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Management Accounting - Module 4

Relevant Costs!

1

The Special Order Pricing Decision! • 

involves the sale of normal or customized products at a discounted or special price!

• 

if idle capacity exists, lowest price = ! variable cost of special order ! + differential fixed costs to the order/units in special order !

• 

if idle capacity does not exist, lowest price = above, plus! –  contribution forgone from normal sales that are lost (i.e. displaced by the special order!

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Management Accounting - Module 4

The Special Order Pricing Decision cont d! • 

loss of normal customers need to be assessed!

• 

if products have short customer use life and/or repeat customers are important, loss of normal customers may have a long-term profitability impact!

• 

problem solving:! –  calculate the incremental income from the special order= CM from special order - any differential fixed costs! –  if positive and does not displace regular sales, accept if it can be contained! –  if positive and displaces regular sales, consider long-term impact of lost customers!

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Problem 1 – Relevant Costs (Special Orders) Anchor Company manufactures several different styles of jewelry cases. Management estimates that during the third quarter of 20x6 the company will be operating at 80% of normal capacity. Because Anchor desires a higher utilization of plant capacity, the company will consider a special order. Anchor has received special-order inquiries from two companies. The first order is from JCP, Inc., which would like to market a jewelry case similar to one of Anchor's cases. The JCP jewelry case would be marketed under JCP's own label. JCP, Inc., has offered Anchor $5.75 per jewelry case for 20,000 cases to be shipped by October 1, 20x6. The cost data for the Anchor jewelry case, which would be similar to the specifications of the JCP special order, are as follows: Regular selling price per unit

$9.00

Costs per unit: Raw materials Direct labor 0.5 hours @ $6.00 Overhead 0.25 machine hours @ $4.00

$2.50 3.00 1.00

Total costs

$6.50

According to the specifications provided by JCP,Inc., the special-order case requires less expensive raw materials. Consequently, the raw materials will cost only $2.25 per case. Management has estimated that the remaining costs, labor time, and machine time will be the same as for the Anchor jewelry case. The second special order was submitted by the Krage Company for 7,500 jewelry cases at $7.50 per case. Like the JCP cases, these jewelry cases would be marketed under the Krage label and have to be shipped by October 1, 20x6. However, the Krage jewelry case is different from any jewelry case in the Anchor line. The estimated per-unit costs of this case are as follows: Raw materials Direct labor 0.5 hours @ $6.00 Overhead 0.5 machine hours @ $4.00

$3.25 3.00 2.00

Total costs

$8.25

In addition, Anchor will incur $1,500 in additional setup costs and will have to purchase a $2,500 special device to manufacture these cases; this device will be discarded once the special order is completed. The Anchor manufacturing capabilities are limited to the total machine hours available. The plant capacity under normal operations is 90,000 machine hours per year or 7,500 machine hours per month. The budgeted fixed overhead for 20x6 amounts to $216,000. All manufacturing overhead costs are applied to production on the basis of machine hours at $4.00 per hour. Anchor will have the entire third quarter to work on the special orders. Management does not expect any repeat sales to be generated from either special order. Company practice precludes Anchor from subcontracting any portion of an order when special orders are not expected to generate repeat sales. Required: Should Anchor Company accept either special order? Justify your answer and show your calculations.

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Management Accounting - Module 4

Make or Buy Decision! • 

decision to make a fabricated part or component internally, or to purchase it from an external supplier!

• 

qualitative factors to consider:! –  quality of the component! –  reliability of the supplier! –  technical capabilities of the supplier! –  financial strength and reputation of the supplier! –  availability of production capacity to manufacture the components!

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Make or Buy Decision - cont d! • 

problem solving - compare the cost to buy with the cost to make!

• 

cost to make = ! –  all variable costs! –  any avoidable fixed costs! –  any opportunity costs of making the component: alternative uses of space, lost CM!

