W HY A LLOC ATE J OINT -P ROCES S C OS T S ?

Why should managerial accountants and managers be concerned with allocating joint-process costs when joint-cost allocations tend to be somewhat arbitrary? Organizations allocate joint costs for many important reasons, including measuring performance, determining and responding to regulatory rate changes, estimating casualty losses, and resolving contractual interests and

KeyTerms and Concepts 475

obligations. Manufacturing companies are required to use joint-process cost allocations for financial and tax reporting to value inventories and cost of goods sold. For example, Humbolt Company must allocate joint-process costs to its products to value inventory and measure income for reporting purposes.

Though there is no precise way of tracing joint-process costs to joint products (as ABC seeks to do in other production processes), the results of allocating joint-process costs in different ways can be very important to managers for planning, performance evaluation, and decision making.

S ummar y

The following items correspond to the learning objectives presented at the beginning of the chapter.

1. Explain the nature of indirect costs. A common, or indirect, cost results from the joint use of a facility or a service by several products, departments, or processes.

2. Explain why companies allocate indirect costs to departments and products. Firms must allocate common costs to develop product cost information for purposes of pricing and bidding, contract cost reimbursement, and motivation.

3. Describe how to allocate service department costs to production departments. First, assign overhead costs that are directly attributable to a service or production department. Second, allocate other overhead costs based on appropriate cost drivers. Third, allocate service department costs to production departments.

4. Explain why activity-based costing is used to allocate service department costs. Applying the techniques of activity-based costing typically results in identifying more accurate cost- allocation bases (cost drivers). This can lead to improved allocations of service department costs to production departments.

5. Identify methods of allocating marketing and administrative costs to departments. Management often applies techniques similar to those employed in allocating service department costs to allocate marketing and administrative costs for purposes of performance evaluation.

6. Explain how to allocate joint-process costs. Joint-process cost allocations arise from the need to assign joint-process costs to two or more products manufactured from a common input. The two methods of allocating joint-process costs are based on net realizable value or physical measures.

7. Explain why joint-process costs are allocated. Companies allocate joint-process costs for several reasons, including performance evaluation, reporting purposes, and establishing regulated rates.

Key Terms and Concepts

Common cost

Net realizable value method

Direct cost

Physical quantities method

Indirect cost

Service department

Joint process

Service department cost allocation

Joint-process costs

Splitoff point

Joint products

Step method

476 Chapter 13 Allocating Costs to Responsibility Centers

S olutions to S elf-Study Problems

SUGGESTEDSOLUTIONTOPROBLEM13.1FORSELF-STUDY S H A N N O N C O M PA N Y

O ve r h e a d A l l o c a t i o n S c h e d u l e fo r Fe b r u a r y Dept. S

Dept. M

Storeroom Maintenance Maintenance Wages ....................................

Total

Dept. A

Dept. B

Dept. C

--- $1,800 Storeroom Wages .........................................

40 20 Supplies Used ...............................................

1) Janitor’s wages a ..........................................

1) Rent---Factory Building a ............................

2) Electricity, etc. b .......................................... 200 b 60 60 40 20 20 (

60 60 Total ...........................................................

2) Misc. Factory Costs b ...................................

$1,800 $2,140 Allocation of Maintenance Dept.

Costs to Other Depts. c ...........................

$2,014 Allocation of Storeroom Dept.

(2,014) d Total Overhead in Depts. A, B, and C ....

Costs to Depts. A, B, and C d ................

b Allocated based on the percentages shown in column ( 1) of Schedule A below; 32% of the total cost to Dept. A, 22% to Dept. B, etc. c Allocated based on the percentages shown in column (

2) of Schedule A; 30% to Dept. A, 30% to Dept. B, etc.

d Allocated based on the percentages shown in column (

3) of Schedule A; 30% to Dept. A, 40% to Dept. B, etc.

Allocated based on the percentages shown in column (

4) of Schedule A; 70% to Dept. A, etc.

Floor Space

Other

Maintenance Requisitions

Dept. A .....................................................................

Dept. B .....................................................................

Dept. C ......................................................................

Dept. S ......................................................................

4 10 10 ---

Dept. M .....................................................................

