The city of Middleville is considering offering public bus service. Setting up t
ID: 2652140 • Letter: T
Question
The city of Middleville is considering offering public bus service. Setting up the service will cost the city $1.4M (where M stands for million). The useful life of the buses is 18 years. Annual maintenance of the buses would cost $120,000 per year and they would need a major overhaul in year 10 that will cost a total of $755,000. This overhaul is in addition to the annual maintenance. Annual labor and administrative costs will begin at $165,000 in year 1 and grow at 2.0% per year thereafter. The buses will generate a revenue of $275,000 in year 1 and it will grow at 5.5% per year thereafter. Reduced parking requirements and other benefits generated by the project will save the city $320,000 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 $405,000. What is the NPV of the bus proposal? The city does not pay taxes and the discount rate is 5.2%. 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
orrect answer is $2847180.43
work is shown as below:
Year Initial Investment Annual Maintenance Major overhaul Annual labor and administrative cost Revenue Other Benefits Salvage Value 0 1100000 1 86000 120000 170000 270000 2 86000 123000 177650 270000 3 86000 126075 185644.25 270000 4 86000 129226.875 193998.2413 270000 5 86000 132457.5469 202728.1621 270000 6 86000 135768.9855 211850.9294 270000 7 86000 139163.2102 221384.2212 270000 8 86000 142642.2904 231346.5112 270000 9 86000 146208.3477 241757.1042 270000 10 86000 149863.5564 252636.1739 270000 11 86000 153610.1453 264004.8017 270000 12 86000 157450.3989 275885.0178 270000 13 86000 161386.6589 288299.8436 270000 14 86000 165421.3254 301273.3365 270000 15 86000 169556.8585 314830.6367 270000 16 86000 173795.78 328998.0153 270000 17 86000 178140.6745 343802.926 270000 18 86000 182594.1913 359274.0577 270000 19 86000 187159.0461 375441.3903 270000 20 86000 191838.0223 392336.2528 270000 21 86000 560000 196633.9728 409991.3842 270000 22 86000 201549.8222 428440.9965 270000 23 86000 206588.5677 447720.8414 270000 24 86000 211753.2819 467868.2792 270000 25 86000 217047.1139 488922.3518 270000 26 86000 222473.2918 510923.8576 270000 27 86000 228035.1241 533915.4312 270000 290000 Discount Rate = 5.9% Present Value of Annual maintenance = 86000*(1-1/1.059^27)/.059 = 1147560.14 Present Value of over haul = 560000/1.059^21 = 168024.59 Present Value of other benefits = 270000*(1-1/1.059^27)/.059 = 3602805.09 Present value of Salvage value = 290000/1.059^27 = 61688.91 Following calculation is as per the formula of growing annuity. Present value = P/(r-g) *( 1 - ((1+g)/(1+r))^n) Present value of Annual labor and admin. Cost = 120000/(.059 - .025)*(1-(1.025/1.059)^27) = 2067046.80 Present Value of Revenue = 170000/(.059-.045)*(1-(1.045/1.059)^27) = 3665317.98 Now, NAV = Present value of Revenue + Present value of salvage value + present value of other benefits - initial investments - Present value of maintenance cost - present value of over haul - present value of annual labor and admin cost NAV = 3665317.98 + 61688.91 + 3602805.09 - 1100000 -1147560.14 - 168024.59 - 2067046.8 NAV= $2847180.45Related Questions
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