Engineering Economy Fundamentals and Cash-Flow Diagrams

Engineering Economy Fundamentals and Cash-Flow Diagrams

$Learning Objectives$

Frame engineering decisions using alternatives, consequences, and a stated economic objective.
Draw and interpret cash-flow diagrams using a consistent sign and timing convention.
Distinguish opportunity cost, sunk cost, fixed cost, variable cost, and incremental cost.
Explain economic equivalence and the role of the Minimum Attractive Rate of Return (MARR).
Apply a disciplined workflow before using any engineering-economy formula.

$Engineering Economy$

Engineering economy is the systematic comparison of the monetary consequences of engineering alternatives over time so that scarce resources can be allocated consistently with a stated decision objective.

$The Engineering Decision Frame$

A defensible economic study begins with feasible alternatives, a common viewpoint, a study period, estimated cash flows, a time-value basis, and a decision criterion. The economic model supports engineering judgment; it does not replace safety, code compliance, reliability, environmental, or service requirements.

$Cash Flow$

A cash flow is a monetary receipt or disbursement assigned to a specific point or period in the study timeline. In this course, inflows are normally positive and outflows negative unless another convention is stated explicitly.

$Time Zero and End-of-Period Convention$

Time $0$ is the decision date. Unless a problem states otherwise, recurring annual amounts occur at the end of each period: year-1 cash flow at $t=1$ , year-2 cash flow at $t=2$ , and so on. A cash-flow diagram must show both timing and sign before factors are selected.

$Interactive Cash-Flow Modeling$

Use the timeline tools to connect engineering events—purchase, operation, maintenance, revenue, overhaul, and salvage—to their correct periods and signs.

Fixed costPHP/periodVariable cost per unitPHP/unitUnit revenue / benefitPHP/unit

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.

MARR per period10.00%

Cash flows

PeriodSigned amountPHP

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.

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.

$Opportunity Cost$

Opportunity cost is the value of the best feasible alternative forgone when a resource is committed to the selected use. For an owned asset, its current market value can be an opportunity cost when keeping it gives up the option to sell it now.

$Sunk Cost$

A sunk cost is a past expenditure that cannot be changed by the present decision. Because all current alternatives share that past, a sunk cost should not be charged again in a forward-looking economic comparison.

$Minimum Attractive Rate of Return (MARR)$

The MARR is the decision maker's required return or economic hurdle rate used to establish equivalence and screen investments. It must be stated on a basis consistent with the cash-flow periods.

$Cost Classification for Engineering Decisions$

Fixed costs do not change with the activity level within the relevant range. Variable costs change with output or usage. Incremental cost is the difference in future cost between alternatives. Classification depends on the decision being modeled; a cost can be fixed for one study and avoidable for another.

$Economic Equivalence$

Two cash-flow patterns are economically equivalent at a stated interest rate when they have the same value at the same focal date or on the same equivalent annual basis.

General Present-Worth Equivalence

Moves each discrete cash flow to time zero using one periodic interest rate.

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

Variables

Symbol	Description	Unit
$PW$	Present worth at time zero	-
$CF_t$	Net cash flow at the end of period t; CF_0 occurs at time zero	-
$i$	Effective interest or discount rate per cash-flow period	-
$t$	Cash-flow period index	-
$n$	Study horizon in periods	-

$Rate and Period Must Match$

A nominal annual rate, effective annual rate, and monthly periodic rate are not interchangeable. Convert the rate to the same period used by the cash-flow timeline before applying equivalence factors.

$Common Modeling Failures$

Do not hide sign conventions, place end-of-year flows at time zero, include sunk costs in a new decision, compare alternatives over inconsistent service requirements, or choose a method before defining the study basis.

$Engineering Economy Problem Setup$

STEP-BY-STEP

Define the decision objective and feasible alternatives.
Establish viewpoint, study period, service requirement, and timing convention.
Draw the cash-flow diagram with signs and units.
Identify the correct periodic rate or MARR basis.
Select a common equivalent-worth or rate-of-return criterion.
Compute using unrounded intermediate values.
Perform a reasonableness and sensitivity check.
State the economic decision together with the assumptions that support it.

$Pre-Calculation Checklist$

Are all alternatives technically feasible and providing the required service?
Is time $0$ explicit?
Are inflows and outflows signed consistently?
Are cash-flow and interest-rate periods aligned?
Have sunk costs been excluded from forward-looking comparisons?
Is the decision criterion stated before calculating?
Are non-economic constraints recorded separately?

Key Takeaways

Engineering economy compares feasible alternatives on a consistent time-value basis.
Cash-flow timing is part of the mathematics; draw the timeline before selecting factors.
Economic equivalence requires a stated rate and a common focal date or annual basis.
Opportunity cost is forward-looking; sunk cost is not relevant to a current choice.
MARR is the hurdle rate for the study and must match the cash-flow period.
A correct calculation built on an inconsistent study basis is still an incorrect engineering decision.