Engineering Economics
Present Worth
The value today of a future cash flow, discounted at the interest rate.
Present worth converts money arriving at different times onto a common basis so alternatives can be compared fairly. A payment further in the future is worth less today, and the discount compounds each period.
The periodic interest rate must match the period of the cash flows. Mixing an annual rate with monthly payments is the classic error in this topic.
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. The utility evaluates projects at 8% a year. Is the replacement worth making?
| Cash flow | Factor | Present worth |
|---|---|---|
| Purchase, year 0 | none, already in today’s money | −$12,000.00 |
| Savings, $2,500 × years 1–6 | (P/A, 8%, 6) = 4.6229 | +$11,557.25 |
| Salvage, $1,500 at year 6 | (P/F, 8%, 6) = 0.6302 | +$945.30 |
| Net present worth | +$502.55 |
The net present worth is positive, so at 8% the new pump more than pays for itself, by about $503 in today’s money. The $9,000 paid for the old pump is a sunk cost and is correctly left out.