Problem for Self-Study

The Helicopter Division of GLD, Inc., is examining helicopter assembly costs at its Indiana plant. It has received an initial order for eight of its new land-surveying helicopters. GLD can adopt the labor-intensive method or the machine-intensive method to assemble the helicopters as per the data shown in the following table:

Screenshot of a spreadsheet shows G L D’s two method’s namely, Labor-intensive assembly method and machine-intensive assembly method.

The spreadsheet shows the computation of the coefficient “b” for an 85% learning curve and 90% learning curve.

(1) Labor-Intensive Assembly Method

  • Direct material cost per helicopter: $40,000

  • Direct -assembly labor time for first helicopter: 2,000 labor-hours

  • Learning curve for assembly labor time per helicopter: 85% cumulative average time

  • Direct -assembly labor cost: $30 per hour

  • Equipment-related indirect manufacturing cost: $12 per direct-assembly labor-hour

  • Material-handling-related indirect manufacturing cost: 50% of direct material cost

(2) Machine-Intensive Assembly Method

  • Direct material cost per helicopter: $36,000

  • Direct -assembly labor time for first helicopter: 800 labor-hours

  • Learning curve for assembly labor time per helicopter: 90% incremental unit time

  • Direct -assembly labor cost: $30 per hour

  • Equipment-related indirect manufacturing cost: $45 per direct-assembly labor-hour

  • Material-handling-related indirect manufacturing cost: 50% of direct material cost

(3) Learning curve for assembly labor time per helicopter for an 85% learning curve is calculated by using the formula on page 384.

  • b equals the quotient of log natural 0.85 and log natural 2 which equals negative 0.162519 divided by 0.693147 which equals negative 0.234465

(4) Learning curve for assembly labor time per helicopter for an 90% learning curve is calculated by using the formula on page 385.

  • b equals the quotient of log natural 0.90 and log natural 2 which equals negative 0.105361 divided by 0.693147 which equals negative 0.152004.

Required

  1. How many direct-assembly labor-hours are required to assemble the first eight helicopters under (a) the labor-intensive method and (b) the machine-intensive method?
  2. What is the total cost of assembling the first eight helicopters under (a) the labor-intensive method and (b) the machine-intensive method?

Solution

  1. 1. 
    1. a. The following calculations show the labor-intensive assembly method based on an 85% cumulative average-time learning model:
Screenshot of a spreadsheet shows the cumulative calculation of total time and individual time on an 85% cumulative average-time learning model.

Details of the spreadsheet are as follows:

Cumulative number of units: 1

  • Cumulative average time per unit: Labor hours: 2,000

  • Cumulative total time: Labor hours (Calculated by multiplying the number of units with the cumulative average time per unit): 2,000

  • Individual time for 1st unit in Labor hours: 2,000

Cumulative number of units: 2

  • Cumulative average time per unit: Labor hours: 1,700 (product of 2000 and 0.85)

  • Cumulative total time: Labor hours (Calculated by multiplying the number of units with the cumulative average time per unit): 3,400

  • Individual time for 2nd unit in Labor hours: 1,400

Cumulative number of units: 3

  • Cumulative average time per unit: Labor hours: 1,546

  • Cumulative total time: Labor hours (Calculated by multiplying the number of units with the cumulative average time per unit): 4,637

  • Individual time for 3rd unit in Labor hours: 1,237

Cumulative number of units: 4

  • Cumulative average time per unit: Labor hours: 1,445 (product of 1,700 and 0.85)

  • Cumulative total time: Labor hours (Calculated by multiplying the number of units with the cumulative average time per unit): 5,780

  • Individual time for 4th unit in Labor hours: 1,143

Cumulative number of units: 5

  • Cumulative average time per unit: Labor hours: 1,371

  • Cumulative total time: Labor hours (Calculated by multiplying the number of units with the cumulative average time per unit): 6,857

  • Individual time for 5th unit in Labor hours: 1,077

Cumulative number of units: 6

  • Cumulative average time per unit: Labor hours: 1,314

  • Cumulative total time: Labor hours (Calculated by multiplying the number of units with the cumulative average time per unit): 7,884

  • Individual time for 6th unit in Labor hours: 1,027

Cumulative number of units: 7

  • Cumulative average time per unit: Labor hours: 1,267

  • Cumulative total time: Labor hours (Calculated by multiplying the number of units with the cumulative average time per unit): 8,871

  • Individual time for 7th unit in Labor hours: 987

Cumulative number of units: 8

  • Cumulative average time per unit: Labor hours: 1,228.25 (product of 1,445 and 0.85)

  • Cumulative total time: Labor hours (Calculated by multiplying the number of units with the cumulative average time per unit): 9,826

  • Individual time for 8th unit in Labor hours: 955.

