1) Facility has an aging cooling system which currently runs 80% of the time the

Question

1) Facility has an aging cooling system which currently runs 80% of the time the plant is open .The cost of operating the cooling system is expected to increase 8% per yer since the cooling system deteriorates and running time increases . The maintenance for the old cooling system is $3000 per year which increases by $500 per year

• New cooling system would only run 60% of the time with a constant yearly maintenace of $2000 per year. The cost of operating the cooling system stays constant during the life of the system. The cost of installing the new system is $70,000

• Assumptions – Both pump uses 250 kW, Electricity cost $0.08/kwh – Plant runs 250 days per year, 24 hours per day – Firm’s discount rate is 12% . If you analyze the two cooling systems over a 5 year period

a) What is the NPV of the savings over a 5 year period the facility gets from installing the new system?

b) What is the annual savings the facility gets by opting for the new system?

Explanation / Answer

The question doesn't seem to be correct as there is limited amount of information for the old system. To calculate the savings from the new system, we will have to ignore that cost of installation of new system.

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Part a)

We will have to calculate NPV of both the systems. NPV in the given case is the present value of cash flows. The formula for calculating NPV is given below:

NPV = - Cash Flow Year 1/(1+Discount Rate)^1 - Cash Flow Year 2/(1+Discount Rate)^2 - Cash Flow Year 3/(1+Discount Rate)^3 - Cash Flow Year 4/(1+Discount Rate)^4 - Cash Flow Year 5/(1+Discount Rate)^5

_________

Electricity Cost (Old System) = 250*80%*24*.08 = $384

Electricity Cost (New System) = 250*60%*24*.08 = $288

NPV (Old System) = -(3,000 + 384)/(1+12%)^1 - (3,500 + 384)/(1+12%)^2 - (4,000 + 384)/(1+12%)^3 - (4,500 + 384)/(1+12%)^4 - (5,000 + 384)/(1+12%)^5 = $15,397.07

NPV (New System) = -(2,000 + 288)/(1+12%)^1 -(2,000 + 288)/(1+12%)^2 -(2,000 + 288)/(1+12%)^3 -(2,000 + 288)/(1+12%)^4 -(2,000 + 288)/(1+12%)^5 = -8,247.73

NPV of Savings from New System = $7,149.34 (-15,397.07 - (8,247.73))

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Part b)

The annual savings from the new system can be calculated as follows:

Annual Savings = NPV of Savings/PVIFA(Discount Rate, Years) where PVIFA is the Present Value Interest Factor for an Annuity

Using Present Value Tables, we get,

Annual Savings = 7,149.34/PVIFA(12%,5) = 7,149.34/3.6048 = $1,983.30

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