10-4: For the data in Problem 10-2 assume that the 5000, 10,000, and 15,000 mile

Question

10-4: For the data in Problem 10-2 assume that the 5000, 10,000, and 15,000 mileage values are, respectively, pessimistic, mots likely, and optimistic estimates. Use a weighted estimate to calculate the equivalent annual cost.

(Problem 10-2: The purchase of a used pickup for $9000 is being considered. Records for other vehicles show that costs for oil, tires and repairs about equal the cost for fuel. Fuel costs are $990 per year if the truck is driven 10,000 miles. The salvage value after 5 years of use drops about 8% per mile. Find the equivalent uniform annual cost if the interest rate is 8%. How much does this change if the annual mileage is 15,000? 5000?)

Explanation / Answer

Since the pessimistic and optimistic answers are symmetric about the most likely value of 16,000, the weighted average is 16,000 km. If 16,000 km per year, then

fuel cost = oil/tires/repair = $990/year, and salvage value = 8,000 - 5x16,000x.05 = 9,000 – 4,000 = 5,000

Therefore,

EUAC16,000 = 9,000(A/P,8%,5) + 2x990 – 5,000(A/F,8%,5) = 9,000x.2505 + 1980 – 5,000x.1705

                 = 2,254.5 + 1,980 - 852.5 = $3,382

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