Annual Equivalent Worth Calculator

Annual Equivalent Worth Equation:

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

Present Worth (P):

currency

Annual Cash Flows (A):

currency/year

Future Worth (S):

currency

Interest Rate (i):

decimal

Number of Years (n):

years

Annual Equivalent Worth (AEW):

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1. What is Annual Equivalent Worth?

Annual Equivalent Worth (AEW) is a financial analysis method that converts all cash flows (present, annual, and future) into an equivalent uniform annual amount. It helps in comparing investment alternatives with different time periods and cash flow patterns.

2. How Does the Calculator Work?

The calculator uses the Annual Equivalent Worth equation:

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

Where:

\( AEW \) — Annual Equivalent Worth (currency/year)
\( P \) — Present Worth (currency)
\( A \) — Annual Cash Flows (currency/year)
\( S \) — Future Worth (currency)
\( i \) — Interest Rate (decimal)
\( n \) — Number of Years (years)
\( (A/P, i, n) \) — Capital Recovery Factor
\( (A/F, i, n) \) — Sinking Fund Factor

Explanation: The equation converts present and future values to equivalent annual amounts using time value of money principles.

3. Importance of AEW Calculation

Details: AEW analysis is crucial for investment decision-making, project evaluation, and comparing alternatives with different lifespans. It provides a uniform basis for comparison across different time periods.

4. Using the Calculator

Tips: Enter all monetary values in the same currency unit. Interest rate should be entered as a decimal (e.g., 0.08 for 8%). Number of years must be a positive integer.

5. Frequently Asked Questions (FAQ)

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

Q2: When should I use AEW analysis?
A: Use AEW when comparing investment alternatives with different service lives or when you need to express results in annual terms for budgeting purposes.

Q3: What does a positive AEW indicate?
A: A positive AEW indicates that the project or investment is economically viable and generates returns above the required rate of return.

Q4: How does interest rate affect AEW?
A: Higher interest rates generally decrease AEW as future cash flows are discounted more heavily, while lower rates increase AEW.

Q5: Can AEW be used for mutually exclusive projects?
A: Yes, AEW is particularly useful for comparing mutually exclusive projects with different lifespans, as it provides an annual basis for comparison.