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.

Star100 $ 66 40 Star150 $ 50 76 20 25 Costs per Unit Direct materials Direct labor Variable overhead Fixed overhead Total cost per unit Price Units sold 91 $ 217 $ $ 121 272 400 2,000 $ 300 4,000

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

Existing Contribution and Profit Star 100 Star 150 Total of Both Per Unit Total Per Unit Total 300 1200000 400 300000 2000000 Sales Direct Material Direct Labor Variable Overheads Total variable cost 66 2640001 40 160000 20 80000 126 504000 76 152000 50 100000 25 50000 151 302000 416000 260000 130000 806000 Contribution Margin 1740 696000 249 498000 1194000 Fixed Cost 91 364000) 121 242000 606000 Profit 332000 256000 588000 A-1 direct labour hours required per unit direct labor cost Labor rate per hour Required Hour per unit Star100 Star 150 $40.00 $50.00 $25.00 $25.00 1.6 2 1.6 Required Hours for additional Production Star100 Star 150 Total Additional Units 2600 2600 Hour per unit Total additional hours required 4160 52001 9360 Total available hours (20000-10400) Order is possible to be fulfilled. 9600

A-2 Statement Showing Differential increase in Profit Differential Revenue Star 100 Star 150 Per UnitTotal 210 546000 260 676000 1222000 Differential Cost Star 100 Star 150 126 327600 151 392600 720200 Differential Profit 501800 Required Hours for additional Production Additional Units Hour per unit Total additional hours required Total Hours Available Hours available to regular production Star 100 Star 150 Total 36001 3600 1.61 2 5760 7200 12960 20000 7040 Contribution Margin from Special Order Star 100 Star 150 Total Sale Price 210 260 Less: Variable cost 126 151 Contribution Per unit 84 109 Total Units 36000 3600 Total Contribution 302400 392400 694800

vailability. So management should give preference to that product which ion per direct labor hour. Statement Showing Contribution in total Special Order Star 100 Star 150 Total Contribution Margin Per Unit 84 109 No. of Units 3600 3600 Total Contribution Margin 302400 392400694800 ours shall be used to produce Star 100 Regular Order Contribution Margin Per unit No. of units Total Contribution Margin Total of Both 174 249 1900 2000 330600 498000 828600 1523400 Toal Contribution Less: Fixed Cost Total Profit 1523400 606000 917400 B-2 Change in Profit Existing Profit Profit if Order is Acceptedd Change in Profit Contribution Margin can be earned Sale Price Less: variable cost Contribution Per Unit Total Units Total Contribution 588000 917400 329400 Increase Star 100 Star 150 Total 300 400 126151 174 249 1900 2000 330600 498000 828600

Statement Showing Contribution in total Special Order Star 100 Star 150 Total Contribution Margin Per Unit 8 4 109 No. of Units 36000 3600 Total Contribution Margin 302400 392400 694800 Regular Order Contribution Margin Per unit No. of units Total Contribution Margin Total of Both 174 249 19001 2000 330600 498000 828600 1523400 Toal Contribution Less: Fixed Cost Total Profit 1523400 606000 917400 B-2 Change in Profit Existing Profit Profit if Order is Acceptedd Change in Profit 588000 917400 329400 Increase

C-1 If overtime is possible Hours Required for overtime Units remaining to be produced Star 100 (4000-1900) Per unit direct labour hour Total Direct Labour hour 2100 1.6 3360 Additional Direct labour cost Additional Variable overheads Total overtime cost per hour Total 37.5 3360 hrs 126000 63360 hrs 20160 146160 Statement Showing Contribution in total Special Order Contribution Margin Per Unit No. Of Units Total Contribution Margin Star 100 Star 150 Total 84 109 36000 3600 302400 392400 694800 Total Contribution Fixed Cost Net Profit 1742640 606000 1136640 Regular Order Contribution Margin Per unit No. of units Total Contribution Margin Total of Both C-2 change in Profit Existing Profit Profit if Order is Acceptedd Change in Profit 5880001 1136640 548640 Increase 174 249 40001 2000 696000 498000 1194000 1888800 Additional Direct Labor cost Additional Variable overheads cost Total Contribution Margin of both after additional cost 126000 20160 1742640

