Question

A construction company can purchase a piece of equipment for $61,000 and spend $100 per day in operating costs. The equipment will have a 5-year life with no salvage value. Alternatively, the company can lease the equipment for $400 per day. The number of days per year the company must require the equipment to justify its purchase at an interest rate of 8% per year is closest to:

options:
(a) 10 days
(b) 42 days
(c) 51 days
(d) 68 days

Answer 1

The construction company must determine the number of days required to justify the purchase of equipment by comparing the present value of purchasing and operating costs against leasing costs. Considering an 8% interest rate over 5 years, option (b) 42 days is the closest number of days that justifies purchasing the equipment.

Step-by-step explanation:

The question involves determining whether a construction company should purchase equipment or lease it based on the number of days the equipment will be used annually and the related costs. The equipment can be purchased for $61,000 with additional operating costs of $100 per day, or leased for $400 per day.

The equipment is expected to have a lifespan of 5 years with no salvage value. This is a break-even analysis, under which we need to calculate the number of days the company must use the equipment each year, so that the cost of purchasing it equals the cost of leasing it, factoring in an 8% interest rate.

To determine the break-even point, we must compare the total costs of both options over the 5-year period. The purchase option includes the upfront cost of $61,000 plus the annual operating costs ($100/day times the number of days used each year). The lease option's total cost is straightforward: $400/day times the number of days used each year. We need to compute the present value of these costs, taking into account the 8% annual interest rate, to accurately compare them.

To find the number of days that justifies the purchase, let's assume the number of days the company will use the equipment per year is 'D'. The present value of operating costs for the purchase option would be $100D for each year, and we would bring this to today's value for each of the 5 years. As for the lease option, its present value would be $400D for each year for 5 years. Setting these equal to each other and solving for 'D' will give us the number of days where the costs break-even. After calculating this, the closest option that justifies the purchase is option (b) 42 days.