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Problem 2 – Make/Buy Powell Dentistry Services operates in a large metropolitan area. Currently, Powell has its own dental laboratory to produce porcelain and gold crowns. The unit costs to produce the crowns are as follows: Porcelain Gold Raw materials $ 55 $ 94 Direct labour 22 22 Variable overhead 5 5 Fixed overhead 22 22 Total $104 $143 Fixed overhead is detailed as follows: Salary (supervisor) Depreciation Rent (lab facility)

$24,000 5,000 26,000

Overhead is applied on the basis of direct labour hours. The rates above were computed using 5,500 direct labour hours. A local dental laboratory has offered to supply Powell all the crowns it needs. Its price is $100 for porcelain crowns and $132 for gold crowns; however, the offer is conditional on supplying both types of crowns-it will not supply just one type for the price indicated. If the offer is accepted, the equipment used by Powell's laboratory would be scrapped (it is old and has no market value), the lab facility would be closed and the supervisor would be laid off. Powell uses 1,500 porcelain crowns and 1,000 gold crowns per year. Required – 1. 2. 3.

Should Powell continue to make its own crowns or should they be purchased from the external supplier? What is the dollar effect of purchasing? Suppose that the lab facility is owned rather than rented and that the $26,000 is depreciation rather than rent. What effect does this have on the analysis in requirement 1? Refer to the original data. Assume that the volume of crowns is 3,000 porcelain and 2,000 gold. Should Powell make or buy the crowns? Explain the outcome.

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Management Accounting - Module 4

Add/Drop a Product, Service or Department! • 

analyze the incremental impact on profits of adding or dropping the product, service or department!

• 

consider:! –  fixed cost allocations! –  cannibalization of existing products! –  alternative uses of space!

• 

problem solving: calculate the incremental income of adding or dropping: incremental CM, avoidable fixed costs, opportunity costs (lost CM)! 6

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Problem 3 – Add/Drop Sales have never been good in Department C of Stacey’s Department Stores, For this reason, management is considering the elimination of the department. A summarized income statement for the store, by departments, for the most recent month is given below:

Sales Variable expenses

Total $1,000,000 574,300

Contribution margin Fixed expenses Salaries Utilities Direct advertising General advertising 1 Rent on building 2 Employment taxes 3 Depreciation of fixtures Insurance and property taxes On inventory and fixtures General office expenses Service department expenses Net income (loss) 1 2 3

$

Department A B $500,000 $320,000 338,000 166,000

C $180,000 70,300

425,700

162,000

154,000

109,700

49,000 6,200 89,000 25,000 38,000 4,900 36,000

18,000 2,600 32,000 12,500 16,000 1,800 12,000

16,000 2,000 27,000 8,000 12,000 1,600 15,000

15,000 1,600 30,000 4,500 10,000 1,500 9,000

7,900 54,000 81,000 391,000

2,300 18,000 27,000 142,200

4,000 18,000 27,000 130,600

1,600 18,000 27,000 118,200

34,700

$ 19,800

$ 23,400

$ (8,500)

Allocated on the basis of sales dollars Allocated on the basis of space occupied Based on salaries paid directly in each department

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The following additional information is available: a. If department C is eliminated, the utilities bill will be reduced by $700 per month. b. All departments are housed in the same building. The store leases the entire building at a fixed annual rental rate. c. One of the employees in department C is Fred Jones, who has been with the company for many years. Mr. Jones will be transferred to another department if Department C is eliminated. His salary is $1,000 per month. Transferring Mr. Jones to the other department will allow that department to avoid hiring an new employee that would have been paid $800 per month. d. The fixtures in department C would be transferred to the other departments if department C is eliminated. One-fourth of the insurance and property taxes in Department C relates to the fixtures of the department. e. The company has two service departments – purchasing and warehouse.. If Department C is eliminated, one employee in the warehouse can be discharged. This employee’s salary is $800 per month. General office expenses will not change, f. The space being occupied by department C could be subleased at a rental rate of $48,000 per month. g. If department C is eliminated, the company expects department A’s sales to increase by 10% and department B’s sales to decrease by 5%. Required – Do you recommend the elimination of department C. Use incremental analysis.

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Management Accounting - Module 4

The Scarce Resource Decision! • 

involves choosing which product to produce when there is a shortage of a resource used in more than one product!

• 

if one resource constraint exists, then the contribution margin per unit of constraining factor is used to rank profitability of products!

• 

if more than one constraint, must formulate and solve a linear programming problem!

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Scarce Resources - cont d! • 

problem solving:! –  calculate the contribution margin for each product! –  divide by the units of scarce resource to obtain the CM per unit of scarce resource! –  maximize profits by meeting demand for products which have a higher CM/unit of scarce resource!

