Question #115248

An irrigation canal contractor wants to determine whether he should purchase a new Caterpillar mini excavator or a used one. The initial cost of the new excavator is $26,500 and has a lifetime of 10 years. Fixed costs for insurance are expected to be $8,000 per year. The excavator will require one operator at $15 per hour and maintenance at $1 per hour. In 1 hour, 0.16 mile of ditch can be prepared.

Alternatively, the contractor can purchase the used one and hire 2 workers at $11 per hour each. The used excavator costs $1000 and has a useful life of 5 years with no salvage value. Its operating cost is expected to be $1.20 per hour, and with the tiller, the two workers can prepare 0.04 mile of ditch in 1 hour.

Determine the number of miles of ditch per year the contractor would have to service for the two options to break even.

Alternatively, the contractor can purchase the used one and hire 2 workers at $11 per hour each. The used excavator costs $1000 and has a useful life of 5 years with no salvage value. Its operating cost is expected to be $1.20 per hour, and with the tiller, the two workers can prepare 0.04 mile of ditch in 1 hour.

Determine the number of miles of ditch per year the contractor would have to service for the two options to break even.

Expert's answer

1.FC and VC new Caterpillar mini:

FC: "26500-26500\\times0.1+8000=31850"

VC: "\\frac{(15+1)}{0.16}=100"

2.FC and VC used one

FC:"1000*0.1=200"

VC:"\\frac{(2\\times11+1.20)}{0.04}=580"

let the number of miles of the ditch per year, then we make an equation for two break even options:

"31850+100\\times x=200+580\\times x"

"31650=480\\times x"

x=65.94 the number of miles of ditch per year

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