The city of Middleville is considering offering public bus service. Setting up t
ID: 2736625 • Letter: T
Question
The city of Middleville is considering offering public bus service. Setting up the service will cost the city $1.7M (where M stands for million). The useful life of the buses is 18 years. Annual maintenance of the buses would cost $135,000 per year and they would need a major overhaul in year 10 that will cost a total of $890,000. This overhaul is in addition to the annual maintenance. Annual labor and administrative costs will begin at $170,000 in year 1 and grow at 1.0% per year thereafter. The buses will generate a revenue of $305,000 in year 1 and it will grow at 4.0% per year thereafter. Reduced parking requirements and other benefits generated by the project will save the city $405,000 per year. The salvage value (price the city can get in the future after maintenance) of the used buses in year 18 is expected to be $480,000. What is the NPV of the bus proposal? The city does not pay taxes and the discount rate is 6.3%. Assume that all cash flows except initial investments happen at the end of the year and you are strongly encouraged to use a spreadsheet to solve this problem.
Explanation / Answer
Annual maintenance cost = $135,000
Useful life of buses = 18 years
Discount rate = 6.3% = 0.063
Present value of annuity = Annuity*{1 – (1+r)-n}/r
Present value of annual maintenance costs = $135,000*(1-1.063-18)/0.063 = $135,000 * 10.5878 = $1,429,353
Present value of Major overhaul cost = $890,000/1.06310 = $890,000/1.8422 = $483,118.01
Present value of growing annuity = P/(r-g) * [1 – {(1+g)/(1+r)}n]
Present value of annual labor and administrative costs = $170,000/(0.063-0.01) * {1 – (1.01/1.063)18} = $3,207,547.17 * 0.6017 = $1,929,981.13
Present value of annual revenue = $305,000/(0.063-0.04) * {1-(1.04/1.063)18} = $13,260,869.57*0.3255 = $4,316,413.05
Present value of other annual benefits = $405,000 * 10.5878 = $4,288,059
Present value of salvage value = $480,000/1.8422 = $260,558.03
Net present value = - Cost of setting up service - Present value of annual maintenance costs – Present value of major overhaul costs – Present value of annual labor and administrative costs + Present value of annual revenue + present value of other annual benefits + present value of annual salvage value
Net present value = - $1,700,000 - $1,429,353 - $483,118.01 - $1,929,981.13 + $4,316,413.05 + $4,288,059 + $260,558.03 = $3,322,577.94
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