  1. Cumulative average-time per unit for the Xth unit in column H is calculated as y=aXb;  see Exhibit 10-11. For example, when X=3, y=2,000×3−0.234465=1,546 labor‐hours.  It requires a total of 9,826 direct assembly labor-hours to assemble the first 8 helicopters.
  2. b. The following calculations show the machine-intensive assembly method based on a 90% incremental unit-time learning model:
Screenshot of a spreadsheet shows the cumulative calculation of total time and average time on a 90% incremental unit-time learning model.

Details of the spreadsheet are as follows:

Cumulative number of units: 1

  • Individual unit time for 1st unit in Labor hours: 800

  • Cumulative total time in Labor hours: 800

  • Cumulative average time per unit in Labor hours (calculated by dividing the total time with number of units): 800

Cumulative number of units: 2

  • Individual unit time for 2nd unit in Labor hours: 720 (product of 800 and 0.9)

  • Cumulative total time in Labor hours: 1,520

  • Cumulative average time per unit in Labor hours (calculated by dividing the total time with number of units): 760

Cumulative number of units: 3

  • Individual unit time for 3rd unit in Labor hours: 677

  • Cumulative total time in Labor hours: 2,197

  • Cumulative average time per unit in Labor hours (calculated by dividing the total time with number of units): 732

Cumulative number of units: 4

  • Individual unit time for 4th unit in Labor hours: 648 (product of 720 and 0.9)

  • Cumulative total time in Labor hours: 2,845

  • Cumulative average time per unit in Labor hours (calculated by dividing the total time with number of units): 711

Cumulative number of units: 5

  • Individual unit time for 5th unit in Labor hours: 626

  • Cumulative total time in Labor hours: 3,471

  • Cumulative average time per unit in Labor hours (calculated by dividing the total time with number of units): 694

Cumulative number of units: 6

  • Individual unit time for 4th unit in Labor hours: 609

  • Cumulative total time in Labor hours: 4,081

  • Cumulative average time per unit in Labor hours (calculated by dividing the total time with number of units): 680

Cumulative number of units: 7

  • Individual unit time for 7th unit in Labor hours: 595

  • Cumulative total time in Labor hours: 4,676

  • Cumulative average time per unit in Labor hours (calculated by dividing the total time with number of units): 668

Cumulative number of units: 8

  • Individual unit time for 8th unit in Labor hours: 583 (product of 648 and 0.9)

  • Cumulative total time in Labor hours: 5,258

  • Cumulative average time per unit in Labor hours (calculated by dividing the total time with number of units): 657.

  1. Individual unit time for the Xth unit in column H is calculated as y=aXb ; see Exhibit 10-12. For example, when X=3, y=800×3−0.152004=677 labor‐hours.  It requires a total of 5,258 direct assembly labor-hours to assemble the first 8 helicopters.
  2. 2. Total costs of assembling the first eight helicopters are as follows:
Screenshot of a spreadsheet shows the total cost of assembly in the labor-intensive assembly method using data from part 1a and machine-intensive assembly method using data from part 1b.

Details of the spreadsheet are as follows:

(A) Labor-intensive assembly method

(1) Direct materials (8 helicopters times $40,000 per helicopter): $320,000

(2) Direct-assembly labor (9,826 hours times $30 per hour): 294,780

(3) Indirect manufacturing costs

  • Equipment related (9,826 hours times $12 per hour): 117,912

  • Materials-handling related (0.50 times $320,000): 160,000

(4) Total assembly costs: $892,692

(B) Machine-intensive assembly method

(1) Direct materials (8 helicopters times $36,000 per helicopter): $288,000

(2) Direct-assembly labor (5,258 hours times $30 per hour): 157,740

(3) Indirect manufacturing costs

  • Equipment related (5,258 hours times $45 per hour): 236,610

  • Materials-handling related (0.50 times $288,000): 144,000

(4) Total assembly costs: $826,350.

  1. The machine-intensive method’s assembly costs are $66,342 lower than the labor-intensive method ($892,692 − $826,350).