The standard direct labour cost of one batch of 100 units of a product is $50.40. This assumes a standard time of 4.2 hours, costing $12 per hour. The standard time of 4.2 direct labour hours is the average time expected per batch based on a product life of 12,800 units or 128 batches. The expected time for the first batch was 20 hours and an 80% learning curve is expected to apply throughout the product’s life.
The company has now completed the production of 32 batches of the product and the total actual direct labour cost was $3,493. The following direct labour variances have also been calculated:
Direct labour rate $85 Adverse
Direct labour efficiency $891 Adverse
Further analysis has shown that the direct labour efficiency variance was caused solely by the actual rate of learning being different from that expected. However, the time taken for the first batch was 20 hours as expected.
Required:
(a) Calculate the actual rate of learning that occurred.
(b) Assuming that the actual rate of learning and the actual labour rate continue throughout the life of the product, calculate the total direct labour cost that the company will incur during the life of the product.
Answer:
(a)
The standard cost of the actual hours worked was $3,493 - $85 = $3,408.
At $12 per hour the actual hours worked were $3,408 / $12 = 284 hours.
So the average time per batch for the first 32 batches was 284 / 32 = 8.875 hours per batch.
32 batches represent 5 doublings of output.
The learning rate was therefore:
5 √ 8.875 / 20 = 0.85 = 85%
(b)
Actual labour rate paid = $3,493 / 284 = $12.30 per hour.
Learning index = log 0.85 / log 2 = -0.2345
Y = 20 x 128-0.2345 = 6.41 hours
Total cost of direct labour = 6.41 x 128 x $12.30 = $10,092
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