Question

Unter Components manufactures low-cost navigation systems for instalation in ide-sharing cars. It sells these systems to various car SETVKes that can customize them for their locale and business model it manufactures two systems, the Star 100 and the Star150, which differ in terms of capabilities. The following Information is available Stur100 $ 64 Star 150 $ 74 24 39 Costs per Unit Direct materials Direct labor Variable overhead Fixed overhead Total cost per unit Price Units sold 39 119 $ 187 $ 238 280 4.000 $ 380 2,000 The average wage rate is $15 per hour. Vartable 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 6-1. If Unter accepts the offer, how many direct labor-hours will be required to produce the additional systems? 3-2. Complete the following table to determine the differential profit Increase for 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 3.400 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 increased 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?

Answer 1

Unter Components Requirement al. Direct labor hours per unit: Labor cost Model per unit Star100 I 24 Star150 30 Wage rate per labor hr. 15 Labor hours per unit 1.6 15 2 Total hours required for the additional business: 2,400 x 1.6 hours + 2,400 x 2.0 hours = 8,640 hours. Current production uses 10,000 direct-labor hours and capacity is 20,000 direct-labor hours, so capacity will not have to be expanded to accept the order. Requirement a2. 1032000 Additional profit (contribution margin): Differential revenues: Star100 2400 x 190 = 456000 Star150 2400 x 240 = 576000 Differential costs Star 100 2400 x 98 = 235200 Star150 2400 x 119 = 285600 Differential profit 520800 511200 64 +24 + 10 = 98; 74 +30 + 15 = 119 Requirement c.1 Star100 Star150 Total 92 3400 312800 121 3400 411400 724200 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): 182 4000 728000 261 2000 522000 1250000 1974200 19800 8960 1945440 22240 - 20000 = 2240 x ( 22.5 - 15 ) = 19800 2240 x 4 = 8960

Requirement b1. Star100 Star150 Total 92 3400 312800 121 3400 411400 724200 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: 182 2350 427700 261 2000 522000 949700 1673900 Total hours required for the additional business: 3,400 x 1.6 hours +3,400 x 2.0 hours = 12,240 hours. The total production time required now is 10,400 hours (for the normal business) plus 12,240 hours for the special order. Because capacity, which is limited to 20,000 hours, cannot be expanded to accept the order, the company will have to reduce production of the units sold to its regular customers. There are two alternatives. The company can reduce the number of Star 100 machines sold or the number of Star150 machines sold. Because direct labor time is the constraining resource, the company needs to compute the contribution margin per direct labor hour for each product: Total Star100 280 98 Revenue per unit Variable cost per unit Contribution margin per unit Divide by Direct-labor hours per unit Contribution margin per hour Star150 380 119 261 2 131 182 1.6 114 Because the Star 100 has the lower contribution margin per hour, the company should reduce the production of this product to sell the special order.

After producing the special order, the company will have 7,760 direct labor hours remaining (20,000 - 12,240). 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 3,760 direct labor hours (7,760 - 4,000) to make 2,350 units of the Star100. The total contribution margin with the special order: Star100 Star150 Total Special order Contribution margin per unit (Price - Variable cost) Number of units Total contribution margin Regular production: Contribution margin per unit Number of units 121 3400 411400 312800 724200 261 182 2350 427700 2000 522000 949700 1673900 $92 = $190 - $98; $121 = $240-$119. The total contribution margin without the special order: Star 100 Star150 Total Regular production: Contribution margin per unit Number of units 182 4000 728000 261 2000 522000 1250000 The difference in profit is $1,673,900 - $1,240,000 = $433,900 The company is better off accepting the special order. (Of course, the company would earn even more profit if it could first produce for the regular customers and use any excess capacity to fill part, but not all, of the special order.)