SUGGESTEDSOLUTIONTOPROBLEM13.2FORSELF-STUDY The joint costs to be allocated amount to $52—the total of the $15 in direct materials costs and

the $37 in conversion costs. The net realizable value for butter is $22, $1.10 per pound times

20 pounds. The net realizable value of the powder is $40.50, $.90 per pound times 45 pounds per 100 pounds of input. The allocation follows:

To cocoa butter: $22 :00

$22 :00 þ $40:50 To cocoa powder:

Questions, Exercises, Problems, and Cases 477

SUGGESTEDSOLUTIONTOPROBLEM13.3FORSELF-STUDY Because there is a total of 65 pounds of output of major products (20 pounds of butter and

45 pounds of powder) at the splitoff point, the allocation is To cocoa butter:

To cocoa powder:

resulting in an allocation of the total $52 to the two products.

Que stions , Exercis e s , Problems , and Ca s e s

REVIEWQUESTIONS

1. Review the meaning of the concepts or terms given in Key Terms and Concepts.

2. Distinguish between a production department and a service department.

3. Distinguish between a direct cost and an indirect cost.

4. Give the steps in the cost allocation process.

5. What is the nature of a joint-production process?

6. What is the objective of joint-cost allocation? C R I T I C A L A N A LY S I S A N D D I S C U S S I O N Q U E S T I O N S

7. For each of the types of common cost in the first column, select the most appropriate allocation base from the second column:

Common Cost

Allocation Base

Building Utilities

Value of Equipment and Inventories

Payroll Accounting

Number of Units Produced

Insurance

Number of Employees

Equipment Repair

Space Occupied

Quality Control Inspection

Number of Service Calls

8. When firms allocate service department costs to production departments, why would they first accumulate these costs at the service department level rather than assigning them directly to production departments?

9. Materials are considered direct with respect both to the manufacturing department using them and to the product. However, indirect materials cannot be associated directly with a specific job or product but may be directly related to the manufacturing department where the indirect materials are used. What are the concepts of direct and indirect costs in this setting?

10. Under what conditions are the results from using the direct method of allocations the same as those from using either other method? Why?

11. Consider a company with two producing departments and one service department. The service department distributes its costs to the producing departments on the basis of number of employees in each department. If the costs in the service department are fixed, what effect

478 Chapter 13 Allocating Costs to Responsibility Centers

would the addition of employees in one department have on the costs allocated to the other department? Comment on the reasonableness of the situation.

12. The manager of an operating department just received a cost report and has made the following comment with respect to the costs allocated from one of the service departments: ‘‘This charge to my division does not seem right. The service center installed equipment with more capacity than our division requires. Most of the service department costs are fixed, but we seem to be allocated more costs in periods when other departments use less. We are paying for excess capacity of other departments when other departments cut their usage levels.’’ How might this manager’s problem be solved?

13. Name some of the costs and benefits of cost allocation.

14. A critic of cost allocation noted, ‘‘You can avoid arbitrary cost allocations by not allocating

any costs.’’ Comment.

15. Discuss reasons for allocating costs to departments.

16. Your division operates a joint production process. Management of the company has decided to shut down your division and liquidate all assets because the division no longer provides a competitive return. Prepare an outline of the costs and benefits (to all affected parties) of the decision to shut down and liquidate your division.

17. Three students share a house. Having better things to do than clean house, they hire someone to come in and clean once each week. How should they share the costs of the housekeeper? One simple solution is to share the cost equally. Suppose, however, that one student’s bedroom is twice as large as each of the other students’ bedrooms. The second student has a small bedroom and uses the house only four days per week. The third student uses the house all week, has a small bedroom, and is generally acknowledged to be the cleanest of the three. Sharing the cost equally is simple, but is it fair?

EXERCISES Solutions to even-numbered exercises are at the end of the chapter after the cases.

18. Allocating overhead to departments and jobs. The accountants of Meridian Production Company, a company that makes television commercials, made the following estimates for a year:

Filming

Editing Printing

Department

Department Department

Estimated Overhead .....................................

Estimated Direct Labor Time .....................

5,500 Hours

6,250 Hours 6,000 Hours

a. Compute the overhead allocation rates for each department using direct labor hours as a

basis.

b. Management wants to know how much the Toyota commercial job cost. The following table shows the materials and labor costs; you will have to add the overhead costs using direct labor hours as the allocation base.

Toyota Commercial

Filming

Editing Printing

Department

Department Department

Direct Material Cost ................................................

Direct Labor Cost .....................................................

Direct Labor Time ....................................................

250 Hours

400 Hours 38 Hours

19. Allocating overhead. Cameron Company has two production departments and a maintenance department. In addition, the company keeps other costs for the general plant in a

Questions, Exercises, Problems, and Cases 479

separate account. The estimated cost data for Year 1 follow:

General Plant

Direct Labor ............................