Existing Contribution and Profit Star 100 Star 150 Total of Both Per Unit Total Per Unit Total 300 1200000 400 300000 2000000 Sales Direct Material Direct Labor Variable Overheads Total variable cost 66 2640001 40 160000 20 80000 126 504000 76 152000 50 100000 25 50000 151 302000 416000 260000 130000 806000 Contribution Margin 1740 696000 249 498000 1194000 Fixed Cost 91 364000) 121 242000 606000 Profit 332000 256000 588000 A-1 direct labour hours required per unit direct labor cost Labor rate per hour Required Hour per unit Star100 Star 150 $40.00 $50.00 $25.00 $25.00 1.6 2 1.6 Required Hours for additional Production Star100 Star 150 Total Additional Units 2600 2600 Hour per unit Total additional hours required 4160 52001 9360 Total available hours (20000-10400) Order is possible to be fulfilled. 9600

A-2 Statement Showing Differential increase in Profit Differential Revenue Star 100 Star 150 Per UnitTotal 210 546000 260 676000 1222000 Differential Cost Star 100 Star 150 126 327600 151 392600 720200 Differential Profit 501800 Required Hours for additional Production Additional Units Hour per unit Total additional hours required Total Hours Available Hours available to regular production Star 100 Star 150 Total 36001 3600 1.61 2 5760 7200 12960 20000 7040 Contribution Margin from Special Order Star 100 Star 150 Total Sale Price 210 260 Less: Variable cost 126 151 Contribution Per unit 84 109 Total Units 36000 3600 Total Contribution 302400 392400 694800

vailability. So management should give preference to that product which ion per direct labor hour. Statement Showing Contribution in total Special Order Star 100 Star 150 Total Contribution Margin Per Unit 84 109 No. of Units 3600 3600 Total Contribution Margin 302400 392400694800 ours shall be used to produce Star 100 Regular Order Contribution Margin Per unit No. of units Total Contribution Margin Total of Both 174 249 1900 2000 330600 498000 828600 1523400 Toal Contribution Less: Fixed Cost Total Profit 1523400 606000 917400 B-2 Change in Profit Existing Profit Profit if Order is Acceptedd Change in Profit Contribution Margin can be earned Sale Price Less: variable cost Contribution Per Unit Total Units Total Contribution 588000 917400 329400 Increase Star 100 Star 150 Total 300 400 126151 174 249 1900 2000 330600 498000 828600

Statement Showing Contribution in total Special Order Star 100 Star 150 Total Contribution Margin Per Unit 8 4 109 No. of Units 36000 3600 Total Contribution Margin 302400 392400 694800 Regular Order Contribution Margin Per unit No. of units Total Contribution Margin Total of Both 174 249 19001 2000 330600 498000 828600 1523400 Toal Contribution Less: Fixed Cost Total Profit 1523400 606000 917400 B-2 Change in Profit Existing Profit Profit if Order is Acceptedd Change in Profit 588000 917400 329400 Increase

C-1 If overtime is possible Hours Required for overtime Units remaining to be produced Star 100 (4000-1900) Per unit direct labour hour Total Direct Labour hour 2100 1.6 3360 Additional Direct labour cost Additional Variable overheads Total overtime cost per hour Total 37.5 3360 hrs 126000 63360 hrs 20160 146160 Statement Showing Contribution in total Special Order Contribution Margin Per Unit No. Of Units Total Contribution Margin Star 100 Star 150 Total 84 109 36000 3600 302400 392400 694800 Total Contribution Fixed Cost Net Profit 1742640 606000 1136640 Regular Order Contribution Margin Per unit No. of units Total Contribution Margin Total of Both C-2 change in Profit Existing Profit Profit if Order is Acceptedd Change in Profit 5880001 1136640 548640 Increase 174 249 40001 2000 696000 498000 1194000 1888800 Additional Direct Labor cost Additional Variable overheads cost Total Contribution Margin of both after additional cost 126000 20160 1742640

