The capital cost of an asset is the cost to purchase and install it, and then di

Question

The capital cost of an asset is the cost to purchase and install it, and then disposes of it at the end of its life. A positive salvage value at the end of the asset's life is treated as a negative cost. Note that capital costs explicitly exclude operating and maintenance cost (O&M; costs). When we write any equation for cost, a negative cash flow becomes a positive cost. This is because it is the custom is not to say, for example, that a new car costs - $30,000. We say the car costs S30.000. EAC for asset capital cost = annualized cost to purchase, install and later dispose of an asset. Therefore, EAC for asset capital cost = P (A/P,i%.N) - S (A/F,i%,N) Using the identity (A/F.i%,N) = (AJP,i%,N) - i we obtain: EAC for asset capital cost = (P - S) (A/P,i%,N) + Si Notation: EAC = equivalent uniform annual cost. O&M; cost = operating and maintenance cost P = asset initial cost. S = asset salvage value end of life An asset with an initial cost of SI2,000, including installation, has an estimated salvage value of 52,000 at the end of its estimated 5-year life. Using an MARR of 15%, what is the equivalent uniform annual cost of owning this asset, not including O&M; costs? P = SI2,000, S = $2,000, N= 5 years If the MARR were zero, then the annualized capital cost would be [ (P - S)/N ] or $2,000 per year. With an MARR greater than zero, however, the annualized cost will be greater than $2,000 because the money tied up in this asset for five years could presumably be earning interest at the MARR rate.

Explanation / Answer

The annual worth method is more accurately described as the method of Equivalent Uniform Annual Cost (EUAC).

Given that there is no maintenance cost, the required EUAC value is:

EUAC = 12,000(A/P, 15%, 5) - 2000(A/F, 15%, 5)

= 12,000(0.2983) - 2000(0.1483)

= 3579.6 - 296.6

= $3283

Hence, the Equivalent Uniform Annual Cost of owing the asset is $3,283.

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