Indirect Labor ........................

Indirect Materials ..................

The general plant services the three departments in the following proportions: 50 percent (Department 1); 30 percent (Department 2); 20 percent (Maintenance). Allocate maintenance costs based on maintenance hours.

Allocate maintenance department and general plant costs to the production departments. Use the step method, starting with general plant costs.

20. Allocating overhead to jobs. Hamilton, Inc., uses a job system of cost accounting. The data presented here relate to operations in its plant during January. Hamilton, Inc., has two production departments and one service department. The actual factory overhead costs during the month are $8,000. At the end of the month Mr. Hamilton allocates overhead costs as follows: Department A, $4,200; Department B, $3,200; Department C, $600. He allocates the service department (Department C) overhead of $600 as follows: two-thirds to Department A, one-third to Department B.

Mr. Hamilton applies factory overhead to jobs at the predetermined rates of 50 percent of direct labor costs in Department A and 75 percent in Department B. The firm delivers the jobs upon completion. The firm completed job nos. 789, 790, and 791 in January. Jobs 788 and 792 are still in process on January 31.

a. Complete the job production record in the following table by filling in the appropriate amounts. Be sure to show supporting calculations. (Job 788 has been done for you.)

b. For Departments A and B, compute the difference between the applied overhead using the predetermined rates and the actual overhead after allocating Department C overhead to Departments A and B.

J o b P r o d u c t i o n R e c o rd

Direct Labor

Direct Matl.

Applied Overhead

Jobs in Jobs in Process,

Total Process, Completed Job Order No.

Jan. 1 A B A B A B Costs Jan. 31 Jobs 788 ................................. $2,400

21. Allocating service department costs using the step method. Gretsky Company has two service departments (maintenance and general factory administration) and two operating departments (cutting and assembly). Management has decided to allocate maintenance costs on the basis of the area in each department and general factory administration costs on the basis of labor hours the employees worked in each of their respective departments.

480 Chapter 13 Allocating Costs to Responsibility Centers

The following data appear in the company records for the current period:

General Factory

Administration Maintenance Cutting Assembly

Area Occupied (square feet) ..........................................

Labor Hours .......................................................................

---

Direct Labor Costs (operating departments only) ....

Service Department Direct Costs ..................................

Use the step method to allocate service departments’ costs to the operating departments, starting with maintenance.

22. Using multiple cost drivers to allocate costs. Assume Johnson Manufacturing uses three allocation bases to allocate overhead costs from departments to jobs: number of different parts, number of machine hours, and number of job setup hours. The information needed to compute the allocation rates follows:

Department A

Department B

Units of

Costs

Activity

Costs Activity

1. Number of Different Parts ...........................

2. Number of Machine Hours Worked ............

3. Number of Hours to Set Up Jobs ..............

Job 300ZX required the following activities:

Department A: 10 parts, 1,000 machine hours, 20 setup hours. Department B: 2 parts, 200 machine hours, 10 setup hours.

Allocate overhead costs to Job 300ZX.

23. Using multiple cost drivers to allocate costs. Assume Beatrice, Inc., uses three allocation bases to allocate overhead costs from departments to jobs: number of different parts, number of machine hours, and number of job setup hours. The information needed to compute the allocation rates follows:

Department X

Department Y

Costs

Units of Activity

Costs Units of Activity

1. Number of Different Parts ........................... $ 8,000

40 Parts

$ 1,600 10 Parts

2. Number of Machine Hours Worked ............ $208,000

32,000 Hours

$60,000 3,000 Hours

3. Number of Hours to Set Up Jobs .............. $ 24,000

300 Hours

$ 8,000 100 Hours

Job CLK430 required the following activities:

Department X: 10 parts, 1,000 machine hours, 20 setup hours. Department Y: 4 parts, 400 machine hours, 10 setup hours.

Allocate overhead costs to Job CLK430.

24. Joint-process costing. Search the Internet for an example of a company that either uses joint-process costing or provides joint-process cost consulting services. Prepare a short presentation that explains (a) the nature of the organization (industry, products, and/or services), (b) how it uses joint-process costing, and (c) how important you believe joint- process costs are to its decision making.

