1. What is the Annual Equivalent Worth Formula?

The Annual Equivalent Worth (AEW) formula converts a present worth amount into an equivalent uniform annual series over a specified period, considering the time value of money through an interest rate. It is commonly used in engineering economics and financial analysis.

2. How Does the Calculator Work?

The calculator uses the Annual Equivalent Worth formula:

Where:

• \( AEW \) — Annual Equivalent Worth (currency/year)
• \( PW \) — Present Worth (currency)
• \( i \) — Interest Rate (decimal)
• \( n \) — Number of Years (years)
• \( (A/P, i, n) \) — Capital Recovery Factor = \( \frac{i(1+i)^n}{(1+i)^n - 1} \)

Explanation: The formula distributes a present amount into equal annual payments that account for both principal repayment and interest over the specified period.

3. Importance of AEW Calculation

Details: AEW calculation is essential for comparing investment alternatives with different time horizons, evaluating project feasibility, and making informed financial decisions in capital budgeting and engineering projects.

4. Using the Calculator

Tips: Enter present worth in currency units, interest rate as a decimal (e.g., 0.08 for 8%), and number of years. All values must be positive and valid (PW > 0, rate > 0, years ≥ 1).

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between AEW and NPV?
A: NPV gives the total present value of cash flows, while AEW converts that present value into an equivalent annual amount for easier comparison of projects with different lifetimes.

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

Q3: How does interest rate affect AEW?
A: Higher interest rates increase the AEW because more money is required annually to recover the initial investment with interest.

Q4: Can AEW be negative?
A: Yes, if the present worth represents a net cost rather than a benefit, the AEW will be negative, indicating an annual cost.

Q5: What are the limitations of AEW analysis?
A: AEW assumes constant interest rates, equal annual payments, and may not capture all real-world complexities like inflation or variable cash flows.