Equivalent Annual Cost
Encyclopedia
In finance the equivalent annual cost (EAC) is the cost per year of owning and operating an asset over its entire lifespan.
EAC is often used as a decision making tool in capital budgeting
when comparing investment projects of unequal lifespans. For example if project A has an expected lifetime of 7 years, and project B has an expected lifetime of 11 years it would be improper to simply compare the net present values (NPVs) of the two projects, unless neither project could be repeated.
EAC is calculated by dividing the NPV
of a project by the present value of an annuity
factor. Equivalently, the NPV of the project may be multiplied by the loan repayment factor.
The use of the EAC method implies that the project will be replaced by an identical project.
Machine A
Investment cost $50,000
Expected lifetime 3 years
Annual maintenance $13,000
Machine B
Investment cost $150,000
Expected lifetime 8 years
Annual maintenance $7,500
The cost of capital is 5%.
The EAC for machine A is: ($50,000/
)+$13,000=$31,360
The EAC for machine B is: ($150,000/
)+$7,500=$30,708
The conclusion is to invest in machine B since it has a lower EAC.
Note: The loan repayment factors (A values) are for t years (3 or 8 years) and 5% cost of capital.
is given by 
= 2.723 and 
is given by 
= 6.463. (See ordinary annuity formulae for a derivation.) The larger an A value is, the greater the present value is on a succession of future annuity payments, thus contributing to a smaller annual cost.
Alternative method:
The manager calculates the NPV of the machines:
Machine A EAC=$85,400/
=$31,360
Machine B EAC=$198,474/
=$30,708
Note: To get the numerators add the present value of the annual maintenance to the purchase price. For example, for Machine A: 50,000 + 13,000/1.05 + 13,000/(1.05)^2 + 13,000/(1.05)^3 = 85,402.
The result is the same, although the first method is easier it is essential that the annual maintenance cost is the same each year.
Alternatively the manager can use the NPV method under the assumption that the machines will be replaced with the same cost of investment each time. This is known as the chain method since 8 repetitions of machine A are chained together and 3 repetitions of machine B are chained together. Since the time horizon used in the NPV comparison must be set to 24 years (3*8=24) in order to compare projects of equal length, this method can be slightly more complicated than calculating the EAC.
In addition, the assumption of the same cost of investment for each link in the chain is essentially an assumption of zero inflation
, so a real interest rate
rather than a nominal interest rate
is commonly used in the calculations.
EAC is often used as a decision making tool in capital budgeting
Capital budgeting
Capital budgeting is the planning process used to determine whether an organization's long term investments such as new machinery, replacement machinery, new plants, new products, and research development projects are worth pursuing...
when comparing investment projects of unequal lifespans. For example if project A has an expected lifetime of 7 years, and project B has an expected lifetime of 11 years it would be improper to simply compare the net present values (NPVs) of the two projects, unless neither project could be repeated.
EAC is calculated by dividing the NPV
Net present value
In finance, the net present value or net present worth of a time series of cash flows, both incoming and outgoing, is defined as the sum of the present values of the individual cash flows of the same entity...
of a project by the present value of an annuity
Annuity (finance theory)
The term annuity is used in finance theory to refer to any terminating stream of fixed payments over a specified period of time. This usage is most commonly seen in discussions of finance, usually in connection with the valuation of the stream of payments, taking into account time value of money...
factor. Equivalently, the NPV of the project may be multiplied by the loan repayment factor.
The use of the EAC method implies that the project will be replaced by an identical project.
A practical example
A manager must decide on which machine to purchase:Machine A
Investment cost $50,000
Expected lifetime 3 years
Annual maintenance $13,000
Machine B
Investment cost $150,000
Expected lifetime 8 years
Annual maintenance $7,500
The cost of capital is 5%.
The EAC for machine A is: ($50,000/
)+$13,000=$31,360The EAC for machine B is: ($150,000/
)+$7,500=$30,708The conclusion is to invest in machine B since it has a lower EAC.
Note: The loan repayment factors (A values) are for t years (3 or 8 years) and 5% cost of capital.
is given by = 2.723 and is given by = 6.463. (See ordinary annuity formulae for a derivation.) The larger an A value is, the greater the present value is on a succession of future annuity payments, thus contributing to a smaller annual cost.Alternative method:
The manager calculates the NPV of the machines:
Machine A EAC=$85,400/
=$31,360Machine B EAC=$198,474/
=$30,708Note: To get the numerators add the present value of the annual maintenance to the purchase price. For example, for Machine A: 50,000 + 13,000/1.05 + 13,000/(1.05)^2 + 13,000/(1.05)^3 = 85,402.
The result is the same, although the first method is easier it is essential that the annual maintenance cost is the same each year.
Alternatively the manager can use the NPV method under the assumption that the machines will be replaced with the same cost of investment each time. This is known as the chain method since 8 repetitions of machine A are chained together and 3 repetitions of machine B are chained together. Since the time horizon used in the NPV comparison must be set to 24 years (3*8=24) in order to compare projects of equal length, this method can be slightly more complicated than calculating the EAC.
In addition, the assumption of the same cost of investment for each link in the chain is essentially an assumption of zero inflation
Inflation
In economics, inflation is a rise in the general level of prices of goods and services in an economy over a period of time.When the general price level rises, each unit of currency buys fewer goods and services. Consequently, inflation also reflects an erosion in the purchasing power of money – a...
, so a real interest rate
Real interest rate
The "real interest rate" is the rate of interest an investor expects to receive after allowing for inflation. It can be described more formally by the Fisher equation, which states that the real interest rate is approximately the nominal interest rate minus the inflation rate...
rather than a nominal interest rate
Nominal interest rate
In finance and economics nominal interest rate or nominal rate of interest refers to the rate of interest before adjustment for inflation ; or, for interest rates "as stated" without adjustment for the full effect of compounding...
is commonly used in the calculations.