Answered: TufStuff, Inc

Cornerstones of Cost Management (Cornerstones Series)

4th Edition

ISBN:9781305970663

Author:Don R. Hansen, Maryanne M. Mowen

Publisher:Don R. Hansen, Maryanne M. Mowen

Chapter10: Decentralization: Responsibility Accounting, Performance Evaluation, And Transfer Pricing

Section: Chapter Questions

Problem 4CE

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TufStuff, Inc., sells a wide range of drums, bins, boxes, and other containers that are used in the chemical industry. One of the company’s products is a heavy-duty corrosion-resistant metal drum, called the WVD drum, used to store toxic wastes. Production is constrained by the capacity of an automated welding machine that is used to make precision welds. A total of 2,000 hours of welding time is available annually on the machine. Because each drum requires 0.4 hours of welding machine time, annual production is limited to 5,000 drums. At present, the welding machine is used exclusively to make the WVD drums. The accounting department has provided the following financial data concerning the WVD drums:

WVD Drums
Selling price per drum		$	149.00
Cost per drum:
Direct materials (Variable)	$52.10
Direct labor (Variable)	3.60
VariableManufacturing overhead	1.35
Fixed Manufacturing overhead	3.15
VariableSelling and administrative expense	0.75
FixedSelling and administrative expense	29.05		90.00

Margin per drum		$	59.00

Management believes 6,000 WVD drums could be sold each year if the company had sufficient manufacturing capacity. As an alternative to adding another welding machine, management has considered buying additional drums from an outside supplier. Harcor Industries, Inc., a supplier of quality products, would be able to provide up to 4,000 WVD-type drums per year at a price of $138 per drum, which TufStuff would resell to its customers at its normal selling price after appropriate relabeling. It has been estimated that variable selling and administrative expenses amount to $0.75 per WVD drum whether it was made or purchased.

Megan Flores, TufStuff’s production manager, has suggested that the company could make better use of the welding machine by manufacturing bike frames, which would require only 0.5 hours of welding machine time per frame and yet sell for far more than the drums. Megan believes that TufStuff could sell up to 1,600 bike frames per year to bike manufacturers at a price of $239 each. The accounting department has provided the following data concerning the proposed new product:

1 Managerial Accounting, 10th Edition

778 Managerial Accounting, 10th Edition

Bike Frames
Selling price per drum		$	239.00
Cost per frame:
Direct materials (Variable)	$99.40
Direct labor (Variable)	28.80
VariableManufacturing overhead	1.90
Fixed Manufacturing overhead	34.10
VariableSelling and administrative expense	1.30
FixedSelling and administrative expense	46.50		212.00

Margin per drum		$	27.00

The bike frames could be produced with existing equipment and personnel.

As indicated earlier, the company has a welding machine that can give only 2,000 hours of welding time. Therefore, it is a constrained resource. Assume that the cost of using welding machine is fixed with respect to welding time. You want to make decisions in such a way to maximizethe company’s profit.

1. The margins of the two products are provided in the report submitted by the Accounting Department. Margin is computed by subtracting both variable and fixed costs from sales price. Would you be comfortable using the margin amounts for making decisions related to the WVD drums and bike frames? Would you rather use contribution margin instead? Why or why not?

Expert Solution

Step 1

1.The product margins computed by the accounting department for the drums and bike frames should not be used in the decision of which product to make. The product margins are lower than they should be due to the presence of allocated fixed common costs that are irrelevant in this decision. Moreover, even after the irrelevant costs have been removed, what matters is the profitability of the two products in relation to the amount of the constrained resource—welding time—that they use. A product with a very low margin may be desirable if it uses very little of the constrained resource. In short, the financial data provided by the accounting department are useless and potentially misleading for making this decision.

