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	$	61			$	71
Direct labor		24				30
Variable overhead		10				15
Fixed overhead		86				116
Total cost per unit	$	181			$	232
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

Dear student, we cannot able to post solution more than four sub-parts of the question as per our policy.

Answer 1 (a1)

Model	Star100	Star150	Total
Direct labor cost per unit	$                  24	$                      30
Divided by: Average wage rate	$                  15	$                      15
Labor hours per unit	1.60	2.00
Multiply: number units for special order	2,400	2,400
Direct labor-hours required	3,840	4,800	8,640

Answer 2 (a2)

Model	Star100	Star150	Total
Direct materials	$                  61	$                      71
Direct labor	$                  24	$                      30
Variable overhead	$                  10	$                      15
Total variable cost per unit	$                  95	$                   116
Multiply: number units for special order	2,400	2,400
Differential costs	$        228,000	$           278,400	$      506,400
Selling Price for special order	$                190	$                   240
Multiply: number units for special order	2,400	2,400
Differential revenue	$        456,000	$           576,000	$ 1,032,000
Less: Differential costs			$      506,400
Differential profit			$      525,600

Answer 3 (b1)

Special Order:	Star100	Star150
Selling price	$                190	$                   240
Less: variable cost	$                  95	$                   116
Contribution margin per unit	$                  95	$                   124
Regular production:	Star100	Star150
Selling price	$                280	$                   380
Less: variable cost	$                  95	$                   116
Contribution margin per unit	$                185	$                   264
Divided by: Labor hours per unit	1.60	2.00
Contribution margin per hour	115.63	132.00
Priority for normal production	Second	First
Model	Star100	Star150	Total
Labor hours per unit	1.60	2.00
Multiply: number units for special order	3,400	3,400
Labor hours required for special order	5,440	6,800	12,240
Labor hours required for Regular production of Star150 (2*2000)			4,000
Labor hours required for Regular production of Star100 (Balancing figure)			3,760
Total direct labor-hours used (Maximum capacity)			20,000
Model	Star100	Star150	Total
Labor hours required	3,760	4,000
Divided by: Labor hours per unit	1.60	2.00
Units produced for Regular production	2,350	2,000
Model	Star100	Star150	Total
Special Order:
Contribution margin per unit	$                  95	$                   124
Multiply: number units for special order	3,400	3,400
Total contribution margin	$        323,000	$           421,600	$      744,600
Regular production
Contribution margin per unit	$                185	$                   264
Multiply: number units	2,350	2,000
Total contribution margin	434,750	528,000	962,750
Total contribution margin for both			$ 1,707,350

Answer 4 (b2)

Model	Star100	Star150	Total
Regular production without special order	4,000	2,000
Multiply: Contribution margin per unit	$                185	$                   264
Total contribution margin before accepting special order	$        740,000	$           528,000	$ 1,268,000
Total contribution margin after accepting special order			$ 1,707,350
Less: Total contribution margin before accepting special order			$ 1,268,000
Increase in profit			$      439,350