Questions, Exercises, Problems, and Cases 481

25. Joint-process costing and net realizable method. A company processes a chemical, DX-1, through a pressure treatment operation. The complete process has two outputs, L and T. The January costs to process DX-1 are $50,000 for materials and $100,000 for conversion costs. This processing results in two outputs, L and T, that sell for a total of $250,000. The sales revenue from L amounts to $200,000 of the total. Using the net realizable method, assign costs to L and T for January.

26. Using joint-process costing to measure product costs. The following information is for Tiger Company, which manufactures products X, Y, and Z from a joint process. Joint product costs were $63,000. Additional information follows.

If Processed Further

Product

Units Produced

Sales Value at Splitoff Sales Values Additional Costs

a. Assuming that joint product costs are allocated using the physical quantities method, what were the total costs of product X (including $18,000 if processed further)?

b. Assuming the joint product costs are allocated using the net realizable value method, what were the total costs of product Y (including the $14,000 if processed further)?

PROBLEMS

27. Consider the following conversation between a self-styled cost allocation expert and Joe, the manager of a diner.

Expert: Joe, you said you put in these peanuts because some people ask for them, but do you realize what this rack of peanuts is costing you? Joe: It’s not going to cost! It’s going to be a profit. Sure, I had to pay $100 for a fancy rack to hold the bags, but the peanuts cost 24 cents a bag, and I sell ’em for 40 cents. Suppose I sell 50 bags a week to start. It’ll take 12 weeks to cover the cost of the rack. After that I have a clear profit of 16 cents a bag. The more I sell, the more I make.

Expert: That is an antiquated and completely unrealistic approach, Joe. Fortunately, modern accounting procedures permit a more accurate picture, which reveals the complexities involved.

Joe: Huh? Expert: To be precise, those peanuts must be integrated into your entire operation and be

allocated their appropriate share of business overhead. They must share a proportion of your expenditures for rent, heat, light, equipment depreciation, decorating, salaries for your waitresses, cook. . . .

Joe: The cook? What’s he got to do with the peanuts? He doesn’t even know I have them. Expert: Look, Joe, the cook is in the kitchen, the kitchen prepares the food, the food is what

brings people in here, and the people ask to buy peanuts. That’s why you must charge a portion of the cook’s wages, as well as a part of your own salary, to peanut sales. This sheet contains a carefully calculated cost analysis, which indicates that the peanut operation should pay exactly $2,278 per year toward these general overhead costs.

Joe: The peanuts? $2,278 a year for overhead? Nuts! The peanuts salesman said I’d make money—put ’em on the end of the counter, he said, and get 16 cents a bag profit. Expert [with a sniff]: He’s not an accountant. Do you actually know what the portion of the counter occupied by the peanut rack is worth to you? Joe: Nothing. No stool there, just a dead spot at the end. Expert: The modern cost picture permits no dead spots. Your counter contains 60 square

feet, and your counter business grosses $60,000 a year. Consequently, the square foot of space occupied by the peanut rack is worth $1,000 per year. Since you have taken that area away from general counter use, you must charge the value of the space to the occupant.

Questions, Exercises, Problems, and Cases 483

continue with the allocated expenses, assigning each item to the various departments. Round all values to the nearest dollar and all percentages to one decimal place.

b. Prepare a condensed income statement with columns for Clothing, Accessories, and Total. Show the total operating expenses calculated in part a. as a single deduction from gross margin.

Salaries: Clerks .....................................................................

Supplies Used ...........................................................

Depreciation of Equipment ...................................

Building Rent ...........................................................

19,000

Payroll Taxes .............................................................

12,300

Workers’ Compensation Insurance .......................

2,080

Fire Insurance ..........................................................

1,000

Delivery Expense ......................................................

1,800

Miscellaneous Expenses .........................................

Cost of Goods Sold ..................................................

Inventory (average) ................................................

Floor Space (square feet) ......................................

Number of Employees .............................................

10 15 25

R OYA L S P E C I A LT Y S H O P AllocationBases

Expense

Bases of Allocation

Salaries---Other

Gross Margin

Supplies Used (unassigned)

Sales

Advertising (unassigned)

Sales

Building Rent

Floor Space

Payroll Taxes

Salaries (including both direct and other allocated salaries)

Workers’ Compensation Insurance

Salaries (including both direct and other allocated salaries)

Fire Insurance

Cost of Equipment and Inventory

Delivery Expense

Sales

Miscellaneous Expenses (unassigned)

Number of Employees

30. Allocating service department costs directly to operating departments. Meyers Com- pany has a commissary with two operating departments: P1, food inventory control, and P2, paper goods inventory control. It has two service departments: S1, computer services, and

Questions, Exercises, Problems, and Cases 485

Use the step method to allocate service department costs sequentially based on hours of service provided. Start with Maintenance and then allocate Quality Control. Check your solution by making certain that the firm finally allocates $310,000 to the production departments.

