Cost estimation, cumulative average-time learning curve. Cost estimation, cumulative average-time learning curve. The Nautilus Company, which is under contract to the U.S. Navy, assembles troop deployment boats. As part of its research program, it completes the assembly of the first of a new model (PT109) of deployment boats. The Navy is impressed with the PT109. It requests that Nautilus submit a proposal on the cost of producing another seven PT109s.

Nautilus reports the following cost information for the first PT109 assembled and uses an 85% cumulative average-time learning model as a basis for forecasting direct manufacturing labor-hours for the next seven PT109s. (An 85% learning curve means b = – 0.234465.):

1. Calculate predicted total costs of producing the seven PT109s for the Navy. (Nautilus will keep the first deployment boat assembled, costed at $725,000, as a demonstration model for potential customers.)

2. What is the dollar amount of the difference between (a) the predicted total costs for producing the seven PT109s in requirement 1, and (b) the predicted total costs for producing the seven PT109s, assuming that there is no learning curve for direct manufacturing labor? That is, for (b) assume a linear function for units produced and direct manufacturing labor-hours.

1 Direct material $100,000 10,000 labor-hours 30 per direct manufacturing labor-hour 20 per direct manufacturing labor-hour 2 Direct manufacturing labor time for first boat 3 Direct manufacturing labor rate 4 Variable manufacturing overhead cost 5 Other manufacturing overhead 6 Tooling costs 25% of direct manufacturing labor costs $500,000 85% cumulative average time" 7 Learning curve for manufacturing labor time per boat 8. 9 Tooling can be reused at no extra cost because all of its cost has been assigned to the first deployment boat. 10 11 PUsing the formula (p. 356), for an 85% learning curve, b = 12 -0.162519 In 0.85 In 2 = -0.234465 0.693147