Question

5. A state highway department is trying to decide whether it should “hot-patch” a short sectionof an existing country road or resurface it. If the hot-patch method is used, approximately 300 cubic meters of material would be required at a cost of $700 per cubic meter (in place). Additionally, the shoulders will have to be improved at the same time at a cost of $24,000. These improvements will last 2 years, at which time they will have to be redone. The annual cost of routine maintenance on the patched up road would be $5000. Alternatively, the state can resurface the road at a cost of $850,000. The surface will last 10 years if the road is maintained at a cost of $2000 per year beginning 4 years from now. No matter which alternative is selected, the road will be completely rebuilt in 10 years. At an interest rate of 9% per year,

   1. make a recommendation on the best alternative based on the annual worth analysis.

   2. make a recommendation based on the present worth method.

Answer 1

vatre of Page wo. Present T Amount to be invested in Alternative 1. Year Amount of fatching 234.000 A Annual cast Discount fects at @ 9% - Discount SOS 9,34,000 .917 842 9,34,000 o-gaucordo 2.34,000 5000 S000 5000 5000 S000 Sood SOUD 5000 SOUD 5000 .772 708 [.650 .596 .547 502 2.34000 4585 201238 3860 169212 3250 142444 2735 11 9978 2300 2110 885712 234.000 0 . - 422 Present value of amount to be in Alternative 2. Resurfacing cost = $850000 Annual wst of Repairs a 3-177 X 8000 a $6354 Total amount = 856354 using bosent value method, Alternative- should be accepted. Using Annual worth Annual wast in Altelpatinet - 12.200w 10 ĉ 122000 Annieel cost in Alternative 2 =2 870000 - 870000 10 2 still Alternate 2 is better.