Chapter 15

1. Chapter 15 Allocation of Support DepartmentCosts, Common Costs, and Revenues CCs: 15-29 (8%) (new) 15-37 (10%) (=11.15-36)

2. Cost allocation: what it means • Some production centers or departments provide output required by other production centers (Service departments). • The costs of these departments are allocated to the internal users according to use and add to their costs • so the costs of service departments providing these products and services go indirectly into the cost of saleable output • Service department‘s costs are allocated using the actual utilization volume times an allocation rate per unit

3. Allocating Support Departments Costs • An operating department (a productiondepartment in manufacturing companies)adds value to a product or service • A support department (service department)provides the services that assist other operatingand support departments in the organization.

4. Directly attributable from general ledger Additional cost not out of pocket Structure of Service Department Cost Attribution Attribution to cost pools of the centers; each activity has exactly one cost driver Support departments Secondary Activities Usage  cost driver rate Reciprocal services Operating departments Primary Activities Product 1  (Traceable costs) Product n

5. Single-Rate andDual-Rate Methods • The single-rate cost allocation methodpools together all costs in a cost pool. • The dual-rate cost allocation methodclassifies costs in each cost pool intotwo cost pools • a variable-cost costpool and • a fixed-cost cost pool • Organizations commit to infrastructure costs onthe basis of a long-run planning horizon. • Budgeted rates let the user department know inadvance the cost rates they will be charged • During the budget period, the supplier department,not the user departments, bears the risk of anyunfavorable cost variances. • When actual rates are used for cost allocation,managers do not know the rates to be useduntil the end of the budget period • The use of budgeted usage to allocate these fixedcosts is consistent with the long-run horizon.

6. Allocating SupportDepartments Costs • Direct method: • Allocates support department costs to operatingdepartments only. • Step-down (sequential allocation) method: • Allocates support department costs to other supportdepartments and to operating departments • charge rates are calculated for support departments according to a rank order. Those departments rank highest that get the least from other departments • at each step support is charged only from the departments whose charge rate has already been calculated • Reciprocal allocation method: • Allocates costs by services provided among allsupport departments • simultaneous equations approach

7. Example • The Canton Division of Smith Corporation has twooperating departments • AssemblyandFinishing and two support departments • Maintenance • allocated using square feet. • Total square feet = 255,000 • Human Resources • allocated usingnumber of employees • Total number of employees = 95 MaintenanceHuman ResourcesAssemblyFinishing Budgeted costs before allocations: $300,000 $2,160,000 $1,700,000 $900,000 Square feet: 5,000 30,000 110,000 110,000 # of employees:8 15 48 27

8. Direct Method Support Departments Operating Departments Maintenance $300,000 $1,700,000 Assembly 110/220 0% 0% 110/220 48/72 Human Resources $2,160,000 $900,000 Finishing 24/72 AssemblyFinishing Original costs: $1,700,000 $ 900,000 Maintenance Allocated:150,000 150,000 Human ResourcesAllocated: 1,440,000 720,000 Total $3,290,000 $1,770,000

9. Step-Down Method • Which support department should be allocated first? • Maintenance provides 12% of its servicesto Human Resources. • Human Resources provides 10% of itsservices to Maintenance. • Maintenance to Human Resources: 12% × $300,000 = $36,000 • Maintenance to Assembly:44% × $300,000 = $132,000 • Maintenance to Finishing:44%× $300,000 = $132,000 • Human Resources costs to be allocated become $2,160,000 + $36,000 = $2,196,000 • Human Resources to Assembly:48 ÷ 72 × $2,196,000 = $1,464,000 • Human Resources to Finishing:24 ÷ 72 × $2,196,000 = $732,000

