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.

Costs per Unit	Star100				Star150
Direct materials	$	58			$	68
Direct labor		24				30
Variable overhead		10				15
Fixed overhead		83				113
Total cost per unit	$	175			$	226
Price	$	280			$	380
Units sold		4,000				2,000

The average wage rate is $15 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 2,400 Star100 systems and 2,400 Star150 systems if the price is lowered to $190 and $240, 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 3,400 each of the two models at $190 and $240, respectively. This customer will purchase the 3,400 units of each model only in an all-or-nothing deal. That is, Unter must provide all 3,400 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 $22.50 per hour. Variable overhead costs for overtime production are $4 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

a1. Direct labor per unit = Direct labor cost per unit / avg. wage rate per hour

Star 100 = 24/15=1.6 per unit

Star 150=30/15= 2 per unit

Total Direct Labor hours required for additional system = 2400*1.6+2400*2 = 8640 labor hours

a2.

Particulars	Star 100	Sub total :	Star 150	Sub total :	Total
Differential Revenue
Units to be sold * Price offered	(2400*190)	4,56,000	(2400*240)	5,76,000	10,32,000
Less: Differential Costs
Direct Material	(2400*70)	-1,68,000	(2400*80)	-1,92,000	-3,60,000
Direct Labor	(2400*24)	-57,600	(2400*30)	-72,000	-1,29,600
Variable Overhead	(2400*10)	-24,000	(2400*15)	-36,000	-60,000
Differential Loss/Profit		2,06,400		2,76,000	4,82,400

b1.

Total Direct Labor hour required fullfil special order:

Star 100 = 3400*1.6 = 5440

Star 150 = 3400*2 = 6800

Total 12,240 direct labor hours will be used to produce special order. After fulfilling the demand for special orders, the remaining capacity left is 7,760 direct working hours, but to meet the demand of regular customers Unter requires 10,400 direct working hours. Now the company will reduce sales to regular customers. But the question is which product sales will reduce Unter.

Particulars	Star 100	Star 150
Contribution Margin per unit	176	255
Direct labor hours per unit	1.6	2
Contribution per direct labor hour	110	127.5

As the Star 150 is offering more contribution per labor hour,hence Unter will supply units of Star 150 fully and reduce the supply of Star 100.

Total Direct-labour hour available	7,760
less: Direct labor hour required 150 (2000*2)	4,000
Direct labor hours available for Star 100	3,760

Unter will supply only 2350 units of Star 100 for regular customers.

Total Contribution Margin:

Particulars	Star 100	Star 150
Contribution Margin per unit	86	115
No. of Units	3,400	3,400
Total Contribution margin	2,92,400	3,91,000	6,83,400
Regular Production:
Contribution Margin per unit	176	255
No. of Units	2,350	2,000
Total Contribution margin	4,13,600	5,10,000	9,23,600
Total Contribution Margin	16,07,000

b2.

Total Profit of Unter under regular Supply:

Particulars	Star 100	Star 150
Contribution Margin per unit	176	255
No. of Units	4,000	2,000
Total Contribution margin	7,04,000	5,10,000	12,14,000
Less: FC	3,80,000	2,50,000	6,30,000
Net Profit :	3,24,000	2,60,000	5,84,000

Total Profit of Unter along with special order:

Particulars	Star 100	Star 150	Total :
Total Contribution margin Special Order	2,92,400	3,91,000	6,83,400
Total Contribution margin Regular Production	4,13,600	5,10,000	9,23,600
Total :	7,06,000	9,01,000	16,07,000
Less: FC			6,30,000
Total :			9,77,000

Profit of the Unter with special order will increase by$393,000.