Uniform Annual Cost (UAC) Calculator – Easily Estimate Annual Equipment Costs

What is Uniform Annual Cost (UAC)?

The Uniform Annual Cost (UAC), also known as Equivalent Annual Cost (EAC), helps convert all costs (initial, salvage, and recurring) of an asset into equal yearly amounts over its useful life. This makes it easier to compare different projects or equipment with varying lifespans.

Formulas Used

1. Capital Recovery Factor (CRF)

This factor converts the present value into an equivalent uniform annual value.

$\text{CRF}=\frac{i(1+i{)}^n}{(1+i{)}^n-1}$

If interest rate $i=0$, use:

$\text{CRF}=\frac{1}{n}$

2. Capital Recovery Cost (CRC)

$\text{CRC}=(P-S)\cdot \text{CRF}+S\cdot i$

Where:

• $P$ = Initial Cost
• $S$ = Salvage Value
• $i$ = Interest Rate
• $n$ = Useful Life (Years)

3. Uniform Annual Cost (UAC)

Example Calculation

Let’s say you are evaluating a piece of machinery with the following data:

• Initial Cost = $10,000
• Salvage Value = $2,000
• Useful Life = 5 years
• Annual Operating & Maintenance Cost = $500
• Interest Rate = 8%

Step 1: Capital Recovery Factor (CRF)

$CRF=\frac{i(1+i{)}^n}{(1+i{)}^n-1}$

Substitute values:

$CRF=\frac{0.08(1+0.08{)}^5}{(1+0.08{)}^5-1}$

$CRF=\frac{0.08\times 1.4693}{1.4693-1}=\frac{0.117544}{0.4693}\approx 0.25046$

Step 2: Capital Recovery Cost (CRC)

$CRC=(10000-2000)\times 0.25046+2000\times 0.08$

$CRC=8000\times 0.25046+160$

$CRC=2003.68+160=2163.68$

Step 3: Calculate Uniform Annual Cost (UAC)

$UAC=2163.68+500=2663.68$

Final Answer

• Capital Recovery Cost: $2163.68
• Uniform Annual Cost (UAC): $2663.68

Frequently Asked Questions (FAQs)

1. What is Uniform Annual Cost (UAC)?

Answer: Uniform Annual Cost (UAC) is the annual equivalent of all costs associated with owning and operating an asset over its useful life. It combines the capital recovery cost and annual operating & maintenance expenses into a single yearly amount.

2. How is UAC different from initial cost or total cost?

Answer: While the initial cost is a one-time purchase cost and total cost includes all expenses over time, UAC spreads all costs into equal yearly payments. This helps compare different assets or projects more easily.

3. What values do I need to calculate UAC?

Answer: To calculate UAC, you typically need:

• Initial Cost
• Salvage Value
• Useful Life (Years)
• Annual Operating & Maintenance Cost
• Interest Rate (%)

4. Why is the interest rate important in UAC?

Answer: The interest rate represents the time value of money. It is used to calculate the Capital Recovery Factor (CRF), which adjusts the cost of the asset based on how money's value changes over time.

5. What happens if the interest rate is 0%?

Answer: If the interest rate is 0%, the Capital Recovery Factor (CRF) becomes a simple fraction:

$\text{CRF}=\frac{1}{n}$​

This means the cost is equally divided over the years without adjusting for interest or inflation.

6. Is UAC the same as Equivalent Annual Cost (EAC)?

Answer: Yes, UAC and EAC are often used interchangeably. Both represent the same concept—converting all costs into an annualized figure to simplify comparisons.

7. When should I use a Uniform Annual Cost Calculator?

Answer: You should use it when:

• Comparing multiple machines, assets, or investment options with different lifespans
• Planning long-term budgets
• Evaluating cost-effectiveness of equipment purchases

8. Can I use this calculator for rental equipment?

Answer: No, UAC is primarily used for owned assets where depreciation, salvage value, and long-term operating costs are factors. For rental scenarios, simple annual or monthly rental cost analysis is more appropriate.