10. xij = aijxij usage of i by j Overhead Allocation Sheet (Step down method) Secondary activities j does not use > j Primary activities Traceable costs One line for each kind of input used. Entries in each line sum up to the respective amount in the cost recording column j = 1 j = 2 j = 3 Costs from general ledger + additional non-out-of- pocket cost S1 S2 S3 p1x12 p1x13 p2x23 Sum of row i = Si ... p3x3j ... S1S2 S3 Sj Total cost driver volume, center j Sum of column j: total cost of center j x1 x2 x3 x3 Cost driver rate p1=S1 /x1 p2 p3p3 Start Cost driver rates

11. Reciprocal MHRAF Maintenance – 12% 44% 44% Human Resources 10% – 60% 30% Total Cost(j) = traceable cost (j) + Saij× Total cost(i) all i where aij denotes j‘s share of total i‘s service 10 M – HR = 3,000,000 – 0.12 M + HR = 2,160,000 9.88 M = 5,160,000 M = 5,160.000 / 9.88 = 522,267 HR = 2,160,000 + 0.12× 522,267 = 2,222,672 M = 300,000 + 0.10 HR HR = 2,160,000 + 0.12 M M – 0.10 HR = 300,000 – 0.12 M + HR = 2,160,000

12. Reciprocal MHRAF Before allocation: $300,000 $2,160,000 $1,700,000 $ 900,000 Allocation: (522,267) 62,672 229,797 229,797 Allocation: 222,267 ($2,222,672) 1,333,603 666,802 Total $3,263,400 $1,796,599 Total cost Assembly Department: $3,263,400 Total cost Finishing Department: $1,796,599

13. Budgeting requirements (cont‘d) • Then the total volumes of cost drivers are determined by the system of equations The same system can be written as a matrix equation: (One equation for each secondary activity i) (I – A)x = y

14. Cost driver rates pi • Activity account balance Activity j Traceable costs KPj Service delivered pj ·xj  Cost of secondary activities    =: kPj (I – AT)p = k

15. Example: „Fall River Company“*) • Service centers: Power Department, Water Department; Production centers: Divisions 1 und 2. • Data: Activity account balances: 240 p1 = 20 p1 + 30 p2 + 4.9 220 p1 – 30 p2 = 4.9 160 p2 = 70 p1 + 10 p2 + 1.25 – 70 p1 + 150 p2 = 1.25  *) Kaplan/Atkinson, Advanced Management Accounting, 3rd ed. p.74-76 and 80-81. Numbers modified.

16. Calculationdirect solution matrix calculus 220 p1 – 30 p2 = 4.9 | ×5 – 70 p1 + 150 p2 = 1.25 1100 p1 – 150 p2 = 24.5 – 70 p1 + 150 p2 = 1.25 + 1030p1 = 25.75 p1 = 0.025 1.75+1.25 150 p2 = = 0.02 Power and water cost: Div. 1: $3.4 mill., Div. 2: $2.75 mill.

17. Why the matrix calculus is useful • The numerical data required are provided in the accounting data base and can automatically downloaded into the matrix A and a vector of traceable unit costs kP. • Spreadsheet software usually offers the function of matrix inversion • so the cost driver rates can be determined automatically.

18. Interpretation of R:=(I - A)-1 • Consider the equation for required total output of service i as a function of external requirementsy: xi (y) = Sjrijyj • Differentiate this function w.r.t. yj . You get: = rij • This means: rij represents the additional total output of service i required per additional unit of external output requirement of service j. • Therefore the matrix Ris sometimes called the total requirement matrix)  xi (y)  yj

19. Interpretation of R:=(I - A)-1 • In particular: • If you purchase one unit of the service i externally (reduce external demand by one unit) • then you need rii units less to be procured internally. • Or, in other words: if you reduce internal pro-curement of the service by one unit, you need to buy only 1/ rii units from an external source. • Since the function xi (y) is linear, this is globally true.

