Future and Annual Worth Analysis

In addition to Present Worth (PW) Analysis, two other primary equivalence methods for evaluating engineering alternatives are Future Worth (FW) and Annual Worth (AW) analysis. These methods offer different perspectives but, when applied correctly, will always lead to the exact same investment decision as Present Worth Analysis.

Future Worth (FW) Analysis

Future Worth (FW) Method

Compares alternatives based on their equivalent value at a future date (usually the end of the project life). It is particularly useful when the primary goal is to maximize future wealth, such as in retirement planning, long-term investments, or assessing the terminal value of a portfolio.

Checklist

Just like with Present Worth Analysis, when comparing mutually exclusive alternatives using Future Worth, you must explicitly evaluate them over the same time period (Least Common Multiple or a defined Study Period). Failing to equalize the lifespans will skew the future compounding and invalidate the comparison.
Key Takeaways
  • Future Value Perspective: Evaluates equivalent project value at the end of the analysis period instead of the beginning.
  • Equivalence Rules: Like PW, mutually exclusive options must absolutely be evaluated over identical time horizons.
  • Decision Rule: A project is justified if its FW≥0FW \ge 0 at the MARR.

Annual Worth (AW) Analysis

Annual Worth (AW) Method

Converts all cash flows (inflows and outflows) into a series of equal annual equivalent amounts spread uniformly over the life of the project. When dealing primarily with costs (and negligible revenues), this method is historically referred to as Equivalent Uniform Annual Cost (EUAC).

The Major AW Advantage

The absolute most significant advantage of the Annual Worth method is that you do not need to use the Least Common Multiple (LCM) of lives when comparing mutually exclusive alternatives with different lifespans.
Because the AW method mathematically assumes continuous replacement of the asset with an identical asset at the end of its life, the AW of one life cycle of an alternative is exactly equal to the AW of any number of identical, continuous life cycles. Therefore, you only need to calculate the AW for one single life cycle of each alternative.

Checklist

Capital Recovery (CR)

A foundational component of any AW analysis for physical assets is Capital Recovery (CR). It represents the equivalent uniform annual cost of owning an asset, accounting for the initial capital investment, the time value of money, and the final salvage value at the end of its useful life.

Capital Recovery Formulas

CR=−P(A/P,i,n)+S(A/F,i,n) CR = -P(A/P, i, n) + S(A/F, i, n)
Where:
  • PP = Initial purchase price or first cost (present worth)
  • SS = Salvage value (future worth at end of life nn)
  • nn = Expected life in years
  • ii = Interest rate (MARR)
Alternatively, using the standard relationship (A/F,i,n)=(A/P,i,n)−i(A/F, i, n) = (A/P, i, n) - i, the formula can be expressed to calculate the loss in value plus interest on the salvage:
CR=−(P−S)(A/P,i,n)−S(i) CR = -(P - S)(A/P, i, n) - S(i)
The total Annual Worth is the Capital Recovery cost plus any equivalent uniform annual revenues minus any equivalent uniform annual operating expenses (AOC):
AWtotal=CR+Arevenues−Aexpenses AW_{total} = CR + A_{revenues} - A_{expenses}
Key Takeaways
  • The AW Advantage: Converts all lump sums into an equivalent uniform annual series. There is absolutely no need to find the LCM of lives when comparing mutually exclusive options.
  • Capital Recovery (CR): The equivalent uniform annual cost of owning an asset, combining the amortization of the initial investment and the return on the eventual salvage value over the asset's life.

Interactive Equivalence Visualizer

Use the simulator below to see how a single set of cash flows (Initial Cost, Annual Benefit, and Salvage Value) can be equivalently expressed as a Total Present Worth, Total Annual Worth, or Total Future Worth. Notice that regardless of the metric chosen, if one is positive (indicating profitability at the MARR), all three will be mathematically positive.

Equivalence Visualizer

Initial Cost (P)10,000 $
Annual Benefit (A)3,000 $ / yr
Salvage Value (S)2,000 $
Life (n)5 yrs
Interest Rate (MARR)10 %

Total PW

$2,614

Total AW

$690

Total FW

$4,210

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Note that PW, AW, and FW all lead to the same accept/reject decision (positive vs negative).
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