P1036 similar to Question Help The WLJ Boat Company which i

P10-36 (similar to) Question Help * The WLJ 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 WLJ Boat submit a proposal on the cost of producing another six PT109sWLJ Boat reports the following cost information for the first PT109 assembled WLJ Boat uses a 90% ncremental unit time learning model as a basis for predicting direct manufacturing labor-hours in its assembling operations. (A 90% learning curve means b·-0.152004.) (Click the icon to view the cost information.) Read the requirements Requirement 1. Prepare a prediction of the total costs for producing the six PT 109s for the Navy. Begin by calculating the cumulative total time in labor-hours. (Round the individual unit time for Xth unit to the nearest whole number.) Number of Individual unit time for Cumulative total time: units Xth unit: Labor-hours Data Table Direct material Direct manufacturing labor time for first boat Direct manufacturing labor rate Variable manufacturing overhead cost Other manufacturing overhead Tooling costs Learning curve for manufacturing labor time per boat $202,000 15,700 labor-hours $46 per direct manufacturing labor-hour $29 per direct manufacturing labor-hour 15% of direct m anufacturing labor costs $282,000 90% incremental unit-timeb Tooling can be reused at no extra cost because all of its cost has been assigned to the first deployment boat In 0.90 0.105361 .693147 b Using the formula for a 90% learning curve. 0.152004 Print Done

Solution

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Calculation of the direct manufacturing labor-hours	b=	-0.152004	90% LC
to produce the 2nd to 7th boats can be calculated			Individual
as follows: y = aXb (to the power of b) where		Cumulative	Unit Time for	Cumulative
y = Time (in labor-hours) to produce the most recent unit	# of	Xth Unit (y)	Total Time:
a = labor hours required for first unit		Units	Labor-Hrs.	Labor-Hrs.
X = cumulative number of units	y=aXb	1	15,700	15,700
b = ln(learning-curve % in decimal form) / ln2		2	14,130	29,830
b = ln 0.90 / ln2 = -0.152004		3	13,285	43,115
		4	12,717	55,832
		5	12,293	68,125
		6	11,957	80,082
		7	11,680	91,762
The DLHs required to produce the 2nd through the 7th boats			76,062
		Incremental
		Unit-time Learning
Cost to produce the 2nd through 7th boats		Model
Direct materials, 6 X $202,000		$1,212,000
Direct manufacturing labor (DML)		$3,498,852
Variable mfg. Overhead		$2,205,798
Other mfg. Overhead (15% of DML$)		$524,828
Total costs for boats 2 through 7		$7,441,478
2. Compare the cost of the 2nd - 7th boats using the \"Incremental Unit-time Learning Model\" with the costs of the 2nd - 7th
boats using the \"Cumulative Average-time Learning Model:
DLH Req		76,062	66,060
		Incremental	Cumulative
		Unit-time Learning	Average-time
Cost to produce the 2nd through 7th boats		Model	Learning Model
Direct materials, 6 X $202,000		$1,212,000	$1,212,000
Direct manufacturing labor (DML) (DLH x rate)		$3,498,852	$3,038,760
Variable mfg. Overhead (DLH x rate)		$2,205,798	$1,915,740
Other mfg. Overhead (15% of DML$)		$524,828	$455,814
Total costs for boats 2 through 7		$7,441,478	$6,622,314
Difference			($819,164)
Why are the predictions different?
The incremental unit-time learning curve has a slower rate of decline in the time required to produce successive units
than does the cumulative average-time learning curve even though the same 90% factor is used for both curves.
The reason is that, in the incremental unit-time learning model, as the number of units double, only the last unit
produced has a time of 90% of the initial time. In the cumulative average-time learning model, doubling the number
of units causes the average time of all the additional units produced (not just the last unit) to be 90% of the initial time.
			Cumulative	Incremental
			Average-time	Unit-time Learning
			Learning Model	Model
		Cumulative	Cumulative	Cumulative
		# of	Total Time:	Total Time:
		Units	Labor-Hrs.	Labor-Hrs.
		1	15,700	15,700
		2	28,260	29,830
		3	39,856	43,115
		4	50,868	55,832
		5	61,464	68,125
		6	71,741	80,082
		7	81,760	91,762
How should WLJ Boat decide which model it should use?
The company should examine its own internal records on past jobs and seek information from engineers, plant managers, and workers
when deciding which learning curve better describes the behavior of direct manufacturing labor-hours on the production of the PT109
boats.