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Problem 4 – Make/Buy + Scarce Resources Stewart Industries has been producing two bearings, components B12 and B18, for use in production. Data regarding these two components follow:

Machine hours required per unit Standard cost per unit: Direct materials Direct labor Manufacturing overhead Variable* Fixed**

B12

B18

2.5

3.0

$ 2.25 4.00

$ 3.75 4.50

2.00 3.75 $12.00

2.25 4.50 $15.00

* Variable manufacturing overhead is applied on the basis of direct labor hours. ** Fixed manufacturing overhead is applied on the basis of machine hours. Stewart's annual requirement for these components is 8,000 units of B12 and 11,000 units of B18. Recently, Stewart's management decided to devote additional machine time to other product lines, with the result that only 41,000 machine hours per year can be dedicated to the production of the bearings. An outside company has offered to sell Stewart the annual supply of the bearings at prices of $11.25 per unit for B12 and $13.50 per unit for B18. Stewart wants to schedule the otherwise idle 41,000 machine hours to produce bearings so that the company can minimize its costs (maximize its net benefits). Required: Determine the combination of purchasing and manufacturing that will maximize benefits.

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Problem 5 – Scarce Resources Innovate Design Inc. sells three types of heat sensitive products: Cool, Warm and Hot. Estimated sales demand, unit selling prices and production requirements are as follows:

Estimated sales demand Unit sales price Production requirements per unit: Material Y9 (in kilograms) Heat sensitive paint (in litres)

Cool

Warm

Hot

600 $16

500 $18

400 $14

8 6

5 12

2 18

The company has existing stocks of 300 units of Cool and 200 units of Hot, but is adopting just-in-time inventory management and expects to reduce inventory to zero by the end of next year. All three products use the same direct materials. In the next year, the available supply of materials will be restricted to 5,000 kilograms of material Y9 and 12,000 litres of heat sensitive paint. Material Y9 costs $0.95 per kilogram and the heat sensitive paint costs $0.50 per litre. All other costs are fixed. Required Calculate the number of units of each product Innovate Design Inc. should produce next year to maximize company profits.

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Management Accounting - Module 4

Joint Processes / Sell or Process Further! • 

when a joint process results in outputs which (1) can be sold at the split-off point AND (2) can be processed further and sold at a higher price!

• 

decision is whether to process further or sell at the split-off point!

• 

decision rule: process further if the incremental revenues less the incremental costs of processing further exceed the sales value at the split-off point!

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Management Accounting - Module 4

Linear Programming!

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Linear Programming! • 

used when there is more than one binding constraint!

• 

objective function - what we want to maximize (CM) or minimize (costs)!

• 

constraints are stated in terms of equations, i.e. - ! ! !5X + 7Y≤ 50,000!

• 

solve by the graphical method!

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Problem 11 – Linear Programming Iris manufacturing produces two products, X and Y. The company utilizes just-in-time inventory techniques whereby little or no raw materials, work-in-process or finished goods inventories are maintained. Careful planning of production schedules is required to ensure the success of the just-in-time inventory systems. For the month of July, the sales manager estimates that the maximum demand will be 2,500 units of product X and 2,000 units of product Y. The company's contract with its raw materials supplier stipulates that a maximum of 32,000 kilograms of direct materials will be delivered to Iris Manufacturing during July at a cost of $1.25 per kilogram. Employee vacations are expected to limit direct labor to 900 hours during July at a rate of $20.00 per hour. Price and production data for each product are as follows:

Selling Price Raw materials Direct labor Variable overhead

X $30.00 per unit 10 kg per unit 12 minutes per unit $7.00 per DLH

Y $32.00 per unit 8 kg per unit 18 minutes per unit $8.50 per DLH

Required: (a)

Formulate and solve the linear programming problem required to determine the production mix plan that will maximize the total contribution margin during the month of July. Calculate the optimum contribution margin for July.

(b)

How much of an overtime premium should Iris Manufacturing be willing to pay per hour to increase its direct labor capacity by 50 hours in July?

