Understanding Equivalent Annual Cost (EAC) for Capital Budgeting

What Is the Equivalent Annual Cost (EAC)?

Equivalent Annual Cost (EAC) provides a financial measure that allows firms to assess the annual cost associated with owning, operating, and maintaining an asset through its lifespan. As an essential tool in capital budgeting, EAC enables companies to evaluate and choose the most cost-effective assets, especially those with differing lifespans, thus informing better investment decisions.

Analyzing the Benefits of Equivalent Annual Cost (EAC)

 Equivalent annual cost (EAC) is often used for capital budgeting and other analyses. But it is used most often to analyze two or more possible projects with different lifespans, where costs are the most relevant variable.

EAC can help calculate the optimal life of an asset, decide between leasing or purchasing, assess maintenance cost impacts, determine cost savings needed for new purchases, and evaluate costs of retaining existing equipment.

EAC calculations consider the discount rate, also known as the cost of capital. Cost of capital is the required return necessary to make a capital budgeting project—such as building a new factory—worthwhile. Cost of capital includes the cost of debt and the cost of equity and is used by companies internally to judge whether a capital project is worth the expenditure of resources.

Calculating Equivalent Annual Cost: The Formula Explained


$\begin{aligned} &\text{EAC} = \frac{ \text{Asset Price} \times \text{Discount Rate} }{ 1 – ( 1 + \text{Discount Rate})^{-n} } \\ &\textbf{where:} \\ &\text{Discount Rate} = \text{Return required to make project} \\ &\text{worthwhile} \\ &n = \text{Number of periods} \\ \end{aligned}$​EAC=1−(1+Discount Rate)−nAsset Price×Discount Rate​where:Discount Rate=Return required to make projectworthwhilen=Number of periods​

Steps to Calculate Equivalent Annual Cost (EAC)

1. Take the asset price or cost and multiply it by the discount rate.
2. The discount rate is also called the cost of capital, which is the required return necessary to make a capital budgeting project, such as building a new factory, worthwhile.
3. In the denominator add 1 + the discount rate and raise the result as an exponent to the number of years for the project. Subtract the result by 1 and divide the numerator figure by the denominator.
4. Many financial online calculators are available to calculate EAC.

Example: Comparing Machines With EAC

EAC helps managers compare the NPVs of projects over various periods to find the best option. Consider two alternative investments in machinery equipment:

1. Machine A has the following:

• An initial capital outlay of $105,000
• An expected lifespan of three years
• An annual maintenance expense of $11,000

2. Machine B has the following:

• An initial capital outlay of $175,000
• An expected lifespan of five years
• An annual maintenance expense of $8,500

 The company’s cost of capital is 5%.

Next, we calculate the EAC, which is equal to the net present value (NPV) divided by the present value annuity factor or A(t,r), while taking into account the cost of capital or r, and the number of years in question or t.

The annuity factor is calculated as follows:

$\begin{aligned} &\text{Annuity Factor} = \frac{ 1 – \frac{ 1 }{ ( 1 + r ) ^ t} }{ r } \\ &\textbf{where:} \\ &r = \text{Cost of capital} \\ &t = \text{Number of periods} \\ \end{aligned}$​Annuity Factor=r1−(1+r)t1​​where:r=Cost of capitalt=Number of periods​

Using the formula above, the annuity factor or A(t,r) of each project must be calculated. These calculations would be as follows:

$\begin{aligned} &\text{Machine A, A(t, r)} = \frac{ 1 – \frac{ 1 }{ ( 1 + .05) ^ 3 } }{ .05 } = 2.72 \\ \end{aligned}$​Machine A, A(t, r)=.051−(1+.05)31​​=2.72​

$\begin{aligned} &\text{Machine B, A(t, r)} = \frac{ 1 – \frac{ 1 }{ ( 1 + .05) ^ 5 } }{ .05 } = 4.33 \\ \end{aligned}$​Machine B, A(t, r)=.051−(1+.05)51​​=4.33​

Next, the initial costs must be divided by the annuity factor or A(t,r) while adding in the annual maintenance cost. The calculation for EAC is:

$\begin{aligned} &\text{EAC Machine A} = \frac{ \$105,000 }{ 2.72 } + \$11,000 = \$49,557 \\ \end{aligned}$​EAC Machine A=2.72$105,000​+$11,000=$49,557​

$\begin{aligned} &\text{EAC Machine B} = \frac{ \$175,000 }{ 4.33 } + \$8,500 = \$48,921 \\ \end{aligned}$​EAC Machine B=4.33$175,000​+$8,500=$48,921​

When cost is the main concern, a manager would pick Machine B due to its EAC being $636 lower than Machine A.

The Difference Between the Equivalent Annual Cost and the Whole-life Cost

Whole-life cost is the total expense of owning an asset over its entire life, from purchase to disposal, as determined by financial analysis. It is also known as a “life-cycle” cost, which includes purchase and installation, design and building costs, operating costs, maintenance, associated financing costs, depreciation, and disposal costs.

 Whole-life cost includes often-overlooked expenses like environmental and social impact factors.

The equivalent annual cost (EAC) is the annual cost of owning, operating, and maintaining an asset over its entire life while the whole life cost is the total cost of the asset over its entire life.

Understanding the Limitations of Equivalent Annual Cost

A limitation with EAC, as with many capital budgeting decisions, is that the discount rate or cost of capital must be estimated for each project.  Forecasts can be inaccurate, and variables may change over the project’s or asset’s lifespan.

The Bottom Line

Equivalent Annual Cost (EAC) is a vital tool for firms in making capital budgeting decisions. It enables the comparison of assets with different lifespans by standardizing their costs to an annual figure. This analysis aids in assessing the net present value of multiple projects, ensuring financial efficiency and strategic decision-making.

However, EAC relies on the accuracy of the estimated discount rate, which can fluctuate over time, necessitating careful consideration in the planning stages. Understanding EAC empowers businesses to make informed investments by weighing the full range of operating, maintenance, and capital costs over an asset’s life.