Equivalent Annual Cost (EAC) is the annual cost of owning, operating, and maintaining an asset throughout its lifespan. It is frequently utilized by businesses during capital budgeting to evaluate the cost-efficiency of various assets with differing lifespans.
Key Insights of EAC
- Comprehensive Cost Analysis: EAC encapsulates all costs associated with an asset across its entire life.
- Decision-Making Tool: It enables a company to juxtapose the cost-effectiveness of assets with unequal lifespans.
- Net Present Value Comparison: Facilitates managers in comparing the NPVs of varied projects accurately to find the most cost-efficient option.
The Essence of Equivalent Annual Cost (EAC)
EAC is essential for multiple purposes including optimal analysis of projects with varied lifespans, deciding between leasing or purchasing, gauging the impact of maintenance costs, determining justification for new investments, and understanding the cost of continuing with existing assets. Cost of capital, which combines debt and equity costs, is a critical variable in these calculations.
Formula for Equivalent Annual Cost
The formula for calculating EAC is:
[ EAC = \frac{ \text{Asset Price} \times \text{Discount Rate} }{1 - (1 + \text{Discount Rate})^{-n}} ]
Where:
- Discount Rate = Return required to make the project worthwhile
- ( n ) = Number of periods
Steps to Calculate Equivalent Annual Cost
- Asset Price and Discount Rate: Multiply the asset price or cost by the discount rate.
- Denominator Calculation: Add 1 to the discount rate and raise the sum to the power of the number of project’s years. Subtract 1 and divide the numerator by this result.
- Use Calculators: Various online financial calculators are available for ease of EAC computation.
Practical Example of Equivalent Annual Cost
Let’s compare two machines - Machine A and Machine B:
Machine A:
- Initial cost: $105,000
- Lifespan: 3 years
- Annual maintenance: $11,000
Machine B:
- Initial cost: $175,000
- Lifespan: 5 years
- Annual maintenance: $8,500
Assuming a 5% cost of capital, the EAC calculation involves the following steps:
Calculate Annuity Factor ( A(t, r) ):
[ \text{Machine A}: A(t,r) = \frac{1 - \frac{1}{(1+0.05)^3}}{0.05} = 2.72 ]
[ \text{Machine B}: A(t,r) = \frac{1 - \frac{1}{(1+0.05)^5}}{0.05} = 4.33 ]
Then, calculate EAC:
[ EAC \text{ Machine A}: \frac{ $105,000 }{2.72} + $11,000 = $49,557 ]
[ EAC \text{ Machine B}: \frac{ $175,000 }{4.33} + $8,500 = $48,921 ]
Based on EAC, Machine B with an EAC of $48,921 is the more cost-effective choice compared to Machine A’s $49,557.
Comparing EAC and Whole-life Cost
While EAC addresses the annual cost over an asset’s lifespan, Whole-life Cost encompasses the total expenditure from purchase to disposal, including otherwise overlooked expenses like environmental and social impacts.
Limitations of Equivalent Annual Cost
A notable limitation of EAC lies in the requirement of an estimated cost of capital or discount rate, which can often prove to be inaccurate due to changing variables throughout the project’s lifecycle.
Understanding these limitations and calculating an accurate EAC fosters informed decision-making in capital budgeting and investment strategies.
Related Terms: Replacement chain method, Net present value, Cost of capital, Whole-life cost.