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Problem 11 a. X 30.00 -12.50 -4.00 -1.40 12.10

Selling price Raw materials: 10kg x 1.25 | 8kg x 1.25 Direct labour: .2 x 20 | .3 x 20 Variable overhead: .2 x 7 | .3 x 8.50

Objective Function Subject to:

TCM = 12.10x + 13.45y .2x + .3y ≤ 900 10x + 8y ≤ 32,000 x ≤ 2,500 y ≤ 2,000 x ≥ 0, y ≥ 0

Y 32.00 -10.00 -6.00 -2.55 13.45

Maximize Direct labour Direct materials Demand Demand Non-negative

Graphing the above, we get the following points: Y \ Y 2,500 Y ≤ 2,000 2,000

A

B X ≤ 2,500

1,500

DL

1,000

C

500

DM

X 500

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1,500

2,000

2,500

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Point A B C

X 1,500 1,714 2,500

Y 2,000 1,857 875

TCM 45,050 45,716 42,019

Point B is optimal. b.

The direct labour constraint changes to : .2x + .3y ≤ 950 If you graph this new line, you will find that it is above the old direct labour line and that in fact, you cannot use the extra 50 hours due to the materials constraint:

Y \ Y 2,500 Y ≤ 2,000 DL

2,000 D

X ≤ 2,500 1,500

1,000

500

DM

X 500

1,000

1,500

2,000

2,500

We get a new point, D which it at the intersection of the direct materials and the Y demand lines. Point D

X 1,600

Y 2,000

TCM 46,260

Thus, we get an incremental $46,260 - 45,716 = $544 by moving from point B to D.

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At this point, we need the following direct labour hours: .2 (1,600) + .3 (2,000) = 920 or an additional 20 hours The maximum we would be willing to pay is $544/20 = $27.20 overtime premium per hour for up to 20 hours.

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Problem 13 - Uncertainty Enrico, a renowned pastry chef employed by a four-star hotel, has decided to leave his job at the hotel and invest $100,000 to open his own upscale pastry shop. His preliminary investigations have uncovered the following: i) There is a 55% chance that the market size in the area will be 600,000 pastries per year and a 45% chance that it will be 450,000 pastries per year. ii) The size of market share that Enrico will capture will depend on the location of his shop. Two possibilities are available: location A, which costs $36,000 annual rent, and location B, which costs $8,000 annual rent. It is estimated that Enrico will capture a 30% share of the total market if he opens a shop in location A and a 21% share of the total market if he opens a shop in location B. The predicted market shares are based on a selling price of $2.00 per pastry. Variable costs are estimated to be $0.80 per pastry and fixed costs, other than rent, are estimated to be $80,000 per year at location A and $50,000 per year at location B. Required a. Determine at which location Enrico should open his shop. b. How much should Enrico be willing to pay to know with certainty the total market size?

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Management Accounting - Module 4

Decision Analysis under Uncertainty!

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Uncertainty! • 

typically involves setting up a pay-off table:!

States

State 1

P = x

State 2

P = 1 - x

Expected

Payoff

Action 1

Action 2

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Management Accounting - Module 4

Uncertainty Example! Jacques operates a hot dog stand on Sunday mornings in the market. Every Friday he has to let the market management know whether or not he will set up his stand inside or outside. If he sets up inside, the rent is $100 for the day. If he sets up outside, the rent s $200 for the day. Each hot dog sells for $2.00 and variable costs per hot dog are $0.50. It is 3:00 on Friday afternoon and Jacques has one hour to decide where the stand will be located. The Weather Network s forecast of rain is 30% for Sunday. He estimates sales volumes to be the following: !

Rain

No Rain

Inside

Outside

300

180

70

400

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Accelerated Program Week 18 Suggested study plan for this week: Primary List 1.

Review what we did in class on Saturday.

3.

Relevant Costing (ch 12) MCQ + all problems - I would not necessarily do these all in one week, but I would spread them out over time. Special Order: 2, 4, 5, 8, 12, 13 Make vs. Buy: 1, 10, 11, Add/Drop: 3, 6, 15 Scarce Resource: 7, 14

Secondary List

Prepare the following for next Saturday: IC6 – Oceanic Airlines IC7 - Altaco IC8 - Sportway IC9 – Fisher Manufacturing IC10 – Piston Co. 2.

Linear Programming (ch 13) MCQ + 1, 2, 3 4, 5, 6, 7 In-Class Problem 12 – Baxter - will be taken up in class next Saturday. Also note that the notes go into way more detail than what I cover or what is expected from you on the Entrance Exam. I would only read pages 4561. Read the rest only if you have an interest in this stuff.

3.

Uncertainty (ch 14) In-Class Problem 14 – Jackson – will be taken up in class next Saturday.

4.

