Consider the bridge project of given Problem. We assumed there would be no toll for crossing. Now suppose the province is considering a toll of S7 per round trip over the bridge. Thev estimate that, if the toll is charged, the number of park visits will rise to only 10 600 per year instead of 11 000.
(a) Compute the present worth of the project if the toll is charged.
(b) Why is the present worth of the project reduced by the toll?
Problem :
A province in Canada is considering the construction of a bridge. The bridge would cross a narrow part of a lake near a provincial park. The major benefit of the bridge would be reduced travel time to a campsite from a nearby urban centre. This lowers the cost of camping trips at the park. As well, an increase in the number of visits resulting from the lower cost per visit is expected.
Data concerning the number of week-Ions; visits and their costs are shown below:
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Number of visits and Average Cost per Visit to Park
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Inputs
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Without Bridge
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With Bridge
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Travel Cost
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140
|
87.5
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Use of equipment
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50
|
50
|
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Food
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100
|
100
|
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Total
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290
|
237.5
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Number of visits
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8000
|
11000
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The following data are available as well:
1. The bridge will take one year to build.
2. The bridge will have a 25-vear life once it is completed. This means that the time horizon for computations is 26 years.
3. Construction cost for the bridge is S3 750 000. Assume that this cost is incurred at the beginning of year 1.
4. Annual operating and maintenance costs for the bridge are given by S7500 + 0.25,/ where $7500 is the fixed operating and maintenance cost per year and q is the number of crossings.
5. Operating and maintenance costs are incurred at the end of each year over which the bridge is in operation. This is at the ends of years 2, 3, . . . , 26.
6. TheMARRis 10%. (Notice that the annual benefits for this project were computed as part of the discussion of Example 10.1.)
(a) Compute the present worth of the project.
(b) Compute the benefit-cost ratio.
(c) Compute the modified benefit-cost ratio.