33. Allocating service department costs (adapted from CPA exam). Cowboy Enterprises has three service departments (administration, maintenance, and computer support) and two production departments (creative and assembly). A summary of costs and other data for each department prior to allocation of service department costs for the year ended June 30, Year 1, follows:

Creative Assembly Direct Material Costs ..............................................

Administration Maintenance Computer Support

$3,130,000 $ 950,000 Direct Labor Costs ...................................................

$1,950,000 $2,050,000 Overhead Costs .........................................................

$1,650,000 $1,850,000 Direct Labor Hours ..................................................

56,250 43,750 Number of Computers .............................................

12 8 20 280 200 Square Footage Occupied ......................................

The company allocates the costs of the administration, maintenance, and computer support departments on the basis of direct labor hours, square footage occupied, and number of computers, respectively. Round all final calculations to the nearst dollar.

a. Assuming that the company elects to distribute service department costs directly to production departments without interservice department cost allocation, what amount of maintenance department costs would the company allocate to the creative department?

b. Assuming the same method of allocation as in part a., what amount of administration department costs would the company allocate to the assembly department?

c. Assuming that the company elects to distribute service department costs to other service departments (starting with the computer support department) as well as the production departments, what amounts of computer support department costs would the company allocate to the maintenance department? (Note: Once the firm has allocated a service department’s costs, no subsequent service department costs are allocated back to it.)

d. Assuming the same method of allocation as in part c., what amount of maintenance department costs would the company allocate to the computer support department?

34. Allocating service department costs (adapted from CPA exam). The DiCaprio Company has three service departments (administration, maintenance, and technology support) and two production departments (creative and output). A summary of costs and other data for each department prior to allocation of service department costs for the year ended December 31, Year 1, follows:

Creative Output Direct Material Costs ..........................

Administration

Maintenance

Technology Support

$4,100,000 $ 800,000 Direct Labor Costs ...............................

$1,950,000 $2,000,000 Overhead Costs .....................................

$1,650,000 $1,800,000 Direct Labor Hours ..............................

112,500 87,500 Number of Computers .........................

24 16 40 560 400 Square Footage Occupied ..................

The company allocates the costs of the administration, maintenance, and technology support departments on the basis of direct labor hours, square footage occupied, and number of computers, respectively. Round all final calculations to the nearest dollar.

a. Assume that the company elects to distribute service department costs directly to production departments without interservice department cost allocation (that is, the direct method of cost allocation). What amount of maintenance department costs would the company allocate to the creative department?

b. Assuming the same method of allocation as in part a., what amount of administration department costs would the company allocate to the output department?

486 Chapter 13 Allocating Costs to Responsibility Centers

c. Assuming that the company elects to use the step mathod, which distributes service department costs to other service departments (starting with the technology support department) as well as the production departments, what amounts of technology support department costs would the company allocate to the maintenance department? (Note: Once the firm has allocated a service department’s costs, no subsequent service department costs are allocated back to it.)

d. Assuming the same method of allocation as in part c., what amount of maintenance department costs would the company allocate to the technology support department?

35. Joint cost allocation and product profitability. Wafers, Inc., processes silicon crystals into purified wafers and chips. Silicon crystals cost $60,000 per tank-car load. The process involves heating the crystals for 12 hours, producing 45,000 purified wafers with a market value of $20,000, and 15,000 chips with a market value of $140,000. The joint cost of the heat process is $25,600.

a. If the crystal costs and the heat process costs are to be allocated on the basis of units of

output, what cost is assigned to each product?

b. If the crystal costs and the heat process costs are allocated on the basis of the net

realizable value, what cost is assigned to each product?

c. How much profit or loss does the purified wafers product provide using the data in this problem and your analysis in requirement a.? Is it really possible to determine which product is more profitable? Explain why or why not.