Prepare the Week 18 Quiz.

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Problem 6 – Add/Drop Profits have been decreasing for several years at Oceanic Airlines. In an effort to improve the company's performance, consideration is being given to dropping several flights that appear to be unprofitable. A typical income statement for one such flight (flight 482) is given below (per flight): Ticket revenue (175 seats x 40% occupancy x $200 ticket price) Less variable expenses ($15 per person)

$14,000 1,050

100.0% 7.5

Contribution margin

12,950

92.5%

Less flight expenses: Salaries, flight crew Flight promotion Depreciation of aircraft Fuel for aircraft Liability insurance Salaries, flight assistants Baggage loading and flight preparation Overnight costs for flight crew and assistants at destination Total flight expenses

1,800 750 1,550 6,800 4,200 500 1,700 300 17,600

Net operating loss

-$4,650

The following additional information is available about flight 482: a. Members of the flight crew are paid fixed annual salaries, whereas the flight assistants are paid by the flight. b. One-third of the liability insurance is a special charge assessed against flight 482 because in the opinion of the insurance company, the destination of the flight is in a "high-risk" area. The remaining two-thirds would be unaffected by a decision to drop flight 482. c. The baggage loading and flight preparation expense is an allocation of ground crews' salaries and depreciation of ground equipment. Dropping flight 482 would have no effect on the company's total baggage loading and flight preparation expenses. d. If flight 482 is dropped, Oceanic Airlines has no authorization at present to replace it with another flight. e. Depreciation of aircraft is due entirely to obsolescence. Depreciation due to wear and tear is negligible. f. Dropping flight 482 would not allow Oceanic Airlines to reduce the number of aircraft in its fleet or the number of flight crew on its payroll. Required – Prepare an analysis showing what impact dropping flight 482 would have on the airline's profits.

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Problem 7 – Special Order Altaco, Ltd. manufactures one product in its Edmonton factory. The general manager, Ellen Simpson, has just received a special request from a customer for 10,000 units of this product to be produced and delivered this month. The customer has suggested a selling price of $3.00 per unit. Simpson is unsure whether she should accept this offer. The company normally produces and sells 50,000 units per month and capacity is at 70,000 units per month. The normal selling price is $4.00 per unit. Simpson approached Frank Giterman, the plant accountant, with the issue. Giterman was unable to provide a proper analysis at that time because he had a meeting to attend. However, in quickly reviewing his files, he provided the following schedule of cost information: Level of Activity (units of production per month) 40,000 50,000 60,000 70,000

Average Unit Cost $3.675 3.500 3.383 3.41

As he rushed off for his meeting, Giterman indicated that if production exceeds 62,000 units per month, an additional supervisor must be hired and costs will increase by $7,700 per month. Required: Note: All requirements are independent situations. Expected activity levels do not include the 10,000 units. 1. 2. 3.

Assume that the company already expects to be working at a level of 50,000 units for the month. Calculate the minimum price the company could charge for this special order without reducing its expected net income. If the company expects to produce and sell 55,000 units this month, calculate the minimum price the company could charge the customer for this special-order job without reducing its expected net income. Assume that the company expects to produce and sell 65,000 units this month. Should the manager accept the customer's order? Support your decision with appropriate calculations.

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Problem 8 – Make/Buy Sportway, Inc., is a wholesale distributor supplying a wide range of moderately priced sporting equipment to large chain stores. About 60 percent of Sportway's products are purchased from other companies, while the remainder of the products are manufactured by Sportway. The company's Plastics Department is currently manufacturing molded fishing tackle boxes. Sportway is able to manufacture and sell 8,000 tackle boxes annually, making full use of its direct labour capacity at available workstations. Following are the selling price and costs associated with Sportway's tackle boxes. Selling price per box Costs per box: Molded plastic Hinges, latches, handle Direct labour ($15/hour) Manufacturing overhead Selling and administrative expenses Profit per box

