A company is developing a new product. During its expected life, 16,000 units of the product will be sold for $82 per unit.
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 eight batches produced. Thereafter, the direct labour cost will remain constant at the same cost per batch as the eighth batch.
The direct labour cost of the first batch of 1,000 units is expected to be $35,000 and a 90 per cent learning effect is expected to occur.
The direct material and other non-labour related variable costs will be $40 per unit throughout the life of the product. There are no fixed costs that are specific to the product.

Required:

(a) (i) Calculate the expected direct labour cost of the eighth batch.

(ii) Calculate the expected contribution to be earned from the product over its lifetime.

(b) It is now thought that a learning effect will continue for all of the 16 batches that will be produced.

Calculate the rate of learning required to achieve a lifetime product contribution of $400,000, assuming that a constant rate of learning applies throughout the product’s life.