flow timelines with time zero and period boundaries.
  5. Convert every cash flow to the same focal date or comparable annual basis.
  6. Calculate with unrounded factors, then check signs, magnitudes, and incremental differences.
  7. Vary influential assumptions and report non-economic constraints alongside the conditional result.

Before Calculating

Key Takeaways
  • Cash-flow timing and sign are data, not decoration.
  • An ordinary uniform series begins at the end of the first period unless stated otherwise.
  • MARR is a documented study assumption and must match the dated cash-flow basis.
  • Compare feasible alternatives on the same service, period, price-level, and focal-date assumptions.
  • Opportunity and incremental costs can affect the decision; sunk past expenditures do not change future alternatives.
  • Present-cost comparisons are conditional on the assumptions and do not override safety or other requirements.

References