A state highway department is trying to decide whether it should \"hot-patch\" a

Question

A state highway department is trying to decide whether it should "hot-patch" a short section of an existing county 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 $5,000. Alternatively, the state can resurface the road at a cost of $850,000. This surface will last 10 years if the road is maintained at a cost of $2,000 per year. No matter which alternative is selected, the road will be completely rebuilt in 10 years. At an interest rate of 8% p.a., which alternative should the state select on the basis of an ANNUAL WORTH analysis? Draw the cash flow diagram

Explanation / Answer

Alternative 1 Alternative 2 Initial Cost 210000 [300 CUBICMTR * $700] 850000 Additional cost of imp after every 2 yr 24000 0 Annual cost $5,000 2000 Life Alternative 1 Alternative 2 Calculation of PV of cash outflow Yr PFV @ 8% Amount PV Amount PV Initial Cost 0 1 210000 210000 850000 850000 Annual Cost 1-10 yr 6.710081399 5000 33550.41 2000 13420.16 Cost of Improvement 0 1 24000 24000 0 0 2 0.85733882 24000 20576.13 4 0.735029853 24000 17640.72 6 0.630169627 24000 15124.07 8 0.540268885 24000 12966.45 PRESENT WORTH 333857.8 863420.2 SUM OF pvf of 8%FOR 10 YRS 6.710081399 ANNUAL WORTH (PRESENT WORTH/SUM OF PFV FOR 10YR) 49754.65 128675.1 Itsbetter to go for Alternative 1 having less annul cash outflow

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