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. Comment on sensitivity of the two total values to the value of the discount rate.