Annual Equivalent Worth Calculator

Annual Equivalent Worth Formula:

\[ AEW = PW \times (A/P, i, n) \]

Annual Equivalent Worth (AEW):

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1. What is Annual Equivalent Worth?

Annual Equivalent Worth (AEW) is a financial metric that converts a present worth amount into an equivalent uniform annual series over a specified period, considering a given interest rate. It helps in comparing investment alternatives with different time horizons.

2. How Does the Calculator Work?

The calculator uses the AEW formula:

\[ AEW = PW \times (A/P, i, n) \]

Where:

\( AEW \) — Annual Equivalent Worth (dollars per year)
\( PW \) — Present Worth (dollars)
\( i \) — Interest rate (decimal)
\( n \) — Number of years
\( (A/P, i, n) \) — Capital recovery factor

Explanation: The capital recovery factor converts a present amount into an equivalent uniform annual series over the project lifetime.

3. Importance of AEW Calculation

Details: AEW is crucial for investment analysis, capital budgeting, and comparing projects with different durations. It helps determine the annual cost or benefit equivalent of a lump-sum investment.

4. Using the Calculator

Tips: Enter present worth in dollars, interest rate as a percentage, and number of years. All values must be positive (PW > 0, interest rate > 0, years ≥ 1).

5. Frequently Asked Questions (FAQ)

Q1: What is the capital recovery factor (A/P)?
A: The capital recovery factor converts a present amount into an equivalent uniform annual series over a specified period at a given interest rate.

Q2: When should I use AEW analysis?
A: Use AEW when comparing investment alternatives with different lifetimes or when you need to express costs/benefits as uniform annual amounts.

Q3: How does interest rate affect AEW?
A: Higher interest rates increase the AEW because the capital recovery factor increases with higher rates, making annual equivalent costs higher.

Q4: Can AEW be negative?
A: Yes, if the present worth represents costs without sufficient benefits, AEW can be negative, indicating an annual net cost.

Q5: What's the difference between AEW and NPV?
A: NPV gives the total net present value, while AEW converts that value into an equivalent uniform annual amount for better comparison across different project durations.