Chapter 4, Problem 53P

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 $40 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

1. 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 $400 and $500, respectively, per unit. If Unter accepts the offer, how many direct labor-hours will be required to produce the additional systems? How much will the profit increase (or decrease) if Unter accepts this proposal? Prices on regular sales will remain the same.
2. b.      Suppose that the car-sharing has offered instead to buy 3,500 each of the two models at $400 and $500, 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. 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.
3. c.       Answer the question in requirement (b), assuming instead that the plant can work overtime. Direct labor costs for the overtime production increase to $60 per hour. Variable overhead costs for overtime production are $10 per hour more than for normal production.

To determine

Identify, if Company U accepts the offer, how many direct labors will be required to produce the additional systems, and calculate the change in profit in case of company accepts the offer.

Explanation of Solution

Calculate direct labor hours per unit:

Particulars	Star 100	Star 150
Labor cost per unit (A)	$60	$80
Wage rate per labor hour (B)	$40	$40
Labor hours per unit (A) ÷ (B)	1.5 hours	2 hours

Table (1)

Calculate total  direct labor hours required for the additional business.

$\begin{array}{c}\left\{\begin{array}{l}\text{Total direct labor hours required }\\ \text{for the additional business}\end{array}\right\}\text{=}\left(\begin{array}{l}\text{Star 100 model DL}\text{Hours }\\ \text{+ Star 150 model DL hours}\end{array}\right)\\ \text{=}\text{(2,500 }\times 1.5\text{hours)}\text{+}\text{(2,500 }\times \text{2 hours)}\\ \text{=}\left(\begin{array}{l}\text{3,750 direct labor hours}\\ \text{ + 5,000 direct labor hours}\end{array}\right)\\ \text{= 8,750 Direct labor hours}\end{array}$

The current production uses 10,000 direct labor hours and capcity is 20,000 direct labor hours. Thus capacity will not have to expanded to accept the order.

Calculate the change in profit:

Particulars	Star 100	Star 150	Total
Units (A)	$2,500	$2,500
Sales price (B)	$400	$500
Variable costs (C)	$220	$270
Differential revenue (A × B)	$1,000,000	$1,250,000	$2,250,000
Less: Differential variable cost (A × C)	$550,000	$675,000	$1,225,000
Differential Profit	$450,000	$575,000	$1,025,000

Table (2)

Thus, the differential operating profit is $1,025,000, so Company U should accept the offer.

Working note 1:

Calculate the variable costs:

Particulars	Star 100	Star 150
Direct materials	$130	$150
Add: Direct labor	$60	$80
Variable overheads	$30	$40
Total variable costs	$220	$270

Table (3)

To determine

Calculate the change in profit in case of acceptance of the offer.

Answer to Problem 53P

The increase in profit is $895,000 if it accepts the offer. So the company should accept the offer.

Explanation of Solution

Calculate total  direct labor hours required for the additional business.

$\begin{array}{c}\left\{\begin{array}{l}\text{Total direct labor hours required }\\ \text{for the additional business}\end{array}\right\}\text{=}\left(\begin{array}{l}\text{Star 100 model DL}\text{Hours }\\ \text{+ Star 150 model DL hours}\end{array}\right)\\ \text{=}\text{(3,500 }\times 1.5\text{hours)}\text{+}\text{(3,500 }\times \text{2 hours)}\\ \text{=}5\text{,250 direct labor hours + 7,000 direct labor hours}\\ \text{= 12,250 Direct labor hours}\end{array}$

The total production time required is 10,000 hours for normal business and 12,250 direct labor hours for the special order, but the direct labor hours capacity is limited to 20,000 hours. In this case, company need to reduce the production of the units sold to the regular customers.

Due to direct labor time is the constraing resource, the companyhaving two alternatives, one is company need to reduce the number of star 100 machines sold to the regular customers, and the second is company need to reduce the number of start 150 machines sold to the regular customers.

Calculate the contribution margin per direct labor hour for each product on the basis of regular customers:

Particulars	Star 100	Star 150
Revenue per unit	$580	$780
Less: Variable cost per unit	$220	$270
Contribution margin per unit (A)	$360	$510
Direct labor hours per unit (B)	1.5	2
Contribution margin per hour (A ÷ B)	$240	$255

Table (4)

Star 100 model has the lower contribution margin per hour compared with the star 150 model. The company should reduce the production of this product to sell the special order.

After producing the special order, the company will have 7,750 direct labor hours (20,000 direct labor hours – 12,250 direct labor hours). Company will produce first 2,000 units of srtar 150 model (4,000 direct labor hours = 2,000 units × 2 direct labor hours). The balance direct labor hours ( 3,750 direct labor hours = 7,750 direct labor hours – 4,000 direct labor hours) to produce 2,500 units of the star 100 model.

