Equivalent Uniform Annual Worth Calculator

EUAC Formula:

\[ EUAC = PW \times \frac{r (1 + r)^n}{(1 + r)^n - 1} \]

Equivalent Uniform Annual Cost (EUAC):

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1. What is Equivalent Uniform Annual Cost?

The Equivalent Uniform Annual Cost (EUAC) method converts a present worth amount into an equivalent uniform annual cost over a specified period. This is commonly used in engineering economics and capital budgeting to compare investment alternatives with different time horizons.

2. How Does the Calculator Work?

The calculator uses the EUAC formula:

\[ EUAC = PW \times \frac{r (1 + r)^n}{(1 + r)^n - 1} \]

Where:

\( EUAC \) — Equivalent uniform annual cost (dollars per year)
\( PW \) — Present worth (dollars)
\( r \) — Interest rate (fraction)
\( n \) — Number of years

Explanation: This formula converts a single present amount into an equivalent series of equal annual payments over the specified time period, considering the time value of money.

3. Importance of EUAC Calculation

Details: EUAC is essential for comparing investment alternatives with different lifetimes, making capital budgeting decisions, and evaluating the true annual cost of ownership for assets and equipment.

4. Using the Calculator

Tips: Enter present worth in dollars, interest rate as a fraction (e.g., 0.05 for 5%), and number of years. All values must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between EUAC and EAA?
A: EUAC (Equivalent Uniform Annual Cost) typically refers to costs, while EAA (Equivalent Annual Annuity) refers to benefits or revenues. The calculation method is identical.

Q2: When should I use EUAC analysis?
A: Use EUAC when comparing projects with different lifetimes, evaluating equipment replacement decisions, or determining the annual cost of capital investments.

Q3: How does interest rate affect EUAC?
A: Higher interest rates generally increase EUAC because the time value of money becomes more significant in the calculation.

Q4: Can EUAC be used for projects with irregular cash flows?
A: For irregular cash flows, you would first need to calculate the present worth of all cash flows, then convert to EUAC using this formula.

Q5: What are the limitations of EUAC analysis?
A: EUAC assumes constant interest rates, equal annual payments, and may not account for inflation or changing economic conditions over long periods.