36. Joint cost allocation and product profitability. Atlantic Timber processes timber into Grade A and Grade B lumber. Timber costs $200 per unit, where one unit equals 1,000 board feet. The process involves cutting timber into the two grades of lumber. Each unit of timber produces .25 unit (250 board feet) of Grade A lumber with a market value of $240 and .75 unit (750 board feet) of Grade B with a market value of $160. The joint cost of the production process is $100 per unit.

a. Assume that the joint costs of the two grades of lumber are to be allocated on the basis of units of output. What cost is assigned to each product (for .25 unit of Grade A and .75 unit of Grade B)?

b. If the joint costs are allocated on the basis of the net realizable value, what cost is assigned to each product? How much profit or loss does the Grade A lumber earn? Is it really possible to determine which product is more profitable? Explain why or why not.

CASES

37. Relating allocation methods to organizational characteristics for a retailer (adapted from CMA exam). Columbia Company is a regional office supply chain with 26 independent stores. The firm holds each store responsible for its own credit and collections. The firm assigns the assistant manager in each store the responsibility for credit activities, including the collection of delinquent accounts, because the stores do not need a full-time employee assigned to credit activities. The company has experienced a sharp rise in uncollectibles the past two years. Corporate management has decided to establish a collections department in the home office that takes over the collection function companywide. The home office of Columbia Company will hire the necessary full-time personnel. The firm will base the size of this department on the historical credit activity of all the stores.

Top management discussed the new centralized collections department at a recent management meeting. Management has had difficulty deciding on a method to assign the costs of the new department to the stores because this type of home office service is unusual. Top management is reviewing alternative methods.

The controller favored using a predetermined rate for charging the costs to the stores. The firm would base the predetermined rate on budgeted costs. The vice-president for sales preferred an actual cost charging system.

In addition, management also discussed the basis for the collection charges to the stores. The controller identified the following four measures of services (allocation bases) that the firm could use: (1) Total dollar sales. (2) Average number of past-due accounts. (3) Number of uncollectible accounts written off.

488 Chapter 13 Allocating Costs to Responsibility Centers

The department manager recommends that the five activity centers within the department accumulate the department costs. The five activity centers are systems analysis, program- ming, data preparation, computer operations (processing), and administration. She then suggests that the firm allocate the costs of the administration activity to the other four activity centers before developing a separate rate for charging users for each of the first four activities.

After reviewing the details of the accounts, the manager made the following observa- tions regarding the charges to the several subsidiary accounts within the department: (1) Salaries and benefits—records the salary and benefit costs of all employees in the

department. (2) Supplies—records paper costs for printers and a small amount for other miscellaneous

costs. (3) Equipment maintenance contracts—records charges for maintenance contracts that

cover all equipment. (4) Insurance—records cost of insurance covering the equipment and the furniture. (5) Heat and air conditioning—records a charge from the corporate heating and air

conditioning department estimated to be the incremental costs to meet the special needs of the computer department.

(6) Electricity—records the charge for electricity based on a separate meter within the

department. (7) Equipment and furniture depreciation—records the depreciation charges for all

equipment and furniture owned within the department. (8) Building improvements depreciation—records the amortization charges for the

building changes required to provide proper environmental control and electrical service for the computer equipment.

(9) Building occupancy and security—records the computer department’s share of the depreciation, maintenance, heat, and security costs of the building; the firm allocates these costs to the department on the basis of square feet occupied.

(10) Corporate administrative charges—records the computer department’s share of the corporate administrative costs. The firm allocates those costs to the department on the basis of number of employees in the department.

a. For each of the 10 cost items, state whether or not the firm should distribute it to the five activity centers; and for each cost item that the firm should distribute, recommend the basis on which it should be distributed. Justify your conclusion in each case.

b. Assume that the costs of the computer operations (processing) activity will be charged to the user departments on the basis of computer hours. Using the analysis of computer utilization shown as a footnote to the department cost schedule presented in the problem, determine the total number of hours that should be employed to determine the charging rate for computer operations (processing). Justify your answer.

S ug ge ste d S olutions to Even -Numb ere d Exercis e s

18. Allocating overhead to departments and jobs.

Filming

Editing Printing

Department

Department Department

Labor Hours Basis ...................................................

$12 per Hour

$16 per Hour $20 per Hour

Filming Department Editing Department Printing Department Total

Material ....................................

---

Labor ........................................

Overhead ..................................

Total .....................................

Suggested Solutions to Even-Numbered Exercises 489

20. Allocating overhead to jobs.

a. H A M I LTO N , I N C .

