Learning Curves 2

Hi Sir

Another question on learning curves

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, certainly for the first four batches produced. 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. The learning index for a 90% learning curve = –0.152

The Finance Director also wishes to consider what will happen if learning continues throughout the product’s life..

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.

Solution.

Contribution= Sales- VC
= 8000*(90-45)
=360,000
we want a contribution of 150,000 so we need a VC of 360,000-150,000=210,000

this is where I get stuck.. since I am not sure on the next steps.