A township is considering making upgrades to a gravel road, including repairing

Question

A township is considering making upgrades to a gravel road, including repairing some washed out sections, widening the road, adding culverts, and filling ditches. The cost of the upgrade will be $40,000. Annual costs to maintain the road will be $4000. Annual benefits to the users of the road are estimated to be $9500 per year, primarily based on reduction in incidents/accidents, and also vehicle general wear-and-tear costs.

a.What is the benefits-to-cost ratio of the road improvement option described above, assuming a MARR of 4% and a project horizon of 30 years?

b.Some of the town board members are suggesting that paving the road would be a better option than that discussed in part “a”. The cost of this project is estimated to be $150,000. Annual costs to maintain the road in this case are estimated to be $1500/year. Annual benefits to the users of the paved road due to reduction in incidents/accidents, and also vehicle general wear-and-tear costs are estimated to be $20,000 per year. Using the same MARR and time horizon as in part “a”, use benefits to costs analysis to determine whether it’s worth the additional investment to pave the road. What is your final decision, based on B/C analysis?

c.In this problem there was no salvage value- had there been one (i.e., if we’d instead analyzed equipment that could be sold at the end of the project life), how would’ve you handled it? Describe specifically how it would’ve changed your B/C equation.

d.What is the breakeven point in terms of initial cost of paving the road, when your decision as to whether go with the gravel option or paved option changes?

e.Calculate the payback period for the two options (gravel vs. paved) using the information from parts “a” and “b”. What is your decision, based on payback period? Do the results concur with part C? In economic analysis is it possible for the payback period analysis to have different results from B/C analysis? Which analysis method would you recommend? Why?

f.In this problem only the economic consequences were evaluated. Do you think this type of decision is only economic, or are there other factors that could/would/should be considered? Briefly discuss…

Explanation / Answer

A)

Upfront cost    40000

Cost                 4000

Benefit            9500

MARR            0.04

To calculate the present value of cost:

4000 * [{(1/(1+0.04)^1} + {(1/(1+0.04)^2} + {(1/(1+0.04)^3} …….+ {(1/(1+0.04)^30}] = 69,168

Similarly, to calculate present value of the benefits:

9500 * [{(1/(1+0.04)^1} + {(1/(1+0.04)^2} + {(1/(1+0.04)^3} …….+ {(1/(1+0.04)^30}] = 164,274

Now total cost incurred today by factoring in the present value of the costs to be incurred in the future, we get 69,168 + 40,000 = 109,168

Hence, benefit to cost ratio = 164274/109168 ~ 1.5

B)

Upfront cost    150000

Cost                 1500

Benefit            20000

MARR            0.04

To calculate the present value of cost:

1500 * [{(1/(1+0.04)^1} + {(1/(1+0.04)^2} + {(1/(1+0.04)^3} …….+ {(1/(1+0.04)^30}] = 25,938

Similarly, to calculate present value of the benefits:

20000 * [{(1/(1+0.04)^1} + {(1/(1+0.04)^2} + {(1/(1+0.04)^3} …….+ {(1/(1+0.04)^30}] = 345,841

Now total cost incurred today by factoring in the present value of the costs to be incurred in the future, we get 25,938 + 150,000 = 175,938

Hence, benefit to cost ratio = 345,841/175,938 ~ 1.97

C)

Had there been a salvage value at the end of period, it would have been added to the benefit since residual value is replicable value. We would have discounted it over 30 periods to get its today’s present value. Irrespective of the residual value, it would have added positively to the present value calculation of the benefits, or increased the numerator of the benefits-cost ratio.

D)

Now clearly in the second case the ratio is higher ie (1.97>1.5), so faster breakeven would be realized in the case of the second option ie paving the road option.

Beakeven is realized when the benefit-cost ratio is 1 ie Sum of present value of the benefits = sum of present value of the costs involved.

By looking at numbers derived from above, clearly it seems that sum of present value of the benefits just exceed the sum of present value of the cost in the 12th year in the case of option B), and in the 16th year in the case of option A)

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