Your plant must replace an air compressor and will keep the new one for 5 years. Model X costs $18,400 and draws 6,200 watts. Model Y costs $21,900 and draws 3,500 watts. Either model will run 2,000 hours per year, and electricity costs $0.14 per kilowatt-hour. Over the 5 years, how much less will the lower-cost model cost in total, counting the purchase price and electricity?
Show answer & explanation
Answer: A
- Hours in 5 years: 2,000 × 5 = 10,000 hours.
- Formula sheet: 1 kWh = 1,000 Wh. X: 6.2 kW × 10,000 h = 62,000 kWh × $0.14 = $8,680. Y: 3.5 kW × 10,000 h = 35,000 kWh × $0.14 = $4,900.
- Totals: X = $18,400 + $8,680 = $27,080; Y = $21,900 + $4,900 = $26,800.
- Difference: $27,080 − $26,800 = $280.00 (Model Y is cheaper).
$280.00: Correct. X: $18,400 + $8,680 = $27,080. Y: $21,900 + $4,900 = $26,800. Model Y costs $280.00 less.
$2,744.00: Counted only 1 year of electricity, which makes Model X look cheaper.
$3,500.00: Compared only the purchase prices.
$3,780.00: Compared only the electricity costs.
$7,280.00: Added the purchase-price difference to the electricity difference instead of letting them offset.
Compare total cost of ownership over the whole period: purchase price plus operating cost, with watts converted to kilowatts. Why this is a Level 7 item: a multi-step economic comparison with a unit conversion, where the cheaper purchase is not the better deal.