-40 Cost estimation, cumulative average-time learning curve. The Pacific Boat 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 Pacific Boat submit a proposal on the cost of producing another six PT109s. Pacific Boat reports the following cost information for the first PT109 assembled and uses a 90% cumu-lative average-time learning model as a basis for forecasting direct manufacturing labor-hours for the next six PT109s. (A 90% learning curve means b = -0.152004.)

Direct material cost

Direct manufacturing labor time for first boat Direct manufacturing labor rate

Variable manufacturing overhead cost

Other manufacturing overhead Tooling costsa

Learning curve for manufacturing labor time per boat bUsing the formula (page 391) for a 90% learning curve,

ln 0.9 ln 2

$ 199,000 14,700 labor hours

$ $

42 per direct manufacturing labor-hour 26 per direct manufacturing labor-hour 20% of direct manufacturing labor costs

$ 279,000 90% cumulative average timeb

aTooling can be reused at no extra cost because all of its cost has been assigned to the first deployment boat. b 5

5

]0.105361 0.693147

5 ]0.152004

1. Calculate predicted total costs of producing the six PT109s for the Navy. (Pacific Boat will keep the first deployment boat assembled, costed at $1,477,600, 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 six PT109s in requirement 1 and (b) the predicted total costs for producing the six 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.