1. A new highway will be constructed and there are two options, designed around
ID: 3143972 • Letter: 1
Question
1. A new highway will be constructed and there are two options, designed around the choice of material for the road surface. Choice A is to use an asphalt surface and B uses concrete.
A: Asphalt The cost for this road is $150/m, two ditches (with grass) at $5/m plus and two concrete culverts, each costing $2500/km. The lifetime of the road and ditches is 10 years and can be replaced at the end of that time at a cost 15% higher than the initial cost. The culverts have a 20 year lifetime. Annual maintenance is $3000/km for the road surface and $0.5/m for each ditch, but this maintenance does not have to be done in year 10 when the road and ditches are redone. The culverts must be cleaned once a year for $100/km each.
B: Concrete The cost for this road is $300/m, plus two paved ditches at $10/m each and two concrete culverts, each costing $2500/km. The lifetime of this structure is 20 years. Annual maintenance is $600/km for the road surface and $0.5/m for each ditch. The culverts must be cleaned once a year for $100/km each.
Compare the two designs base on their present value of total cost/km, assuming that the desired economic life of the road is 20 years. Plot the present value of the total cost/km of both choices as a function of discount rate between i=0 and i=0.1. (Don’t forget the case of the limit where i => 0.) Note the break-even point for the discount rate and make a recommendation based on your results. There is no total length of the road, but rather a comparison for cost/km for the two options.
Explanation / Answer
a)
Cost of the road=150/m
= 150000/km
Two ditches = 5/m
= 5000/km
Two concrete culverts=2500(2) =5000/km
At 11th year replacement of cost of road=150+15%=172.5/m=172500/km
Present value of replacement of cost of road=172500((1/1+0.1)10) =172500(0).466=80385/km
At 11th year replacement of cost of ditches=5+15%=5.75/m=5750/km
Present value of replacement of cost of ditches=5750(1/1+0.1)10=5750(0.466=2680)/km
Annual maintenance= 3000/km per year for road and 1000/km for ditches but not required in year 10 and 100/km for culverts
= (4100(19)) +100=78000
Present value of annual maintenance= (4100(5.867))+(100(0.466))+(4100(2.688))
=35122
Total cost when i=0
150000+5000+5000+172500+5750+78000=416250
Total cost when i=0.1
150000+5000+5000+80385+2680+35122=278187
B) Concrete
Cost of the road=300/m
= 300000/km
Two ditches = 10
= 20000/km
Two concrete culverts=2500(2) = 5000/km
Annual maintenance= 600/km per year for road and 1000/km for ditches and 100/km for culverts
=1700(20) =34000/km
Present value of annual maintenance=1700(9.021)
=15336
Total cost when i=0
300000+20000+5000+34000=359000
Total cost when i=0.1
300000+20000+5000+15336=340336
When i>0, recommendation is to use Asphalt.
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