Question

Unter Components manufactures low-cost navigation systems for installation in ride-sharing cars. It sells these systems to various car services that can customize them for their locale and business model. It manufactures two systems, the Star100 and the Star150, which differ in terms of capabilities. The following information is available. Star150 $ 69 50 25 Costs per Unit Direct materials Direct labor Variable overhead Fixed overhead Total cost per unit Price Units sold Star100 $ 59 40 20 84 $ 203 $ 300 4,000 114 $ $ 258 400 2,000 The average wage rate is $25 per hour. Variable overhead varies with the quantity of direct labor-hours. The plant has a capacity of 20,000 direct labor-hours, but current production uses only 10,400 direct labor-hours. Required: a. A nationwide car-sharing service has offered to buy 2,600 Star100 systems and 2,600 Star150 systems if the price is lowered to $210 and $260, respectively, per unit. a-1. If Unter accepts the offer, how many direct labor-hours will be required to produce the additional systems? a-2. Complete the following table to determine the differential profit increase or decrease) if Unter accepts this proposal. Prices on regular sales will remain the same. b-1. Suppose that the car-sharing has offered instead to buy 3,600 each of the two models at $210 and $260, respectively. This customer will purchase the 3,600 units of each model only in an all-or-nothing deal. That is, Unter must provide all 3,600 units of each model or none. Unter's management has decided to fill the entire special order for both models. In view of its capacity constraints, Unter will reduce sales to regular customers as needed to fill the special order. Complete the table below to determine the total contribution margin with the special order added. b-2. How much will the profits change if the order is accepted? Assume that the company cannot increase its production capacity to meet the extra demand. C-1. Assume that, in the situation presented in requirement b-1, the plant can work overtime. Direct labor costs for the overtime production increased to $37.50 per hour. Variable overhead costs for overtime production are $6 per hour more than for normal production. Complete the table below to determine the total contribution margin. c-2. How much will the profits change in this situation?

Answer 1

Part A 1

Direct labor hours

9360 hours

Model	Labor cost per unit	÷	Wage rate per labor-hour	=	Labor-hours per unit
Star100	40		25		1.6
Star150	50		25		2.0

Direct labor hours = (2600*1.6)+(2600*2) = 9360 hours

Part A 2

Differential revenues:
Star100 (2600*210)	546000
Star150 (2600*260)	676000	1222000
Differential costs:
Star100 (2600*119)	309400
Star150 (2600*144)	374400	683800
Differential profit		$538200

Differential costs includes only variable costs (direct materials + direct labor + variable overhead)

Part B 1

	Star100	Star150	Total
Special order:
Contribution margin per unit	91	116
Number of units	3600	3600
Total contribution margin	327600	417600	$745200
Regular production:
Contribution margin per unit	181	256
Number of units	1900	2000
Total contribution margin	343900	512000	855900
Total contribution margin for both:			$1601100

	Star100	Star150
Revenue per unit	300	400
Variable cost per unit	119	144
Contribution margin per unit	183	256
Divide by Direct-labor hours per unit	1.6	2
Contribution margin per hour	114.38	128.00

The production of Star100 should be reduced as it has the lower contribution margin per hour.

Of 20000 direct labor hours, 12960 hours ((3600*1.6)+(3600*2))will be used for special order. Of remaining 7040, 4000 hours will be used to produce 2000 units of Star150 and then 3040 units will be used to produce 1900 units of Star100.

Contribution margin = price – variable costs

210-119 = 91

260-144=1166

Part B-2

Increase in profit

$365100

Total contribution margin without the special order

Regular production:
Contribution margin per unit	181	256
Number of units	4000	2000
Total contribution margin	724000	512000	1236000

Difference in profit = 1601100-1236000 = $365100

Part C-1

	Star100	Star150	Total
Special order:
Contribution margin per unit	91	116
Number of units	3600	3600
Total contribution margin	327600	417600	745200
Regular production:
Contribution margin per unit	181	256
Number of units	4000	2000
Total contribution margin	724000	512000	1236000
Additional direct labor costs [(23,360 hours – 20,000 hours) × $(37.50-25)]			42000
Additional variable overhead (3,360 hours × $6 per hour)			20160
Total contribution margin for both:			$2043360

Part C-2

Increase in profit

$807360

Total contribution margin without the special order

Regular production:
Contribution margin per unit	181	256
Number of units	4000	2000
Total contribution margin	724000	512000	1236000

Difference in profit = 2043360-1236000 = $807360