Equivalent Uniform Annual Cost Formula

EUAC Formula:

\[ EUAC = (P \times A/P, i, n) + A - (S \times A/F, i, n) \]

Initial Cost (P):

currency

Annual Operating Cost (A):

currency/year

Salvage Value (S):

currency

Interest Rate (i):

decimal

Years (n):

years

Equivalent Uniform Annual Cost (EUAC):

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1. What is the Equivalent Uniform Annual Cost Formula?

The Equivalent Uniform Annual Cost (EUAC) formula converts all costs associated with an investment into an equivalent uniform annual amount. This allows for easy comparison between alternatives with different lifespans and cost patterns in life-cycle costing analysis.

2. How Does the Calculator Work?

The calculator uses the EUAC formula:

\[ EUAC = (P \times A/P, i, n) + A - (S \times A/F, i, n) \]

Where:

\( P \) — Initial cost (currency)
\( A \) — Annual operating cost (currency/year)
\( S \) — Salvage value (currency)
\( i \) — Interest rate (decimal)
\( n \) — Number of years
\( A/P \) — Capital recovery factor
\( A/F \) — Sinking fund factor

Explanation: The formula distributes the initial cost and salvage value over the project lifespan as equivalent annual amounts, then combines with the annual operating cost.

3. Importance of EUAC Calculation

Details: EUAC is essential for comparing investment alternatives with different lifespans and cost patterns. It provides a standardized basis for decision-making in capital budgeting and engineering economics.

4. Using the Calculator

Tips: Enter all costs in the same currency unit. Interest rate should be entered as a decimal (e.g., 0.08 for 8%). All values must be valid (non-negative costs, interest rate between 0-1, years positive).

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between A/P and A/F factors?
A: A/P (capital recovery factor) converts present worth to annual worth, while A/F (sinking fund factor) converts future worth to annual worth.

Q2: When should I use EUAC analysis?
A: Use EUAC when comparing alternatives with different service lives, or when you need to express costs on an annual basis for budgeting purposes.

Q3: How does salvage value affect EUAC?
A: Higher salvage value reduces EUAC since it represents recovered value at the end of the project life.

Q4: What if the interest rate is zero?
A: When interest rate is zero, both A/P and A/F factors simplify to 1/n (straight-line depreciation).

Q5: Can EUAC be negative?
A: Yes, if the salvage value and/or annual benefits exceed the costs, EUAC can be negative, indicating a net annual benefit.