28.03.2023 - 08:51

# Old Town needs to resurface a section of its roads this spring. The town council is considering using one of two technologies. The first involves putting down stone and gravel the first year and gradi

Question:

Old Town needs to resurface a section of its roads this spring. The town council is considering using one of two technologies. The first involves putting down stone and gravel the first year and grading the road on an annual basis for the next 10 years. The second involves the application of a road surface called Sure-Pack. Sure- Pack requires maintenance only every five years. Based on experience, the town counselors know the gravel road will last 10 years. The folks in Hilltown, the next town up Route 1, Sure-Packed their roads and expect to get 15 years from them before they will need to be resurfaced again. The cash flows for each alternative are shown in the table below which continues in the next column.

If Old Town’s discount rate is 8 percent, which alternative should they choose? Use an annualized cost analysis to support your answer.

Year Gravel sure – pack
0 $200000$300000
1 15000
2 15000
3 15000
4 15000
5 15000 55000
6 15000
7 15000
8 15000
9 15000
10 15000 55000
11
12
13
14
15
Old Town should choose the Sure-Pack alternative because it has a lower annualized cost. To calculate the annualized cost, we need to find the present value of all cash flows for each alternative using the discount rate of 8%. For the Gravel alternative, the present value of the initial cost of $200,000 is simply$200,000. For the annual maintenance costs, we can use the formula for the present value of an annuity to find that the total present value of the maintenance costs for the 10 years is $103,639. Therefore, the total present value of the Gravel alternative is$303,639. For the Sure-Pack alternative, the present value of the initial cost of $300,000 is$300,000. The present value of the maintenance cost at year 5 is $35,331. Therefore, the total present value of the Sure-Pack alternative is$335,331. To compare the two alternatives, we need to annualize the costs. The formula for annualized cost is the present value of costs divided by the present value of an annuity factor. The factor is calculated using the formula for the present value of an annuity factor with the discount rate and number of years. For the Gravel alternative, the annualized cost is $36,384. For the Sure-Pack alternative, the annualized cost is$29,802. Therefore, Old Town should choose the Sure-Pack alternative because it has a lower annualized cost.