Johnson Industries received a contract to delelop and produc

Johnson Industries received a contract to delelop and produce four high-density long-distance receiver/transmitters for cellular telephones. The first took 2,400 labor hours and $42,000 worth of purchased and manufactured parts; the second took 1,580 labor hours and $31,920 in parts; the third took 1,300 labor hours and $27,770 in parts; and the fourth took 1,011 labor hours and $23,620 in parts. a. How many labor hours should Johnson estimate are needed for the additional 12 units? b. How much should Johnson estimate the parts cost will be for the additional 12 units?

Solution

a.  

Learning curve % for labor hours:

Learning % for 1-2 units = 1580/2400 = 65.83%

Learning % for 2-3 units = 1300/1580 = 82.28%

Learning % for 3-4 units = 1011/1300 = 77.77%

Average learning % = (65.83+82.28+77.77)/3 = 75.29% or 75% (rounded off).

If additional 12 units are required then cumulative total = 4+12 = 16

For 16 units the cumulative index at 75% = 7.635. Thus total time required to produce extra 12 units (apart from the 4 units already produced) = 7.635*2400 = 18,324 hours

b. parts cost:

Learning % for 1-2 units = 31920/42000 = 76%

Learning % for 2-3 units = 27770/31920 = 87%

Learning % for 3-4 units = 23620/27770 = 85.06%

Average learning % = 76%+87%+85.06%/3 = 82.68%. This will be rounded off to the nearest 85%. For 16 units cumulative index at 85% = 10.383

Thus parts cost for additional 12 units = 42000*10.383 = $436,086