Calculate the change in operating profit:

$\begin{array}{c}\left\{\begin{array}{l}\text{Change in }\\ \text{operating profit}\end{array}\right\}\text{= }\left(\begin{array}{c}\text{Net operating income using special order}\\ \text{ and normal production (2) }\\ -\text{Net operating income in normal production (3)}\end{array}\right)\\ \text{= \$2,155,000 }-\text{ \$1,260,000}\\ \text{= }\$895,000\end{array}$

Thus, the changes in profit are $895,000, if it accepts the offer. So the company should accept the offer.

Working note 2:

Calculate the contribution margin in case of special order and normal production:

Particulars	Star 100	Star 150	Total
Special order:
Sales price	$400	$500
Less: Variable cost	$220	$270
Contribution margin per unit (A)	$180	$230
Number of units (B)	3,500	3,500
Total contribution margin ( 1 =A × B)	$630,000	$805,000	$1,435,000
Regular production:
Sales price	$580	$780
Less: Variable cost	$220	$270
Contribution margin per unit (A)	$360	$510
Number of units (B)	2,500	2,000
Total contribution margin ( 2 =A × B)	$900,000	$1,020,000	$1,920,000
Total contribution margin (1 + 2)	$1,530,000	$1,825,000	$3,355,000
Less: Fixed Costs	$720,000	$480,000	$1,200,000
Net Operating Income (3)	$810,000	$1,345,000	$2,155,000

Table (5)

Working note 3:

Total contribution margin in case of normal course of business:

Particulars	Star 100	Star 150	Total
Regular production:
Sales price	$580	$780
Less: Variable cost	$220	$270
Contribution margin per unit (A)	$360	$510
Number of units (B)	4,000	2,000
Total contribution margin ( C =A × B)	$1,440,000	$1,020,000	$2,460,000
Less: Fixed costs	$720,000	$480,000	$1,200,000
Net operating Income (4)	$720,000	$540,000	$1,260,000

Table (6)

To determine

Calculate the change in profit in case of acceptance of the offer with the given change.

Answer to Problem 53P

The change in profit is $1,367,500 if it accepts the offer. So the company should accept the offer.

Explanation of Solution

Contribution margin:

The excess of sales price over the variable expenses is referred to as the contribution margin. It is computed by deducting the variable expenses from the sales revenue. A contribution margin income statement is prepared in order to record the contribution margin.

Calculate the change in operating profit:

$\begin{array}{c}\left\{\begin{array}{l}\text{Change in }\\ \text{Operating profit}\end{array}\right\}\text{= }\left(\begin{array}{c}\text{Net operating income of special order and normal production (4) }\\ -\text{Net operating income in normalproduction (3)}\end{array}\right)\\ \text{= \$2,627,500 }-\text{ \$1,260,000}\\ \text{= }\$1,367,500\end{array}$

Thus, the change in profit is $1,367,500 if, it accepts the offer. So the company should accept the offer.

Working note 4:

Calculate the contribution margin in case of special order:

Particulars	Star 100	Star 150	Total
Special order:
Sales price	$400	$500
Less: Variable cost	$220	$270
Contribution margin per unit (A)	$180	$230
Number of units (B)	3,500	3,500
Total contribution margin ( 1 =A × B)	$630,000	$805,000	$1,435,000
Regular production:
Sales price	$580	$780
Less: Variable cost	$220	$270
Contribution margin per unit (A)	$360	$510
Number of units (B)	4,000	2,000
Total contribution margin ( 2 =A × B)	$1,440,000	$1,020,000	$2,460,000
Gross contribution margin (1 + 2)	$2,070,000	$1,825,000	$3,895,000
Less: Additional direct labor costs			$45,000
Additional variable overhead			$22,500
Total contribution margin			$3,827,500
Less: Fixed costs	$720,000	$480,000	$1,200,000
Net operating Income			$2,627,500

Table (7)

Working note 5:

Calculate the additional labor costs:

$\begin{array}{c}\text{Labor costs = Additonal labor hours }\times \text{ Labor rate}\\ \text{= (22,500 - 20,000)}\text{}\times \text{ \$20}\\ \text{= \$45,000}\end{array}$

Calculate the additional variable costs:

$\begin{array}{c}\text{Variable costs = Additonal labor hours }\times \text{ Variable cost rate}\\ \text{= (22,500 - 20,000)}\text{}\times \text{ \$10}\\ \text{= \$22,500}\end{array}$