Question

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.

Answer 1

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