WTI is planning to launch a new component. Production volume will be limited, with only 128 components to be produced in total.
WTI expects the manufacture of the first component to take 25 direct labour hours. It is anticipated there will be a 90 percent learning curve that will continue until all 128 components have been produced. Direct labour is paid at a rate of $15 per hour.
Non labour-related costs are expected to be $265 per component; this will apply to all 128 components produced. There are no product-specific fixed costs associated with this new component.
WTI is going to use a target costing approach for the new component. Based on the market research it has undertaken, WTI plans to sell the components for $530 each. WTI requires an average profit margin of 20 percent of the selling price over the life of this new component.
The learning index for a 90 percent learning curve = -0.152.

Required:
(a) Calculate the time required to produce the 128th component.
(b) Calculate the value of any cost gap between the target cost of 128 components in total and the expected cost of 128 components in total.
(c) Calculate the rate of learning required to close the cost gap you calculated in part (b) in order to achieve the required profit margin of 20 percent.