A mechanical engineer must recommend an A/C system to a commercial building owne

Question

A mechanical engineer must recommend an A/C system to a commercial building owner. The owner uses and MARR of 6%, but is not sure how long he will own the building. A conventional split system has a design life of 10 years, a cost of $48,000, and annual operating costs of $16,000. A chilled water system has an initial cost of $72,000 and annual operating costs of $15,000. Assuming each unit has no salvage value and will be identically replaced for the life of the building, determine how long the chilled water system needs to last for it to be the best choice (i.e. determine the breakeven useful life for the chilled water system). Express your answer in years to the nearest whole year.

Explanation / Answer

Solution:

Given that Initial cost = $72,000,

Annual operating costs = $15,000 and

MARR = 6%

To determine the breakeven useful life, we equate initial cost and present value of annual operating costs

Initial cost = Annual operating costs (PVIFA @ MARR, n)

$72,000 = $15,000 (PVIFA @ 6%, n)

72,000/15,000 = (PVIFA @ 6%, n)

4.8 = PVIFA @ 6%, n

Using Present value interest factor annuity table, we get

PVIFA @ 6%, 5 = 4.21236

PVIFA @ 6%, 6 = 4.91732

Using Interpolation,

5 + (4.8 - 4.21236)/ (4.91732 - 4.21236) x (6 - 5)

5 + 0.83

5.83 years ~ 6 years

Hence, the chilled water system needs to last for 6 years.

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