Question
In: Finance
The pavement in a new parking lot is expected to require no maintenance for the first...
The pavement in a new parking lot is expected to require no maintenance for the first two years of its life. At EOY3, the first resurfacing will have to be made costing $50,000. Every two years thereafter, the lot will need resurfacing. However, the cost for each resurfacing is expected to increase by 3% from the time before. The useful life of the parking lot is 26 years and no maintenance occurs in year 26.
a. What is the present worth of the resurfacing costs given a nominal discount rate of 5%.
b. Assume the parking lot costs $8,500,000 to construct. If the parking lot is expected to serve on average 400 vehicles per work day and the daily fee must cover both the amortized cost of the construction and the resurfacing costs, what should the daily per vehicle charge be? Assume that parking fees are charged only on week days (or 260 days per year).
Solutions
Expert Solution
Part a
Present worth of resurfacing costs at discount rate of 5 % is computed below :-
| Year | Maintenance Cost | PVF @ 5% | Present Value |
| a | b | c | d = b*c |
| 1 | $0.00 | 0.952 | $0.000 |
| 2 | $0.00 | 0.907 | $0.000 |
| 3 | $50,000.00 | 0.864 | $43,191.880 |
| 4 | $0.00 | 0.823 | $0.000 |
| 5 | $51,500.00 | 0.784 | $40,351.598 |
| 6 | $0.00 | 0.746 | $0.000 |
| 7 | $53,045.00 | 0.711 | $37,698.091 |
| 8 | $0.00 | 0.677 | $0.000 |
| 9 | $54,636.35 | 0.645 | $35,219.078 |
| 10 | $0.00 | 0.614 | $0.000 |
| 11 | $56,275.44 | 0.585 | $32,903.085 |
| 12 | $0.00 | 0.557 | $0.000 |
| 13 | $57,963.70 | 0.530 | $30,739.390 |
| 14 | $0.00 | 0.505 | $0.000 |
| 15 | $59,702.61 | 0.481 | $28,717.979 |
| 16 | $0.00 | 0.458 | $0.000 |
| 17 | $61,493.69 | 0.436 | $26,829.495 |
| 18 | $0.00 | 0.416 | $0.000 |
| 19 | $63,338.50 | 0.396 | $25,065.197 |
| 20 | $0.00 | 0.377 | $0.000 |
| 21 | $65,238.66 | 0.359 | $23,416.919 |
| 22 | $0.00 | 0.342 | $0.000 |
| 23 | $67,195.82 | 0.326 | $21,877.031 |
| 24 | $0.00 | 0.310 | $0.000 |
| 25 | $69,211.69 | 0.295 | $20,438.405 |
| 26 | $0.00 | 0.281 | $0.000 |
| Present Value of Maintenace/resurfacing cost | $366,448.145 |
Therefore, Present worth of resurfacing costs at discount rate of 5 % is $ 366,448.145
Part b: Determination of Daily per Vehicle charge
Total cost of Parking Lot (for 26 years) = Construction cost + Resurfacing cost
= $ 8,500,000 + $ 366,448.145 = $ 8,866,448.145
Total vehicle-days in 26 years = 400 vehicles per day * 260 days per year * 26 years
= 2,704,000 vehicle days
Daily price to be charged per vehicle = Total cost of Parking Lot / Total vehicle days
= $ 8,866,448.145 / 2,704,000 vehicle days
Daily price to be charged per vehicle = $ 3.279 (approx)
jeff jeffy answered 1 year agoRelated Solutions
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