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.

Answer is 15 to check your answer. Show all equations for positive feedback.

Explanation / Answer

Conventional Split System Nature of Cashflows Year Discount Factor @ 6% Cashflow Discounted Cashflows a b a*b Purchase of Machinery 0 1.0000 $48,000.00 $48,000.00 Operating Cash outflows 1 - 10 7.3601 $16,000.00 $117,761.39 PV Cash outflows $165,761.39 PV of Net Cash outflows (A) $165,761.39 Annuity Factor for Machine Life (B) 7.3601 Equated Annual Cost (A/B) $22,521.66 Equated Annual Cost of Chilled water system has to lower than $22521.66 EAC = (72000 + 15000 * Annuity Factor at 6% for n years)/Annuity Factor at 6% for n years Let Annuity Factor at 6% for n years be x or, 22521.66 = (72000 + 15000x) /x or, 22521.66x = 72000 + 15000x or, 7521.66x = 72000 or, x = 9.5724 From Annuity Tables, When n = 14, Annuity Factor = 9.2950 When n = 15, Annuity Factor = 9.7122 Years for Chilled Water system = 14 + (9.5724 - 9.2950) / (9.7122 - 9.2950) = 14 + 0.2774/0.4173 = 14.66 years or 15 years

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