$86.00 $ 8.00 9.00 18.75 12.50 17.00

65.25 $20.75

Because Sportway believes it could sell 12,000 tackle boxes if it had sufficient manufacturing capacity, the company has looked into the possibility of purchasing the tackle boxes for distribution. Maple Products, a steady supplier of quality products, would be able to provide up to 9,000 tackle boxes per year at a price of $68 per box delivered to Sportway's facility. Bart Johnson, Sportway's product manager, has suggested that the company could make better use of its Plastics Department by manufacturing skateboards. To support his position, Bart has a market study that indicates an expanding market for skateboards and a need for additional suppliers. He believes that Sportway could expect to sell 17,500 skateboards annually at a price of $45 per skateboard. Bart's estimate of the costs to manufacture the skateboards follows: Selling price per skateboard Costs per skateboard: Molded plastic Wheels, hardware Direct labor ($15/hour) Manufacturing overhead Selling and administrative expenses Profit per skateboard

$45.00 $5.50 7.00 7.50 5.00 9.00

34.00 $11.00

In the Plastics Department, Sportway uses direct labor hours as the application base for manufacturing overhead. Included in the manufacturing overhead for the current year is $50,000 of factory-wide, fixed manufacturing overhead that has been allocated to the Plastics Department. For each unit of product that Sportway sells, regardless of whether the product has been purchased or is manufactured by Sportway, an allocated $6 fixed

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overhead cost per unit for distribution is included in the selling and administrative expenses for all products. Total selling and administrative expenses for the purchased tackle boxes would be $10 per unit. Required In order to maximize the company's profitability, prepare an analysis based on the data presented that will show which product or products Sportway, Inc., should manufacture and/or purchase. It should also show the associated financial impact. Support your answer with appropriate calculations.

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Problem 9– Relevant Costs Fisher Manufacturing Co. produces and sells its product AA100 to well-known cosmetics companies for $940 per ton. The marketing manager is considering the possibility of refining AA100 further into finer perfumes before selling them to the cosmetics companies. Product AA101 is expected to command a price of $1500 per ton, and AA102 a price of $1700 per ton. The maximum expected demand is 400 tons for AA101 and 100 tons for AA102. The annual plant capacity of 2400 hours is fully utilized at present to manufacture 600 tons of AA100. The marketing manager proposed that Fisher sell 300 tons of AA100, 100 tons of AA101, and 75 tons of AA102 in the next year. It requires four hours of capacity to make one ton of AA100, two hours to refine AA100 further into AA101, and four hours to refine AA100 into AA102 instead. The plant accountant has prepared the following cost sheet for the three products: COSTS PER TON AA100 AA101 Direct materials: Chemicals and fragrance AA100 Direct labor Manufacturing support: Variable Fixed Total manufacturing costs Selling support: Variable Fixed

Proposed sales level Maximum demand

AA102

$560 0 60

$ 400 800 30

$ 470 800 60

60 120 $800

30 60 $1,320

60 120 $1,510

20 10

30 10

30 10

$830

$1,360

$1,550

300 tons 600 tons

100 tons 400 tons

75 tons 100 tons

Required (a) (b)

(c)

Determine the production levels for the three products under the present constraint on plant capacity that will maximize operating income. Suppose a customer is very interested in the new product AAl0l. It has offered to sign a long-term contract for 400 tons of AA101. It is also willing to pay a higher price if the entire plant capacity is dedicated to the production of AA101. What is the minimum price for AA101 at which it becomes worthwhile for Fisher to dedicate its entire capacity to the production of AA101? Suppose, instead, that the capacity can be increased temporarily by 600 hours if the plant is operated overtime. Overtime premium payments to workers and supervisors will increase direct labor and variable manufacturing support costs by 50% for all products. All other costs will remain unchanged. Is it worthwhile operating the plant overtime? If the plant is operated overtime for 600 hours, what are the optimal production levels for the three products? Show details to your calculations.

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Problem 10 – CVP Analysis / Regression / Relevant Costs The Piston Co. is a firm operating in the automotive industry. The controller had decided to use regression analysis to predict manufacturing overhead for next year's budget. She ran a number of regressions based on data from the company's most recent ten-year history. Partial outputs from two of the regressions run by the controller are as follows:

Dependent variable Independent variable

First Regression

Second Regression

Overhead Cost

Overhead Cost

Machine Hours

Direct Labour Hours

0.72 4.5 18.54

0.94 11.7 10.62

r2 t value b coefficient Required a)

Which regression would you choose and why?

b)

For inventory costing purposes, the Piston Co. used an overhead allocation rate based on machine hours for its four main product lines. Recent gross margin statements are as follows: A Selling price per unit Cost of goods sold: Materials Labor @ $16/direct labor hour Overhead @ $20/machine hour Gross margin per unit

Product B

C

D

$100

$115

$128

$155

12 32 20 64

16 24 40 80

25 40 30 95

30 32 60 122

$ 36

$ 35

$33

$33

Using the results of the second regression run by the controller and the following additional data, determine the number of units of each of the four product lines (at standard mix) that the Piston Co. will need to sell in order to achieve its target of a 9% after-tax return on sales. The company's effective tax rate is 40%.

