Question

Problem 1) The City of Bryan is currently paying a local repair shop to maintain their fleet of asphalt trucks. The shop charges $450 per truck per month. The City estimates that for an initial cost of $150,000 they could open their own repair facility and handle the repairs at a cost of $200/truck/month, including all wages, overhead, etc. At the end of 100 months they will close the facility, which will have a $60,000 salvage value. If the city’s nominal MARR is 12%/year, how many trucks would they have to have in their fleet to make the change economically attractive?

Answer 1

Current charges =$450 per truck per month, with own facility charges=$200 per truck per month so net benefit per month per truck=450-200=$250

Now MARR=12% per annum=12/12=1% per month

Present value of total cash flow =0 will determine minimum fleet required Hence,

-150000+200*x/1.01+200*x/1.01^2+....200*x/1.01^100+60000/1.01^100 assuming x as the number of trucks in the fleet

Sum of gp=a(1-r^n)/(1-r) with a as first term and r as common difference for total n term

-150000+60000/1.01^100+200x/1.01(1-(1/1.01)^100)/(1-(1/100))=0 gives,12605.78x=127817.33=10.14 or minimum 11 trucks has to be there in the fleet to make this economically attractive