Equivalent Uniform Annual Worth Formula

EUAW Formula:

\[ EUAW = A + (P - A) \times (A/P, i, n) \]

Annual Amount (A):

currency

Present Amount (P):

currency

Interest Rate (i):

Number of Years (n):

years

Equivalent Uniform Annual Worth (EUAW):

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1. What is Equivalent Uniform Annual Worth?

Equivalent Uniform Annual Worth (EUAW) is a financial analysis method that converts all cash flows (both present and future) into an equivalent uniform annual amount. It is commonly used in engineering economics and capital budgeting to compare investment alternatives with different lifespans and cash flow patterns.

2. How Does the Calculator Work?

The calculator uses the EUAW formula:

\[ EUAW = A + (P - A) \times (A/P, i, n) \]

Where:

\( EUAW \) — Equivalent uniform annual worth (currency/year)
\( A \) — Annual amount (currency)
\( P \) — Present amount (currency)
\( i \) — Interest rate (decimal)
\( n \) — Number of years
\( (A/P, i, n) \) — Capital recovery factor

Explanation: The formula converts a combination of present and annual amounts into an equivalent uniform annual series, making it easier to compare different investment options.

3. Importance of EUAW Calculation

Details: EUAW analysis is crucial for comparing investment alternatives with different time horizons, evaluating project feasibility, and making informed capital budgeting decisions in engineering and business contexts.

4. Using the Calculator

Tips: Enter annual amount in currency units, present amount in currency units, interest rate as a percentage, and number of years. All values must be valid (n > 0, i ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between EUAW and NPV?
A: NPV gives the present value of all cash flows, while EUAW converts all cash flows to an equivalent uniform annual amount, making it easier to compare projects with different durations.

Q2: When should I use EUAW analysis?
A: Use EUAW when comparing investment alternatives with different service lives, when annual budgeting is important, or when you need to express results in annual terms for management reporting.

Q3: What does the (A/P, i, n) factor represent?
A: This is the capital recovery factor that converts a present amount into an equivalent uniform annual series over n periods at interest rate i.

Q4: Can EUAW be negative?
A: Yes, a negative EUAW indicates that the project or investment is not economically viable as it results in a net annual loss.

Q5: How does inflation affect EUAW calculations?
A: If cash flows are in real terms, use real interest rates. If in nominal terms, use nominal interest rates that include expected inflation.