J o b O r d e r P ro d u c t i o n R e c o r d M o n t h of J a n u a r y

Direct Labor

Direct Material

Applied Overhead

Job Jobs in Jobs in Order

Process, Completed

9,000 --- Total .......................... $4,100

b Amount ¼ 50% of direct labor. Amount ¼ 75% of direct labor.

b. Overhead

Dept. A

Dept. B

4,600 a 3,400 b 8,000

Over (Under) Applied ..........................................................................

a $4,600 ¼ $4,200 þ ( 2 b $3,400 3 ¼ $3,200 þ ( 1

22. Using multiple cost drivers to allocate costs. S t e p 1 : D e r i ve ov e r h e a d a p p l i c a t i o n ra t e s

Department A

Department B

Number of Parts $4,000 7 40 parts ¼ $100 per part

$800 7 10 parts ¼ $80 per part

Machine Hours 208,000 7 16,000 hours

$60,000 7 1,500 hours

¼ $13 per machine hour

¼ $40 per machine hour

Setup Hours $24,000 7 300 hours

$8,000 7 100 hours

¼ $80 per setup hour

S t e p 2 : A p p l y ove r h e a d t o J o b 3 0 0 Z X Department A:

Department B:

24. Joint-process costing. Solutions will vary.

490 Chapter 13

Allocating Costs to Responsibility Centers

26. Using joint-process costing to measure product costs.

¼ 14,000 units Total units produced ¼ 28,000 units Joint product costs ¼ $63,000

a. Total units of X

Amount allocated from joint costs: 14,000

Additional processing costs 18,000 Total costs of Product X

b. Net realizable value of Y at splitoff ¼ $ 70,000 Total net realizable value at splitoff ¼ $200,000 Joint product costs

¼ $ 63,000 Amount allocated from joint costs:

Additional processing costs 14,000 Total costs of Product Y

Compound Interest Examples and Applications

Learning Objectives

1. Understand why accountants and financial 3. Convert written problem descriptions into a managers need to master compound interest

form suitable for analytic solution.

methods. 4. Find the internal rate of return on a series of 2. Distinguish between future and present value

equally spaced cash flows.

and between single payments and annuities.

Managerial accountants and managers deal with interest calculations because expenditures for an asset most often precede the receipts for services that the asset produces. Cash received sooner has more value than cash received later. The difference in timing can affect whether or not acquiring an asset is profitable. Amounts of cash received at different times are like different commodities. Managers use interest calculations to make valid comparisons among amounts of cash their firm will pay or receive at different times.

Managers evaluate a series of cash payments over time, such as from an investment project, by finding the present value of the series of payments. The present value of a series of payments is

a single amount of cash at the present time that is the economic equivalent of the entire series. This appendix illustrates the use of compound interest techniques with a comprehensive series of examples that use the tables appearing after this appendix. Calculators and personal computers do the same computations if you know which buttons to push or functions to use.

Future Value

If you invest $1 today at 10 percent compounded annually, it will grow to $1.10000 at the end of

1 year, $1.21000 at the end of 2 years, $1.33100 at the end of 3 years, and so on, according to the following formula

F ¼ Pð1 þ rÞ n n ,

where

F n ¼ accumulation or future value P ¼ one-time investment today R ¼ interest rate per period N ¼ number of periods from today:

492 Appendix Compound Interest Examples and Applications

Verification of Net Present Value of $10,717

EXHIBIT A.1

Single Cash Flow of $13,500 at the End of Year 3 Discounted at 8 Percent per Year

Beginning

Interest at Ending 8 Percent

The amount F n is the future value of the present payment, P, compounded at r percent per period for n periods. Table 1, following this appendix, shows the future values of P ¼ $1 for various periods and for various interest rates.

Example 1 How much will $1,000 deposited today at 8 percent compounded annually be worth 10 years

from now? One dollar deposited today at 8 percent will grow to $2.15892; therefore, $1,000 will grow to $1,000

Pre s ent Value

This section deals with the problems of calculating how much principal, P, you must invest today to have a specified amount, F n , at the end of n periods. You know the future amount, F n , the interest rate, r, and the number of periods, n; you want to find P. To have $1 one year from today when deposits

earn 8 percent, you must invest P of $0.92593 today. That is, F 1 ¼ P(1.08) 1 or $1 Because F ¼ P(1 þ r) n , dividing both sides of the equation by (1 þ r) n n yields

ð1 þ rÞ n n or P ¼

ð1 þ rÞ n ¼F ð1 þ rÞ

Table 2 following this appendix shows discount factors or, equivalently, present values of $1 for various interest (or discount) rates for various periods.

