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?

Please do not solve a and b's only c's part needed

Answer 1

Labor Hours per unit = Labor cost/Rate per hour
Star100 = 24/15 = 1.6 hours
Star150 = 30/15 = 2 hours
a-1 Hours required = 2,400*1.6 + 2,400*2 = 8,640 hours
No additional fixed costs will be incurred as spare capacity exists
a-2
Differential Revenues
Star 100	456,000
Star 150	576,000	1,032,000
Differential Costs:
Star 100	228,000
Star 150	278,400	506,400
Differential Profit(loss)		525,600
b-1
	Star 100	Star 150	Total
Special Order
Contribution Margin per unit	95	124
Number of units	3400	3400
Total Contribution Margin	323,000	421,600	744,600
Regular Production:
Contribution Margin per unit	185	264
Number of units	2,350	2,000
Total Contribution Margin	434,750	528,000	962,750
Total Contribution Margin for both			1,707,350
Total labor hours	20,000
Used in Special Order	12240
Remaining	7,760
Used in Star150 since CM per hour is higher	4,000
used in Star100	3,760
Star 100 units	2,350
Change in profits = Contribution Margin from special order – contribution margin lost on regular sales
= 744,600 –185*1650
=$439350
	Star 100	Star 150	Total
Special Order
Contribution Margin per unit	95	124
Number of units	3400	3400
Total Contribution Margin	323000	421600	744,600
Regular Production:
Contribution Margin per unit	185	264
Number of units	4,000	2,000
Total Contribution Margin	740,000	528,000	1,268,000
Total Contribution Margin for both			2,012,600
Additional direct labor cost			19,800
Additional variable overhead			10,560
Total CM with additional cost			1,982,240
c-2 change in profits = 1982240- 1,268000
=$714240