Learning Curves (Appendix B)
Refer to the example in Appendix B. The numbers in Exhibit 5.21 for the fifth, sixth, and seventh units were given.
|
Labor Time |
|
|
|
|
Required to |
|
|
|
|
Produce the X th |
|
|
|
|
Unit (i.e., the last |
Cumulative |
|
|
Unit |
single unit |
Total Time |
|
|
Produced |
produced)1 |
in Labor |
Total |
Average Cost |
(X ) |
(Y ) |
Hours2 |
Cost3 |
per Unit4 |
1 |
100 |
100 |
$ 5,000.00 |
$5,000.00 |
2 |
80 |
180 |
9,000.00 |
4,500.00 |
3 |
70.21 |
250.21 |
12,510.50 |
4,170.17 |
4 |
64 |
314.21 |
15,710.50 |
3,927.63 |
5 |
59.56 |
373.77 |
18,688.50 |
3,737.70 |
6 |
56.17 |
429.94 |
21,497.00 |
3,582.83 |
7 |
53.45 |
483.39 |
24,169.50 |
3,452.78 |
8 |
51.2 |
534.59 |
26,729.50 |
3,341.19 |
Exhibit 5.21
Learning Curve Time and Costs
1 Going down the column, the labor time for each unit comes from the formula, Y = aXb. For example, the labor time to produce the third unit is found as follows: Y _ 100 hours to produce the first unit times 3, because this is the third unit produced, to the exponent 0.3219, which is the learning rate coefficient for an 80% learning rate.
So,
Y = 100 × 3 0.3219 = 70.21 hours
2 This is the sum of the hours worked on the units. For example, three units requires
100.00 + 80.00 + 70.21 = 250.21 hours
3 This is the total cost of the labor time worked, which is the cumulative total time in labor hours times the $50 per hour labor cost given in the text on page 169. For example, the total cost of producing three units = 250.21 hours × $50 = $12,510.50.
4 This is the average cost per unit, which is the total cost of the units produced divided by the number of units produced. For example, the average cost per unit of producing three units = $12,510.50 ÷ 3 = $4,170.17.
Required
Using the formula Y = aXb and the data given in the problem, verify the labor time required and the cost amounts for the fi fth, sixth, and seventh units. (“Verify” means that you should check the accuracy of the amounts given in Exhibit 5.21.)