A large induced-draft fan is needed for an upgraded industrial process. The moto

Question

A large induced-draft fan is needed for an upgraded industrial process. The motor to drive this fan is rated at 100 horsepower, and the motor will operate at full load for 8760 hours per year. The motor's efficiency is 90%. Because the motor is fairly large, a demand charge of $90 per kilowatt per year will be incurred in addition to an energy change of $0.08 per kilowatt-hour. If the installed cost of the motor is $3,500, what is the present worth of the motor over a 10 year period when the MARR is 15% per year?

Explanation / Answer

We need to calculate values of total kW at 90% efficiency and total kWh per year. The process for same is given below:

The motor is of 100 hp and each hp is .7457 kW. Therefore, total kW will be 100*.7457 = 74.57 kW.

The input power that will be required at 90% efficiency is calculated below:

Required Input Power at 90% Efficiency = Total kW/Efficiency = 74.57kW/90% = 82.86 kW

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The total kWh per year can be calculated as follows:

Total kWh Per Year = Required Input Power at 90% Efficiency*Number of Hours = 82.86*8,760 = 725,815 hours

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The total value of demand charge and energy cost required to operate the motor is calculated as follows:

Demand Charge = Total kW Per Year*Demand Charge Per kW Per Year = 82.86*90 = $7,547

Energy Cost =Total kWh Per Year*Energy Cost Per Hour = 725,815*.08 = $58,065

The total cost per year, will therefore, be $65,522 (7,547 + 58,065)

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The present worth can be calculated with the use of following formula:

Present Worth = -Cash Flow Year 0 - Cash Flow Year 1/(1+MARR)^1 - Cash Flow Year 2/(1+MARR)^2 - Cash Flow Year 3/(1+MARR)^3 - Cash Flow Year 4/(1+MARR)^4 - Cash Flow Year 5/(1+MARR)^5 - Cash Flow Year 6/(1+MARR)^6 - Cash Flow Year 7/(1+MARR)^7 - Cash Flow Year 8/(1+MARR)^8 - Cash Flow Year 9/(1+MARR)^9 - Cash Flow Year 10/(1+MARR)^10

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Using the calculations performed above, we get,

Present Worth = -3,500 - 65,522/(1+15%)^1 - 65,522/(1+15%)^2 - 65,522/(1+15%)^3 - 65,522/(1+15%)^4 - 65,522/(1+15%)^5 - 65,522/(1+15%)^6 - 65,522/(1+15%)^7 - 65,522/(1+15%)^8 - 65,522/(1+15%)^9 - 65,522/(1+15%)^10 = -$332,340 or $332,340 (depending on the requirements of the question)

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