Engineering Economics
Cash Flow Diagram
A timeline showing when each cost and benefit occurs, with direction indicated by arrow.
A cash flow diagram places each payment on a horizontal timeline, with receipts drawn upward and disbursements downward. It takes seconds and eliminates the two errors that dominate economics questions: sign mistakes and off-by-one period errors.
Draw it before selecting a factor. Choosing the wrong factor is usually a symptom of not having drawn the diagram.
How much of the FE Civil exam is Engineering Economics?
Worked example
A county water utility is deciding whether to replace an ageing pump. A new one costs $12,000 installed, would cut the energy bill by $2,500 a year for 6 years, and could be sold for $1,500 at the end of year 6. The existing pump cost $9,000 when it was bought in 2019. Lay out the cash flows before choosing any factor.
- The $12,000 purchase sits at year 0 and points down: it is paid now, before the first year begins.
- The $2,500 savings run from year 1 to year 6, not from 0 to 5. A saving is earned over a year and counted at its end, so there are 6 arrows and the first is at year 1.
- Year 6 carries two upward arrows: the last saving and the $1,500 salvage. Keep them apart. One belongs to a uniform series and the other is a single future sum, and they take different factors.
- The $9,000 paid for the old pump in 2019 appears nowhere. It was spent whichever way the decision goes, so it cannot change the decision.