Assuming direct labor is a fixed cost, the contribution margin per unit for each product is calculated as follows:

		Manufactured
	Purchased WVD Drums	WVD Drums	Bike Frames
Selling price......................................................	$149.00	$149.00	$239.00
Variable costs:
Direct materials.............................................	138.00	52.10	99.40
Variable manufacturing overhead.................	0.00	1.35	1.90
Variable selling and administrative...............	0.75	0.75	1.30
Total variable cost.............................................	138.75	54.20	102.60
Contribution margin.........................................	$ 10.25	$ 94.80	$136.40

Assuming direct labor is a fixed cost, the contribution margin per welding machine hour for each product is calculated as follows:

	Manufactured
	WVD Drums	Bike Frames
Contribution margin per unit (above) (a)..................................	$94.80	$136.40
Welding hours per unit (b)........................................................	0.4 hour	0.5 hour
Contribution margin per welding hour (a) ÷ (b).......................	$237.00 per hour	$272.80 per hour

Because the contribution margin per unit of the constrained resource (i.e., welding time) is larger for the bike frames than for the WVD drums, the frames make the most profitable use of the welding machine (assuming direct labor is a fixed cost). Consequently, the company should manufacture as many bike frames as possible up to demand and then use any leftover capacity to produce WVD drums. Buying the drums from the outside supplier can fill any remaining unsatisfied demand for WVD drums. The necessary calculations are carried out below.

	(a)	(b)	(c)	(a) × (c)		(a) × (b)
	Quantity	Unit Contribution Margin	Welding Time per Unit	Total Welding Time	Balance of Welding Time	Total Contribution
Total hours available..................................					2,000
Bike frames produced................................	1,600	$136.40	0.5	800	1,200	$218,240
WVD Drums—make.................................	3,000	$94.80	0.4	1,200	0	284,400
WVD Drums—buy....................................	3,000	$10.25				30,750
Total contribution margin...........................						533,390

Less: Contribution margin from present operations: 5,000 drums × $94.80 CM per drum.................................................						474,000
Increased contribution margin and net operating income....................................						$ 59,390

Assuming direct labor is a variable cost, the contribution margin per unit for each product is calculated as follows:


		Manufactured
	Purchased WVD Drums	WVD Drums	Bike Frames
Selling price......................................................	$149.00	$149.00	$239.00
Variable costs:
Direct materials.............................................	138.00	52.10	99.40
Direct labor...................................................	0.00	3.60	28.80
Variable manufacturing overhead.................	0.00	1.35	1.90
Variable selling and administrative...............	0.75	0.75	1.30
Total variable cost.............................................	138.75	57.80	131.40
Contribution margin.........................................	$ 10.25	$ 91.20	$107.60

Assuming direct labor is a variable cost, the contribution margin per welding hour for each product is calculated as follows:

	Manufactured
	WVD Drums	Bike Frames
Contribution margin per unit (above) (a)..................................	$91.20	$107.60
Welding hours per unit (b)........................................................	0.4 hour	0.5 hour
Contribution margin per welding hour (a) ÷ (b).......................	$228.00 per hour	$215.20 per hour

When direct labor is assumed to be a variable cost, the conclusion is reversed from the case in which direct labor is assumed to be a fixed cost—the WVD drums appear to be a better use of the constraint than the bike frames. The assumption about the behavior of direct labor really does matter.

Assuming direct labor is a variable cost, the optimal product mix and increase in net operating income is computed as follows:

	(a)	(b)	(c)	(a) × (c)		(a) × (b)
	Quantity	Unit Contribution Margin	Welding Time per Unit	Total Welding Time	Balance of Welding Time	Total Contribution
Total hours available.................................					2,000
WVD Drums—make................................	5,000	$91.20	0.4	2,000	0	$456,000
Bike frames produced..............................	0	$107.60	0.5	0	0	0
WVD Drums—buy..................................	1,000	$10.25				10,250
Total contribution margin.........................						466,250

Less: Contribution margin from present operations: 5,000 drums × $91.20 CM per drum................................................						456,000
Increased contribution margin and net operating income...................................						$ 10,250

The case strongly suggests that direct labor is fixed: “The bike frames could be produced with existing equipment and personnel.” Nevertheless, it would be a good idea to examine how much labor time is really needed under the two opposing plans.

	Production	Direct Labor-Hours Per Unit	Total Direct Labor-Hours
Plan 1:
Bike frames...........................	1,600	1.6*	2,560
WVD drums.........................	3,000	0.2**	600
			3,160
Plan 2:
WVD drums.........................	5,000	0.2**	1,000

* $28.80 ÷ $18.00 per hour = 1.6 hour

** $3.60 ÷ $18.00 per hour = 0.2 hour

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