Question

6-16. A special-purpose 30 -horsepower electric motor has an efficiency of 90%. Its purchase and installation price is $2,200. A second 30 -horsepower high-efficiency motor can be purchased for $3,200, and its efficiency is 93%. Either motor will be operated 4,000 hours per year at full load, and electricity costs $0.10 per kilowatt-hour ( kWh ). MARR =15% per year, and neither motor will have a market value at the end of the eight-year study period. (6.4□ 므) a. Which motor should be chosen? b. For an incremental investment of $1,000 in the more efficient motor, what is the PW of the energy savings over the eight-year period?

Answer 1

a. The high-efficiency motor should be chosen since it has a lower present worth of cost and energy consumption over the eight-year study period.

b. The present worth of the energy savings resulting from an incremental investment of $1,000 in the more efficient motor over the eight-year study period is $172.13.

Step-by-step explanation:

a. To compare the two motors, we need to calculate the present worth of each motor's total cost and energy consumption over the eight-year study period. Let's start with the special-purpose motor:

The cost of the special-purpose motor is $2,200. The annual energy consumption of the motor is:

Energy consumption = (30 hp) x (0.746 kW/hp) x (1/0.9) x (4,000 hours/year) = 100,800 kWh/year

The annual energy cost is:

Annual energy cost = 100,800 kWh/year x $0.10/kWh = $10,080/year

The present worth of the annual energy cost over the eight-year study period, using a MARR of 15%, is:

PW = $10,080 x [(1 - (1 + 0.15)^-8) / 0.15] = $55,320.15

The present worth of the special-purpose motor, including the purchase and installation cost and the present worth of the annual energy cost, is:

PW = $2,200 + $55,320.15 = $57,520.15

Now let's calculate the present worth of the high-efficiency motor:

The cost of the high-efficiency motor is $3,200. The annual energy consumption of the motor is:

Energy consumption = (30 hp) x (0.746 kW/hp) x (1/0.93) x (4,000 hours/year) = 96,774.19 kWh/year

The annual energy cost is:

Annual energy cost = 96,774.19 kWh/year x $0.10/kWh = $9,677.42/year

The present worth of the annual energy cost over the eight-year study period, using a MARR of 15%, is:

PW = $9,677.42 x [(1 - (1 + 0.15)^-8) / 0.15] = $53,148.02

The present worth of the high-efficiency motor, including the purchase and installation cost and the present worth of the annual energy cost, is:

PW = $3,200 + $53,148.02 = $56,348.02

Therefore, the high-efficiency motor should be chosen, since it has a lower present worth of cost and energy consumption over the eight-year study period.

b. To calculate the present worth of energy savings resulting from an incremental investment of $1,000 in the more efficient motor, we need to compare the present worth of the energy cost of the high-efficiency motor with and without the incremental investment. With the incremental investment, the present worth of the high-efficiency motor is:

PW = $4,200 + $53,148.02 = $57,348.02

The present worth of the energy savings over the eight-year study period, using a MARR of 15%, is:

PW = ($57,520.15 - $57,348.02) = $172.13

Therefore, the present worth of the energy savings resulting from an incremental investment of $1,000 in the more efficient motor over the eight-year study period is $172.13.