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 $ 68    $ 78

Direct labor    30 40

Variable overhead 15 20

Fixed overhead 93 123

Total cost per unit $ 206    $ 261

Price    $ 290 $ 390

Units sold 4,000 2,000

The average wage rate is $20 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 $200 and $250, 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 3,500 each of the two models at $200 and $250, 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 increased to $30.00 per hour. Variable overhead costs for overtime production are $5 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?

Really needing help with B-2, C-1, and C-2. Thanks,

Answer 1

a)
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 $200 and $250, respectively, per unit.
a-1. If Unter accepts the offer, how many direct labor-hours will be required to produce the additional systems?
Model	Labour cost per unit	wages rate per hour	Labours per unit
Star 100	30	$             20.00	1.50
Star 150	40	$             20.00	2.00
	Special order quantity	Total hours required
Star 100	2500	3,750.00
Star 150	2500	5,000.00
		8,750.00
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.
	star 100	star 150
Differential revenues
Special order Units	2500	2500
Selling Price	$           200.00	$           250.00
Incremental revenues	$    500,000.00	$    625,000.00	$  1,125,000.00
Differential costs
Special order Units	2500	2500
Total variable costs	$           113.00	$           138.00
Differential cost	$    282,500.00	$    345,000.00	$     627,500.00
Differential profit			$     497,500.00
b)
Model	Labour cost per unit	wages rate per hour	Labours per unit
Star 100	30	$             20.00	1.50
Star 150	40	$             20.00	2.00
	Special order quantity	Total hours required
Star 100	3500	5,250.00
Star 150	3500	7,000.00
		12,250.00
Plant Capacity in direct Labour Hours	20,000.00
Capacity used for Special order	12,250.00
Capacity remains  for regular order	7,750.00
	star 100	star 150
Revenue Per Unit	$           290.00	$           390.00
Variable Cost per unit	$           113.00	$           138.00
Contribution Margin Per Unit	$           177.00	$           252.00
Direct Labours per unit	1.50	2.00
Contribution Margin per Hour	118	126
Lowest Contribution Margin per hour	118
Hours Over capacity	2,250.00
Total lost Contribution Mrgin	265,500.00
After producing the special order, the company will have 7,750 direct labor hours remaining (20,000 – 12,250). It will use these to first produce the 2,000 units of the Star150 (4,000 = 2,000 x 2.0 direct labor hours). The company will then use the remaining 3,750 direct labor hours (7,750 – 4,000) to make 2,500 units of the Star100.
*  $87 = $200 – $113; $262 = $250 –$138.
The total contribution margin with the special order:
Special order	star 100	star 150
contribution marigin per unit (*)	$             87.00	$           262.00
number of units	3500	3500
total contribution margin	$    304,500.00	$    917,000.00	$  1,221,500.00
regular production
contribution margin per unit	$           177.00	$           252.00
number per unit	2500	2000
total contribution margin	$    442,500.00	$    504,000.00	$     946,500.00
total contribution for both.			$  2,168,000.00
Regular production
contribution marigin per unit	$           177.00	$           252.00
number of units	4000	2000
total contribution margin	$    708,000.00	$    504,000.00	$  1,212,000.00
The difference in profit is $2,168,000 - $1,212,000	$    956,000.00
c)
Special order	star 100	star 150
contribution marigin per unit	$             87.00	$           262.00
number of units	3500	3500
total contribution margin	$    304,500.00	$    917,000.00	$  1,221,500.00
regular production
contribution margin per unit	$           177.00	$           252.00
number per unit	$        4,000.00	$        2,000.00
total contribution margin	$    708,000.00	$    504,000.00	$  1,212,000.00
total contribution for both.			$  2,433,500.00
Additional direct-labor costs [(22,250 hours – 20,000 hours) x $30]			$       67,500.00
Additional variable overhead (2,250 hours x $5 per hour)			$       11,250.00
			$  2,354,750.00
The difference in profit is $2,354,750 – $1,121,000 =	$ 1,142,750.00

a-1. If Unter accepts the offer, how many direct labor-hours will be required 26 to produce the additional systems? Labour cost per unit wages rate per hour 27 Model 28 Star 100 29 Star 150 Labours per unit =B28/C28 =B29/029 40 20 30 31 32 Star 100 33 Star 150 Special order quantity 2500 2500 Total hours required =B32D28 =B33D29 =C32+C33 star 100 star 150 a-2. Complete the following table to determine the differential profit increase (or decrease) if Unter accepts this proposal. Prices on regular sales 36 will remain the same. 37 38 Differential revenues 39 Special order Units 40 Selling Price 41 Incremental revenues 42 Differential costs 43 Special order Units 44 Total variable costs 45 Differential cost 46 Differential profit 47 2500 200 =B39*B40 2500 250 =C39C40 =B41+C41 =B39 =B3+B4+B5 =B43B44 =C39 =C3+C4+C5 =C43C44 =B45+245 =D41-D45


48 b) 49 Model 50 Star 100 51 Star 150 52 Labour cost per unit =B28 =B29 wages rate per hour =C28 =C29 Labours per unit =B50/C50 =B51/C51 54 Star 100 55 Star 150 Special order quantity 3500 3500 Total hours required =B54D50 =B55*D51 =C54+C55 58 Plant Capacity in direct Labour Hours 59 Capacity used for Special order 60 Capacity remains for regular order 20000 =C56 =B58-B59 63 Revenue Per Unit 64 Variable Cost per unit 65 Contribution Margin Per Unit 66 Direct Labours per unit 67 Contribution Margin per Hour star 100 290 =B44 =B63-164 =D50 =B65/B66 star 150 390 =C44 =C63-C64 =D51 =C65/C66 68 69 Lowest Contribution Margin per hour 70 Hours Over capacity 71 Total lost Contribution Mrgin =B67 =10000-160 =B69*B70 72 After producing the special order, the company will have 7,750 direct labor hours remaining (20,000 - 12,250). It will use these to first produce the 2,000 units of the Star150 (4,000 = 2,000 x 2.0 direct labor hours). The company will then use the remaining 3,750 direct labor hours (7,750 - 734,000) to make 2,500 units of the Star100. 74 $87 = $200 - $113; $262 = $250-$138.

star 100 = 200-364 3500 =B78%B79 star 150 =400-C64 3500 =C78C79 =B80+C80 76 The total contribution margin with the special order: 77 Special order 78 contribution marigin per unit (*) 79 number of units 80 total contribution margin 81 regular production 82 contribution margin per unit 83 number per unit 84 total contribution margin 85 total contribution for both. 86 87 Regular production 88 contribution marigin per unit 89 number of units 90 total contribution margin =B65 2500 =B82 383 =C65 2000 =C82083 B84+C84 =D80+D84 =B82 4000 =B88 389 =C82 2000 =C88089 =B90+C90 91 92 The difference in profit is $2,168,000 - $1,212,000 =D85-D90 star 100 =B78 =B79 =B96*B97 star 150 =C78 =C79 =C96.097 =B98+C98 94 c) 95 Special order 96 contribution marigin per unit 97 number of units 98 total contribution margin 99 regular production 100 contribution margin per unit 101 number per unit 102 total contribution margin 103 total contribution for both. 104 Additional direct-labor costs [(22,250 hours - 20,000 hours) $30] 105 Additional variable overhead (2,250 hours x $5 per hour) 106 =B88 =B89 =B90 =C88 =C89 =C90 =B102+C102 =D98+D102 =2250*30 =2250*5 =D103-D104-1105 107 The difference in profit is $2,354,750 - $1,121,000 = =D106-D90