Equivalence in engineering economics is the principle that two cash-flow streams that occur at different times can be considered equal in value when adjusted properly using the time value of money. $1,000 today is equivalent to $1,100 a year from now if the prevailing interest rate is 10% — they have the same economic value, just located at different points in time.
Three flavours of equivalence get distinguished:
Mathematical equivalence is the calculation: and friends. Two amounts at different times have equal mathematical-present-value if the formula says so at the given interest rate. This is just arithmetic — given the rate and the times, the equivalence is unambiguous.
Decisional equivalence is the assumption that the decision-maker is genuinely indifferent between the two amounts at the two times. That is, if I offer you $1,000 today or $1,100 a year from now, and at the prevailing 10% rate you have no preference, then you’re operating under decisional equivalence. In practice people have preferences for liquidity, certainty, current spending, etc. that distort this — but for engineering analysis we assume decisional equivalence holds.
Market equivalence is the practical condition that you can actually make the exchange at zero cost. The market provides the mechanism to convert money at different times: bank accounts, bonds, loans, savings instruments. For market equivalence to hold, you need to be able to transact at the interest rate frictionlessly. In reality, the lending rate (the rate at which you can deposit money) is usually different from the borrowing rate (the rate at which you can take loans), and both involve fees. We assume these frictions are negligible.
When all three hold — mathematical, decisional, market — moving cash flows around in time is meaningful and the equivalent values are comparable. The two assumptions (decisional, market) are idealisations that engineering analysis uses to keep the math tractable. They’re rarely exactly true but are usually close enough for the resulting decision to be sound.
The practical implication for project evaluation: pick a single point in time (usually for PW, or end-of-life for FW), use the equivalence formulas to move every cash flow to that point, then add or compare. Everything in Present worth method, Future worth method, Annual worth method, Internal rate of return rests on equivalence.
For the mechanics of moving cash flows around, see Compound interest factor and Cash flow diagram.