An engineering consulting office is considering whether to purchase or lease a c
ID: 2762539 • Letter: A
Question
An engineering consulting office is considering whether to purchase or lease a computer printing system. The small system can be purchased for $40,000 with a life of four years and salvage value of $2,000. Operating expenses are expected to be $60 per day and annual maintenance to be $500 per year. An identical system can be leased for $ 125 per day, including maintenance and operating expenses. Determine the number of days per year that the system would have to be used to make the purchase economical. The desired ROI of the firm is 15%.Explanation / Answer
Number of days in a year = X
Annual operating expenses = X × $60 = $60X
Total expenses = Annual operating + Annual maintenance
= $60X + $500
PW = Initial cost + Present value of total expenses – Present salvage value
= 40,000 + (60X + 500) (PV accumulated 15%, 4 years) – 2,000 (PV at 15%, 4 years)
= 40,000 + (60X + 500) × 2.8550 – 2,000 × 0.5718
= 40,000 + 171.30X + 1,427.50 – 1,143.60
= 40,283.90 + 171.30X
Lease expense per day = $125
Lease expense per year = $125X
PW of lease expense = 125X (PV accumulated 15%, 4 years)
= 125X × 2.8550
= 356.875X
The purchase will be economical if PW of purchase = PW of lease expense
40,283.90 + 171.30X = 356.875X
185.575X = 40,283.90
X = 40,283.90 / 185.575 = 217
Answer: The number of days per year would be 217.