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    $ 130 $ 150

Direct labor 60 80

Variable overhead    30 40

Fixed overhead    180 240

Total cost per unit $ 400    $ 510

Price $ 580 $ 780

Units sold 4,000 2,000

The average wage rate is $40 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 10,000 direct labor-hours.

Required: a. A nationwide car-sharing service has offered to buy 2,500 Star100 systems and 2,500 Star150 systems if the price is lowered to $400 and $500, 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. Supposed that the car-sharing service has offered instead to buy 3,500 each of the two models at $400 and $500, respectively. This customer will purchase the 3,500 units of each model only in an all-or-nothing deal. That is, Unter must provide all 3,500 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 inrease to $60 per hour. Variable overhead costs for overtime production are $10 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

	a-1
			Star100	Star 150	Total
	A	Total Quantity required	2,500	2,500
	B	Direct labor hour per unit	60	80
	C=A*B	Total Direct labor cost	$150,000	$200,000	$350,000
	D	Total Direct labor cost	$350,000
	E	Direct labor cost per hour	$40
	F=D/E	Total Direct labor hours required	8750
	a-2
		Differential Profit Increase
			Star100	Star150	Total
	G	Additional quantities sold	2,500	2,500
	H	Price per unit	$400	$500
	I=G*H	Additional Revenues generated	$1,000,000	$1,250,000	$2,250,000
		Variable Costs:
		Direct Materials	$130	$150
		Direct Labor	$60	$80
		Variable Overhead	$30	$40
	J	Total Variable Cost per unit	$220	$270
	K=G*J	Additional Variable Costs	$550,000	$675,000	$1,225,000
	L=I-K	Additional Contribution	$450,000	$575,000	$1,025,000
		Differential Profit Increase	$1,025,000
	b-1		Star100	Star 150	Total
		Total Quantity required	3,500	3,500
		Direct labor hour per unit	60	80
		Total Direct labor cost	$210,000	$280,000	$490,000
		Total Direct labor cost	$490,000
		Direct labor cost per hour	$40
		Total Direct labor hours required	12250
		Balance Labor hours available	7750	(20000-12250)
			Star100	Star 150
	A	Labor Cost Per unit	$60	$80
	B	Labor Cost per hour	$40	$40
	C=A/B	Labor hour per unit	1.5	2
	D	Sales Price per unit	$580	$780
	E	Variable Cost Per unit	$220	$270
	F=D-E	Unit Contribution Margin	$360	$510
	G=F/C	Contribution per labor hour	$240	$255
		Star 150 should be manufactured to full demand =		2000	(Other thanNew Order)
		Labor hours required for Star 150	4000	(2000*2)
		Balance hours availabke	3750	(7750-4000)
		Number of Star100 to be manufactured	2500	(3750/1.5)	(Other thanNew Order)
			Star100	Star 150	Total
	H	Production for Existing Order Quantity	2500	2000
	I	Price Per Unit	$580	$780
	J=H*I	Sales Revenue from existing order	$1,450,000	$1,560,000	$3,010,000
	K	Production for special Order	3500	3500
	L	Price Per Unit	$400	$500
	M=K*L	Sales Revenue from Special Order	$1,400,000	$1,750,000	$3,150,000
	N=J+M	Total Sales Revenue	$2,850,000	$3,310,000	$6,160,000
	P=H+K	Total Production Quantity	6000	5500
	Q	Variable Cost per unit	$220	$270
	R=P*Q	Total Variable Costs	$1,320,000	$1,485,000	$2,805,000
	S=N-R	Total Contribution Margin	$1,530,000	$1,825,000	$3,355,000
		Total Contribution Margin	$3,355,000
						Profit Change b-2 Star100 Total Star 150 Production Quantity if the Special order is not accepted 4000 2000 $580 $780 B Price Per unit Variable Cost Per Unit $220 $270 C $360 Contribution per unit $510 D B-C $1,020,000 $2,460,000 E-A*D Total Contribution(Without Special Order) $1,440,000 Total Contribution(Without Special Order) $2,460,000 $3,355,000 Total Contribution(With Special Order) Profit Change with Special Order $895,000 (3355000-2460000)