Unter Components manufactures low-cost navigation systems for installation in ri
ID: 2413680 • Letter: U
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:
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. Supposed that the car-sharing service 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 increase 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?
Costs per Unit Star100 Star150 Direct materials $ 70 $ 80 Direct labor 24 30 Variable overhead 10 15 Fixed overhead 95 125 Total cost per unit $ 199 $ 250 Price $ 280 $ 380 Units sold 4,000 2,000
Explanation / Answer
A)
A1) Direct Labour required per unit = Direct Labour cost per unit/ Average wage rate per hour
Star 100 = 24/15 = 1.6 direct labour-hours per unit
Star 150 = 30/15 = 2 direct labour-hours per unit
Total Direct labour-hours required for additional system = 2,400*1.6 + 2400*2
= 8,640 direct labour-hours
A2)
Star 100
Star 150
Total
Differential Revenue
(units to be sold * price offered)
(2400*190)
456000
(2400*240)
576000
1032000
Less: Differential Costs
-Direct Material
(2400*70)
-168000
(2400*80)
-192000
-360000
- Direct Labour
(2400*24)
-57600
(2400*30)
-72000
-129600
- Variable Overhead
(2400*10)
-24000
(2400*15)
-36000
-60000
Differential profit (loss)
206400
276000
482400
B1)
Total Direct Labour-hour required fulfil special order:
Star 100 = 3400*1.6 = 5440
Star 150 = 3400*2 = 6800
Total 12,240 direct labour-hours will be used to produce special order. After meeting demand for special order remaining capacity left is 7,760 direct labour-hours, but to meet the demand of regular customers Unter requires 10,400 direct labour-hours. Now the unter will reduce sales to regular customers. But the question is, which product’s sales will Uter reduce.
Star 100
Star 150
Contribution Margin per unit
176
255
Direct labour-hours per unit
1.6
2
Contribution per direct labour hour
110
127.5
As the Satr 150 is offering more contribution per labour hour, hence Unter will supply units of Star 150 fully and reduce the supply of Star 100.
Total Direct-labour hour available
7760
less: Direct-labour hour required for Star 150 (2000*2)
4000.00
Direct labour-hours available for Star 100
3760
Unter will supply only 2350 units (3760/1.6) of Star 100 for regular customers
Total Contribution Margin:
Star 100
Star 150
Total
Special Order
Contribution Margin Per Unit
86
115
Number of Units
3400
3400
Total Contribution Margin
292400
391000
683400
Regular Production
Contribution Margin Per Unit
176
255
Number of Units
2350
2000
Total Contribution
413600
510000
923600
Grand total
1607000
B2)
Total Profit of Unter under regular Supply:
Regular Production
Star 100
Star 150
Total
Contribution Margin Per Unit
176
255
Number of Units
4000
2000
Total Contribution
704000
510000
1214000
Less: Fixed Cost
380000
250000
630000
Net Profit
584000
Total Profit of Unter along with special order:
Star 100
Star 150
Total
Special Order
Contribution Margin Per Unit
86
115
Number of Units
3400
3400
Total Contribution Margin
292400
391000
683400
Regular Production
Contribution Margin Per Unit
176
255
Number of Units
2350
2000
Total Contribution
413600
510000
923600
Total Contribution
1607000
Less: fixed costs
630000
Net Profit
977000
Profit of the Unter with special order will increase by $393,000.
Star 100
Star 150
Total
Differential Revenue
(units to be sold * price offered)
(2400*190)
456000
(2400*240)
576000
1032000
Less: Differential Costs
-Direct Material
(2400*70)
-168000
(2400*80)
-192000
-360000
- Direct Labour
(2400*24)
-57600
(2400*30)
-72000
-129600
- Variable Overhead
(2400*10)
-24000
(2400*15)
-36000
-60000
Differential profit (loss)
206400
276000
482400
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