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Additional data: Fixed manufacturing overhead costs Fixed selling costs Standard product mix (e.g., Product A accounts for 3 of every 10 company products sold) c)

$335,000 $ 50,000 A:B:C:D = 3:1:2:4

It is expected that, next year, the Piston Co.'s production capacity of 30,000 machine hours will be reached. Demand for each of the four product lines next year is estimated as follows: A B C D

Units 5,000 1,500 3,500 7,000

Determine the optimal production strategy for the Piston Co. (i.e., how many units of each product line should be produced and sold?). Use the data and assumptions provided in part (b). (Ignore standard mix.)

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Problem 12 – Linear Programming Baxter, Inc., manufactures two industrial products, X-10, which sells for $90 a unit, and Y-12, which sells for $85 a unit. Each product is processed through both of the company's manufacturing departments. The limited availability of labor, material, and equipment capacity has restricted the firm's ability to meet the demand for its products. The production department believes that linear programming can be used to routinize the production schedule for the two products. It has the following weekly data: Amount Required per Unit Weekly X-10 Y-12 Direct material: Supply limited to 1,800 pounds at $12 per pound Direct labor Department 1: Supply limited to 10 people at 40 hours each at an hourly cost of $6 Department 2: Supply limited to 15 people at 40 hours each at an hourly rate of $8 Machine time Department 1: Capacity limited to 250 hours Department 2: Capacity limited to 300 hours

4 pounds

2 pounds

2/3 hour

1 hour

1.25 hours

1 hour

0.5 hour 0 hours

0.5 hour 1 hour

Baxter's overhead costs are accumulated on a plantwide basis and are assigned to products on the basis of the number of direct labor-hours required to manufacture the product. This base is appropriate for overhead assignment because most of the variable overhead costs vary as a function of labor time. The estimated overhead cost per direct labor-hour follows: Variable overhead cost Fixed overhead cost Total overhead cost per direct labor-hour

$6 6 $12

The production department formulated the following equations for the linear programming statement of the problem: A = Number of units of X-10 to be produced. B = Number of units of Y-12 to be produced Objective function to minimize costs:

Minimize 85A + 62B

Constraints:

4A + 2B ≤ 1,800 pounds 2/3A + 1B ≤ 400 hours 1.25A + 1B ≤ 600 hours A ≥ 0, B ≥ 0

Material Department 1 labor Department 2 labor Other

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Required a. b. c.

The formulation of the linear programming equations prepared by Baxter's production department is incorrect. Write a brief memo to management explaining what errors were made in its formulation. Formulate and label the proper equations for the linear programming statement of Baxter's production problem. Solve the linear program.

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Problem 14 - Uncertainty Jackson, Inc., manufactures and distributes a line of toys. The company neglected to keep its doll house line current. As a result, sales have decreased to approximately 10,000 units per year from a previous high of 50,000 units. The doll house was recently redesigned and is considered by company officials to be comparable to its competitors' models. Joan Blocke, the sales manager, is not sure how many units can be sold next year, but she is willing to place probabilities on her estimates. Blocke's estimates of the number of units that can be sold during the next year and the related probabilities are as follows: Estimated Sales in Units

Probability

20,000 30,000 40,000 50,000

.10 .40 .30 .20

The units will sell for $20 each. The entire year's sales must be manufactured in one production run. If demand is greater than the number of units manufactured, sales will be lost. If demand is below supply, the extra units cannot be carried over to the next season and must be discarded The disposal costs of discarding one doll house is $2 per doll house. Variable costs are as follows: Manufacturing Selling

$8 2

Fixed costs are $140,000 for production volumes of 20,000 to 30,000 and $160,000 for volumes of 40,000 and more. The company must decide on the optimal size of the production run. Required 1. 2.

Based on the above information, optimal size run do you recommend? If the company could hire a consultant that could predict with a high degree of accuracy what the sales in units would be, what is the most you would be willing to pay this consultant?

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