A local construction company is considering the purchase of a small-load tractor

Question

A local construction company is considering the purchase of a small-load tractor for dirt scraping and levelling. The tractor has the following estimates: initial cost of $75,000, a life expectancy of 15 years, a $5,000 salvage value, an operating cost of $30 per day, and an annual maintenance cost of $6,000. Alternatively, the construction company can lease the same tractor and a driver as needed for $210 per day. The company has a MARR of 12% per year. Compute the number of days per year that the scraper would be required to justify its purchase.

Explanation / Answer

let x be the number of days scraper is required

Net costs of scraper should be equal to 210 * x inorder to justify the purchases

hence

anuual costs = 30*x + 6000

210* x*PVIFA(12%,15) = -75000 + (30*x +6000) * PVIFA(12%,15) +5000 PVIF(12%,15)

210*x *6.8109 =   75000 + (30*x +6000) * 6.8109 - 5000* 0.1827

180 *x * 6.8109 = 114951.9

hence x = 93.76 days

hence number of days required per year to justify the decision is 94 days

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