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	$	62			$	72
Direct labor		40				50
Variable overhead		20				25
Fixed overhead		87				117
Total cost per unit	$	209			$	264
Price	$	300			$	400
Units sold		4,000				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

Answer with working notes is given below

a-1 Star 100 Total Direct Labor Direct labor hour rate labor hour per unit $40 $25 Star 150 $50 A $25 B 2.00 A/B 1.60 Additional units Total Direct labor hours 2,600 4,160 5 2,600 ,200 9,360 a-2 $546,000 $676,000 $1,222,000 Differential Revenue Star 100 (2,600 X $210) Star 150 (2,600 X $260) Differential costs Star 100 ( 2,600 x $122) Star 150 (2,600 X $147) Differential profit (loss) $317,200 $382,200 $699,400 $522,600 Working notes: Star 100 | $300 Star 150 $400 A $62 $72 $50 S40 Regular Sales Selling price Variable cost: Direct material Direct labor Variable overhead Total variable cost Contribution per unit Labor hour per unit Contribution per labor hour Ranking $20 $25 $122 $178 1.60 $111.25 $147 B $253 A-B 2.00 $126.50 Star 150 $260 Special order Selling price Total variable cost Contribution per unit Star 100 $2100 $122) $88) $147 $113 Labor hour allocation Total Existing units Special order Total units Labor hour per unit Total Labor hours Labor hours available Star 100 4,000 3,600 7,600 1.60 12,160 Star 150 2,000 3,600 5,600 2.00 11,200 23,360 20,000 5,760 7,2001 Labour hour allocation: Special order Balance labor hour Allocation to Star 150 Balance to Star 100 Production units ($3,040/1.6) 12,960 7,040 4,000 3,040 4,000 3,040 1,9001 b-1 Star 100 Star 150 Total $88 3,6001 $316,800 $113 3,600 $406,800 $723,600 Special order: Contribution margin per unit Number of units Total Contribution margin Regular production: Contribution margin per unit Number of units Total Contribution margin Total Contribution margin for both $178 1,9001 $338,200 $253 2,000 $506,000 $844,200 $1,567,800 b-2 Total Existing Contribution Total units sold Contribution per unit Total Contribution Star 100 4,000 $178 $712,000 Star 150 2,000 $253 $506,000 $1,218,000 B Revised Contribution with special order $1,567,800 A Incremental Profit $349,800 A-B C-1 Star 100 Star 150 Total $88 3,600 $316,800 $113 3,600 $406,800 $723,600 Special order: Contribution margin per unit Number of units Total Contribution margin Regular production: Contribution margin per unit Number of units Total Contribution margin Total Contribution margin for both Additional direct-labor costs Additional variable overhead Total contribution margin for both (with additional costs) $178 4,000 $712,000 $253 2,000 $506,000 $1,218,000 $1,941,600 $126,000 (2,100 units X 1.6*$37.50) $20,160 (2,100 units X 1.6*$6) $1,795,440 C-2 Increase in profit $227,640 ($1,795,440 - $1,567,800)