20. Interpretation of R:=(I - A)-1 • This means: If you close down service center i then you • can save the total reciprocal cost pixi for this center • must procure xi / rii units of the service externally • You will break even if the external procurement price pi satisfies: pi xi / rii= pixi i.e. you may pay at most an external price of pi = pi rii

21. Interpretation of RT:=(I-AT)-1 • So we get the reciprocal cost per unit as a function of the traceable cost: cj(kP) = SikiP rij • Similarly to the above: = rij  cj (kP)  kiP

22. Reciprocal method: Extension • Dual rate system for assigning committed costs: Peak load pricing • Assigning • committed cost according to capacity reservations by users • flexible cost according to actual usage • if a service is outsourced: • reciprocal method shows the effect on required total volume (capacity) of cost drivers for all service departments

23. Allocating Common Costs • Two methods for allocating common cost • Stand-alone cost allocation method • actual cost is allocated in the ratio of stand-alone costs • Incremental cost allocation method • a sequence of cost objects is defined • each object bears the incremental cost according to the sequence • Shapley Value • the average of incremental costs over all possible sequences is charged to the object • the Shapley Value can be justified based on a set of plausible axioms

24. Example • A consultant in Tampa is planning to go toChicago and meet with an international client. • The round-trip Tampa/Chicago/Tampaairfare costs $540. • The consultant is also planning to attenda business meeting with a North Carolinaclient in Durham. • The round-trip Tampa/Durham/Tampaairfare costs $360. • The consultant decides to combine the twotrips into a Tampa/Durham/Chicago/Tampaitinerary that will cost $760. • Stand-alone method: • Cost for international client: 760 × 540/(540 + 360) = 456 • Cost for North Carolina client: 760 × 360/(540 + 360) = 304 • Incremental method, international client first: • Cost for international client: 540 • Cost for North Carolina client: 760 – 540 = 220 • Shapley Value: 540 360 220400 760/2 760/2

25. Revenues and Bundled Products • A bundled product is a package of two or moreproducts (or services) sold for a single price. Bundled product sales are also referred toas “suite sales.” The individual components of the bundle alsomay be sold as separate items at their own“stand-alone” prices. • Examples Banks Hotels Tours • Checking • Safetydeposit boxes • Investmentadvisory • Lodging • Food and beverageservices • Recreation • Transportation • Lodging • Guides

26. Revenue Allocation Methods • English Languages Institute buys Englishlanguage software programs locally andthen sells them in Mexico and Central America • English sells the following programs:Grammar, Translation, and Composition • These programs are offered stand-aloneor in a bundle Stand-alone Unit PriceCost Grammar $255 $180 Translation $ 85 $ 45 Composition $185 $ 95 Bundle (Suites)Price Grammar + Translation $290 Grammar + Composition $350 Grammar + Translation + Composition $410

27. Revenue Allocation Methods • The two main revenue allocation methods • The stand-alonemethod with alternative weights • Selling prices • Unit costs • Physical units • Stand-aloneproduct revenues • The incrementalmethod with alternative sequences

28. Stand-Alone RevenueAllocation Method • Consider the Grammar and Translationsuite, which sells for $290 per copy. • 1a) Grammar: $290× 255/(255 + 85) = $217.50 Translation: $290× 85/(255 + 85) = $72.50 1b) Grammar: $290× 180/(180 + 45) = $232 Translation: $290× 45/(180 + 45) = $58 1c) Grammar: $290/2 = $145 Translation: $290/2 = $145 1d) Assume that the stand-alone revenues in 2003 Grammar $734,400; Translation $81,600, Composition$133,200. Grammar: $734,400 ÷ $816,000 = 0.90, $290 × 0.90 = $261 Translation: $81,600 ÷ $816,000 = 0.10, $290 × 0.10 = $29

29. Incremental RevenueAllocation Method • The first-ranked product is termed theprimary product in the bundle • If the suite selling price exceeds the stand-alone price of the primary product, theprimary product is allocated 100%of its stand-alone revenue. • The second-ranked product is termedthe first incremental product • The third-ranked product is the secondincremental product, and so on. • Assume that Grammar is designatedas the primary product: • Grammar and Translation suite selling price= $290 per copy • Allocated to Grammar: $255 • Remaining to be allocated: ($290 – $255) = $35 > Translation