A company is developing a new product. During its expected life it is expected that 8,000 units of the product will be sold for $90 per unit.
The direct material and other non-labour related costs will be $45 per unit throughout the life of the product.
Production will be in batches of 1,000 units throughout the life of the product. The direct labour cost is expected to reduce due to the effects of learning for the first four batches produced. Thereafter the labour cost will remain at the same cost per batch as the 4th batch. The direct labour cost of the first batch of 1,000 units is expected to be $40,000 and a 90% learning effect is expected to occur.
There are no fixed costs that are specific to the product.
Required:
(a)
(i) Calculate the average direct labour cost per batch of the first four batches.
(ii) Calculate the direct labour cost of the 4th batch.
(iii) Calculate the contribution earned from the product over its lifetime.
Note: The learning index for a 90% learning curve = -0.152
Due to the low lifetime product volume of 8,000 units the company now believes that learning may continue throughout its entire product life.
(b) Calculate the rate of learning required (to the nearest whole percentage) to achieve a lifetime product contribution target of $150,000, assuming that a constant rate of learning applies throughout the product's life.