A large city in the mid-West needs to acquire a street-cleaning machine to keep

Question

A large city in the mid-West needs to acquire a street-cleaning machine to keep its roads looking nice year round. A used cleaning vehicle will cost $85,000 and have a $18,000 market (salvage) value at the end of its five-year life. A new system with advanced features will cost $175,000 and have a $58,000 market value at the end of its five-year life. The new system is expected to reduce labor hours compared with the used system. Current street-cleaning activity requires the used system to operate 8 hours per day for 25 days per month. Labor costs $45 per hour (including fringe benefits), and MARR is 12% per year compounded monthly. Find the breakeven percent reduction in labor hours for the new system.

Explanation / Answer

Used Cleaning Vehicle:
Initial Cost = $85,000
PV of salvage value = $18,000/(1.12)5 = $10,213.68
Actual Cost today = $85,000 - $10,213.68 = $74,786.32

New System:
Initial Cost = $175,000
PV of salvage value = $58,000/(1.12)5 = $32,910.76
Actual cost today = $175,000 - $32,910.76 = $142,089.20

Difference in the cost of projects today:
$142,089.20 - $74,786.32 = $67,302.93

Labor cost per month for used vehicle:
$45 x 8 x 25 = $9,000

So, we need to find out monthly savings, PV of which will be $67,302.93 at discount rate of 12%.
Formula to be used: Pmt = Lr / (1-(1+r)-t)

The present value is L, the discount rate per period is r (12%/12 = 1% per month), the number of periods is t (5 Years x 12 = 60 months), and Pmt is the monthly savings.

Pmt = [($67,302.93 x 0.01) / (1-(1+0.01)-60)] = $1,497.12

Savings required per labor hour = $1,497.12 / (8 x 25) = $7.49

So, break-even percent reduction = $7.49/$45 = 16.63%

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