updated answer with $ symbol

Existing Contribution and Profit Star 100 Star 150 Total of Both Per Unit Total Per Unit Total $300.00 $1,200,000.00 $400.00 $800,000.00 $2,000,000.00 Sales Direct Material Direct Labor Variable Overheads Total variable cost $66.00 $40.00 $20.00 $126.00 $264,000.00 $76.00 $152,000.00 $160,000.00 $50.00 $100,000.00 $80,000.00 $25.00 $50,000.00 $504,000.00 $151.00 $302,000.00 $416,000.00 $260,000.00 $130,000.00 $806,000.00 Contribution Margin $174.00 $696,000.00 $249.00 $498,000.00 $1,194,000.00 Fixed Cost $91.00 $364,000.00 $121.00 $242,000.00 $606,000.00 Profit $332,000.00 $256,000.00 $588,000.00 A-1 direct labour hours required per unit direct labor cost Labor rate per hour Required Hour per unit Star100 $40.00 $25.00 1.6 Star 150 $50.00 $25.00 1.6 Required Hours for additional Production Star100 Star 150 Additional Units 2600 Hour per unit Total additional hours required 4160 Total available hours (20000-10400) Order is possible to be fulfilled. Total 2600 2 52001 9360 9600

A-2 Statement Showing Differential increase in Profit Differential Revenue Star 100 Star 150 Per Unit Total $210.00 $546,000.00 $260.00 $676,000.00 $1,222,000.00 Differential Cost Star 100 Star 150 $126.00 $327,600.00 $151.00 $392,600.00 $720,200.00 Differential Profit $501,800.00 Required Hours for additional Production Additional Units Hour per unit Total additional hours required Total Hours Available Hours available to regular production Star100 Star 150 Total 3600 3600 1. 62 5760 7200 1 2960 20000 7040 Contribution Margin from Special Order Star 100 Star 150 Total Sale Price $210.00 $260.00 Less: Variable cost $126.00 $151.00 Contribution Per unit $84.00 $109.00 Total Units 3600 3600 Total Contribution $302,400.00 $392,400.00 $694,800.00

Now we can see that, there is a constraint on the direct labour hours availability. So management should give preference to that product which gives higher contribution per direct labor hour. Existing regular Star 100 Star 150 Contribution per unit $174.00 $249.00 Direct Labor hour Contribution per direct labour hour $108.75 $124.50] 1.6 Management shall meet the demand of Star 150 first, than remaining hours shall be used to produce Star 100 Assumed that sale price to regular customer is not changed. 2000 Hours required to produce Star 150 Units Hour per unit Total Remaining Hours for Star 100 (7040-4000) Units of Star 100 possible to be produced Hours Available Per Unit hour required Total Units can be produced 4000 3040 3040 1.6 1900 Contribution Margin can be earned Sale Price Less: variable cost Contribution Per Unit Total Units Total Contribution Star 100 Star 150 Total $300.00 $400.00 $126.00 $151.00 $174.00 $249.00 1900 2000 $330,600.00 $498,000.00 $828,600.00

Statement Showing Contribution in total Special Order Star 100 Star 150 Total Contribution Margin Per Unit $84.00 $109.00 No. of Units 3600 3600 Total Contribution Margin $302,400.00 $392,400.00 $694,800.00 Regular Order Contribution Margin Per unit No. of units Total Contribution Margin Total of Both $174.00 $249.00 1900) 2000 $330,600.00 $498,000.00 $828,600.00 1523400 Toal Contribution Less: Fixed Cost Total Profit $1,523,400.00 $606,000.00 $917,400.00 B-2 Change in Profit Existing Profit Profit if Order is Acceptedd Change in Profit $588,000.00 $917,400.00 $329,400.00 Increase

C-1 If overtime is possible Hours Required for overtime Units remaining to be produced Star 100 (4000-1900) Per unit direct labour hour Total Direct Labour hour 2100 1.6 33601 per hour $37.50 3360 hrs $6.00 3360 hrs Additional Direct labour cost Additional Variable overheads Total overtime cost Total $126,000.00 $20,160.00 $146,160.00 Statement Showing Contribution in total Special Order Contribution Margin Per Unit No. Of Units Total Contribution Margin Star 100 Star 150 Total $84.00 $109.00 3600 3600 $302,400.00 $392,400.00 $694,800.00 Total Contribution Fixed Cost Net Profit $1,742,640.00 $606,000.00 $1,136,640.00 Regular Order Contribution Margin Per unit No. of units Total Contribution Margin Total of Both C-2 change in Profit Existing Profit $588,000.00 Profit if Order is Acceptedd $1,136,640.00 Change in Profit $548,640.00 Increase $174.00 $249.00 4000 2000 $696,000.00 $498,000.00 $1,194,000.00 $1,888,800.00 Additional Direct Labor cost Additional Variable overheads cost Total Contribution Margin of both after additional cost $126,000.00 $20,160.00 $1,742,640.00