Question

United Research Associates (URA) had received a contract to produce two units of a new cruise missile guidance control. The first unit took 5,000 hours to complete and cost $30,000 in materials and equipment usage. The second took 4,500 hours and cost $24,000 in materials and equipment usage. Labor cost is charged at $20 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 hours

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            $

Answer 1

Learning rate for labour hours = Time for 2^nd unit / Time for 1^st unit = L1 = 4500/5000 = 0.90

Learning rate for material and equipment usage

= Material and equipment cost for 2^nd item / Material and equipment cost for 1^st item

= 24000/30000

= 0.80 )( or 80 % )

We will use standard learning curve to table to arrive at required answers :

Answer to question a :

The last unit will be 22^nd unit .

Using learning curve table , Time required to build 22^nd unit = 3125.49 hours

Thus , labour cost to build 22^nd unit ( @ $20 per hour ) = $20 x $3125.49 = $62509.80

Using learning curve table , material and equipment cost to build 22^nd unit = $11090.67

Therefore, total cost to build the last unit = Labour cost + Material and equipment cost = $62509.80 + $11090.67 = $73600.47 ($73600 rounded to nearest whole number )

COST OF LAST UNIT = $ 73600

Answer to question b :

Using learning curve table,

Total labour hours to build 22 missile guidance control = 79312 hours

Total labour hours to build first 2 missile guidance control = 5000 + 4500 = 9500 hours

Therefore , total time to build 20 missile control

= Total labour hours to build 22 missile control – Total labour hours to build first 2 missile control

= 79312 hours – 9500 hours

= 69812 hours

Average time for 20 missile guidance control = 69812/ 20 = 3490.60

AVERAGE T TIME FOR 20 MISSILE GUIDANCE CONTROL = 3490.60 HOURS

Answer to question c :

Total labour cost ( @$20/ hour ) to build 20 missile guidance control = $ 20/ hour x 69812 hour ( as calculated above) = $1396240

Using Learning curve table,

Total material and equipment cost to build 22 units         = $336897

Total material and equipment cost to build first 2 units = $54,000

Therefore , total material and equipment cost to build 20 missile guidance control = $336897 - $54,000 = $282897

Thus, total cost for 20 missile guidance control

= Total labour cost + Total material and equipment cost

= $1396240 + $282897

= $ 1679137

Average cost of guidance control = $1679137/20 = $83956.85 ( $83957 rounded to nearest whole number )

AVERAGE COST OF GUIDANCE CONTROL = $83957