Question

You are required to evaluate two systems. The cost of a used system is $75,000. Through a new system, labor hours can be decreased by 20% as compared to the used system. The cost of a new system is $150,000. Both systems have a useful life of five years. According to estimations, the market value of the used system will be $20,000 in five years, and the market value of the new system will be $50,000 in five years. The used system has to operate 8 hours per day for 20 days per month. If labor costs $40 per hour and the MARR is 1% per month, which system should be recommended?

Answer 1

For evaluating our decision we should evaluate PW (Present Worth) of both systems i.e. PW of New System and PW of Used System. We should select the alternative which has minimum cost.

Given MARR = 1% per month

Current Labor Cost = $40 per hour

Alternative 1 - PW of Used System

Monthly Labor cost for Used System = Labor cost per hour * hours per day * days per month

= $40 * 8 * 20

= $6,400

PW = Cost of a Used System + PVIFA of Monthly Labor cost for Used System - PVIF of Market Value at end of 5 Years i.e. 60 Months

= $75,000 + PVIFA (1%,60) * $6,400 + PVIF (1%, 60) * $20,000

= $75,000 + $2,87,712.25 - $11,008.99

= $351.703.26

Alternative 2 - PW of New System

Labour Cost per Hour = $40 / hour * (1 - 20%) = $32

Monthly Labor cost for New System = Labor cost per hour * hours per day * days per month

= $32 * 8 * 20

= $5,120

PW = Cost of a New System + PVIFA of Monthly Labor cost for New System - PVIF of Market Value at end of 5 Years i.e. 60 Months

= $150,000 + PVIFA (1%,60) * $5,120 - PVIF (1%, 60) * $50,000

= $150,000 + $230,169.80 - $27,522.48

= $352,647.32

Since PW of Used System is less than New System hence we should continue with old system.