United Research Associates (URA) had received a contract to produce two units of
ID: 391474 • Letter: U
Question
United Research Associates (URA) had received a contract to produce two units of a new cruise missile guidance control. The first unit took 4,000 hours to complete and cost $40,000 in materials and equipment usage. The second took 2,800 hours and cost $24,000 in materials and equipment usage. Labor cost is charged at $18 per hour. The company expects “learning” to occur relative to labor and also relative to the pricing of materials and equipment.
The prime contractor has now approached URA and asked to submit a bid for the cost of producing another 20 guidance controls. Use Exhibit 6.4 and Exhibit 6.5.
a. What will the last unit cost to build? (Round your answer to the nearest dollar amount.) Cost of last unit b. What will be the average time for the 20 missile guidance controls? (Round your answer to the nearest whole number.) Average time c. What will the average cost be for guidance control for the 20 in the contract? (Round your answer to the nearest dollar amount.) Average cost hoursExplanation / Answer
According to learning curve theory, the time per unit decreases at a constant rate each time the output doubles (e.g., unit 1 to 2, 2 to 4, and 3 to 6). The ratios of these observed times will give us an approximate rate.
Learning curve for Labor time = Time for unit 2/Time for Unit 1 = 2800/4000 = 70%
Learning curve for Pricing = Time for unit 2/Time for Unit 1 = 24000/40000 = 60%
a) Total units to build are 2+20 = 22 units
Time to build 22nd unit = Time for 1st unit*Learning curve factor for 22nd unit at 70% = 4000*.2038 = 815.2 hours
Labor cost at 18$ per hour = 815.2*18 = 14673.6 $
Material cost for 22nd unit = Cost for 1st* Learning curve factor for 22nd unit at 60% = 40000*0.1025 = 4100$
Total cost = 14673.6 + 4100 = 18773.6 $
b) Total time to build 22nd units = Time for 1st unit*Total time factor for 22 units at 70% curve = 4000*7.819 = 31276
Time for next 20 units = Time for 22 units - Time for 1st & 2nd unit = 31276 - 4000 - 2800 = 24476 hours
Average time = 24476/20 = 1223.80 hours = 1224 hours
c) Total material to build 22nd units = material cost for 1st unit*Total time factor for 22 units at 60% curve = 40000*5.379 = 215160
Material Cost for next 20 units = Material Cost for 22 units -Material cost for 1st & 2nd unit = 215160 - 40000 - 24000 = 151160
Labor cost from b) = 24476*18 = 440568
Total cost for next 20 items = 151160+440568 = 591728 $
Average cost = 591728/20 = 29584.4 $ = 29586 $
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