Engineering Economics Notes

Last reviewed 16 Sept 2026 · 6 min read

Time value of money

Money available today is worth more than the same amount in the future because it can earn interest (and because of inflation and risk). Engineering economics compares alternatives by bringing cash flows to a common point in time.

Simple and compound interest

FormulaInterest

Simple interest: $I = P i n$ , $F = P (1 + in)$ Compound interest: $F = P (1 + i)^{n}$

Effective annual rate for nominal rate $r$ compounded $m$ times a year:

i_{e f f} = (1 + \frac{r}{m})^{m} - 1

Continuous compounding: $i_{e f f} = e^{r} - 1$

Cash flow diagram

A horizontal time line (periods 0, 1, 2, …, n) with upward arrows for receipts and downward arrows for payments — end-of-period convention.

Interest factors

Notation: $P$ = present worth; $F$ = future worth; $A$ = uniform end-of-period annual amount; $G$ = uniform gradient; $i$ = interest rate per period; $n$ = number of periods.

FormulaDiscrete compounding factors

Factor	Find / given	Formula
Single payment compound amount	$F / P$	$(1 + i)^{n}$
Single payment present worth	$P / F$	$\frac{1}{( 1 + i ) ^{n}}$
Uniform series compound amount	$F / A$	$\frac{( 1 + i ) ^{n} - 1}{i}$
Sinking fund	$A / F$	$\frac{i}{( 1 + i ) ^{n} - 1}$
Uniform series present worth	$P / A$	$\frac{( 1 + i ) ^{n} - 1}{i ( 1 + i ) ^{n}}$
Capital recovery	$A / P$	$\frac{i ( 1 + i ) ^{n}}{( 1 + i ) ^{n} - 1}$
Arithmetic gradient to annual series	$A / G$	$\frac{1}{i} - \frac{n}{( 1 + i ) ^{n} - 1}$

Relations: $A / P = A / F + i$ ; perpetuity (n → ∞): $P = A / i$ (capitalised cost).

Methods of comparing alternatives

Method	Criterion
Present worth (PW / NPV)	Convert all cash flows to present; choose maximum NPV (or minimum PW of costs). Alternatives must be compared over the same study period (least common multiple of lives or a common horizon)
Annual worth (equivalent uniform annual cost, EUAC)	Convert to equal annual amounts; useful for unequal lives (assuming repeatability)
Future worth	Convert all to the end of the study period
Rate of return (IRR)	Interest rate at which NPV = 0; accept if IRR ≥ minimum attractive rate of return (MARR); for mutually exclusive alternatives use incremental IRR
Benefit–cost ratio	$B / C = \frac{P W of benefits}{P W of costs}$ ; accept if ≥ 1; incremental B/C for alternatives — common for public projects
Payback period	Time to recover initial investment from net cash inflows; simple but ignores time value (unless discounted) and cash flows after payback

Downloaded from civilgyantests.com · Not for resale. Verify every code clause and date against the official source.