Example 2 What is the present value of $1 due 10 years from now if the interest rate (or, equivalently, the

discount rate) r is 12 percent per year? From Table 2, 12-percent column, 10-period row, the present value of $1 to be received

10 periods hence at 12 percent is $0.32197.

Example 3 You project that an investment will generate cash of $13,500 three years from today. What is the

net present value today of this cash receipt if the discount rate is 8 percent per year? One dollar received 3 years hence discounted at 8 percent has a present value of $0.79383. See Table 2, 3-period row, 8-percent column. Thus the project has a present value of $13,500

Chan gin g the Comp oundin g Perio d: Nomin al and Ef fe c tive R ate s

‘‘Twelve percent, compounded annually’’ represents the price for a loan; this price means interest increases, or converts to, principal once a year at the rate of 12 percent. Often, however, the price for a loan states an annual interest rate and that compounding will take place more than once a year. A savings bank may advertise that it pays interest of 6 percent, compounded quarterly. This kind of payment means that at the end of each quarter the bank credits savings accounts with

Annuities 493

interest calculated at the rate of 1.5 percent ( ¼ 6 percent/4). The investor can withdraw the interest payment or leave it on deposit to earn more interest.

If you invest $10,000 today at 12 percent compounded annually, it will grow to a future value

1 year later of $11,200. If the rate of interest is 12 percent compounded semiannually, the bank adds 6-percent interest to the principal every 6 months. At the end of the first 6 months, $10,000 will have grown to $10,600; that amount will grow to $10,600 of the year. Notice that 12 percent compounded semiannually results in the same amount as

12.36 percent compounded annually. Suppose that the bank quotes interest as 12 percent, compounded quarterly. It will add an additional 3 percent of the principal every 3 months. By the end of the year, $10,000 will grow to $10,000

equivalent to 12.55 percent compounded annually. At 12 percent compounded monthly, $1 will grow to $1

12 ¼ $1.12683, and $10,000 will grow to $11,268. Thus, 12 percent com-

pounded monthly is equivalent to 12.68 percent compounded annually. For a given nominal rate, such as the 12 percent in the preceding examples, the more often interest compounds, the higher the effective rate of interest paid. If a nominal rate, r, compounds m times per year, the effective rate is equal to (1 þ r/m) m

In practice, to solve problems that require computation of interest quoted at a nominal rate r percent per period compounded m times per period for n periods, use the tables or computer software functions for rate r/m and m for 5 years is equivalent to the rate found in the interest tables for r ¼ 12/4 ¼ 3 percent for m

Example 4 What is the future value 5 years hence of $600 invested at 8 percent compounded quarterly?

Eight percent compounded four times per year for 5 years is equivalent to 2 percent per period compounded for 20 periods. Table 1 shows the value of F 20 ¼ (1.02) 20 to be 1.48595. Six hundred dollars, then, would grow to $600

Example 5 How much cash must you invest today at 12 percent compounded semiannually to have $1,000

four years from today? Twelve percent compounded two times a year for 4 years is equivalent to 6 percent per period compounded for 8 periods. The present value, Table 2, of $1 received 8 periods hence at 6 percent per period is $0.62741; that is, $0.62741 invested today for 8 periods at an interest rate of

6 percent per period will grow to $1. To have $1,000 in 8 periods (4 years), you must invest $627.41 (

Example 6

A local department store offers its customers credit and advertises its interest rate at 18 percent per year, compounded monthly at the rate of 1 1 2 percent per month. What is the effective annual interest rate? One and one-half percent per month for 12 months is equivalent to (1.015) 12 percent per year. See Table 1, 12-period row, 1 1 2 -percent column, where the factor is 1.19562.

Example 7 If prices increased at the rate of 6 percent during each of two consecutive 6-month periods, how

much did prices increase during the entire year? If a price index is 100.00 at the start of the year, it will be 100.00

2 ¼ 112.36 at the end of the year. The price change for the entire year is (112.36/100.00)

Annuitie s

An annuity is a series of equal payments, one per equally spaced period of time. Examples of annuities include monthly rental payments, semiannual corporate bond coupon (or interest) payments, and annual payments to a lessor under a lease contract. Armed with an understanding of the tables for future and present values, you can solve any annuity problem. Annuities arise so often, however, and solving them is so tedious without special tables or computer functions that annuity problems merit special study and the use of special tables or functions.

494 Appendix Compound Interest Examples and Applications

W HY A LLOC ATE J OINT -P ROCES S C OS T S ?