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

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

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

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

Single-Rate and Dual-Rate Methods The single-rate cost allocation method pools together all costs in a cost pool. The dual-rate cost allocation method classifies costs in each cost pool into two cost pools a variable-cost cost pool and a fixed-cost cost pool Organizations commit to infrastructure costs on the basis of a long-run planning horizon. Budgeted rates let the user department know in advance the cost rates they will be charged During the budget period, the supplier department, not the user departments, bears the risk of any unfavorable cost variances. When actual rates are used for cost allocation, managers do not know the rates to be used until the end of the budget period The use of budgeted usage to allocate these fixed costs is consistent with the long-run horizon.

Allocating Support Departments Costs Direct method: Allocates support department costs to operating departments only. Step-down (sequential allocation) method: Allocates support department costs to other support departments 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 all support departments simultaneous equations approach

Example The Canton Division of Smith Corporation has two operating departments Assembly and Finishing and two support departments Maintenance allocated using square feet. Total square feet = 255,000 Human Resources allocated using number of employees Total number of employees = 95 Maintenance Human Resources Assembly Finishing 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

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

Step-Down Method Which support department should be allocated first? Maintenance provides 12% of its services to Human Resources. Human Resources provides 10% of its services 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

Overhead Allocation Sheet (Step down method) 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 Costs from general ledger + additional non-out-of- pocket cost S1 S2 S3 j = 1 j = 2 j = 3 p1 x12 p1 x13 p2 x23 Sum of row i = Si ... p3 x3j ... S1 S2 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 p3 p3 Start Cost driver rates

Reciprocal M HR A F Maintenance – 12% 44% 44% Human Resources 10% – 60% 30% Total Cost(j) = traceable cost (j) + S aij × 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

Reciprocal M HR A F 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

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

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

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.

Calculation direct 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 + 1030 p1 = 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.

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.

Interpretation of R:=(I - A)-1 Consider the equation for required total output of service i as a function of external requirements y: xi (y) = Sj rij yj 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 R is sometimes called the total requirement matrix)  xi (y)  yj

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.

Interpretation of R:=(I - A)-1 This means: If you close down service center i then you can save the total reciprocal cost pi xi 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= pi xi i.e. you may pay at most an external price of pi = pi rii

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

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

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

Example A consultant in Tampa is planning to go to Chicago and meet with an international client. The round-trip Tampa/Chicago/Tampa airfare costs $540. The consultant is also planning to attend a business meeting with a North Carolina client in Durham. The round-trip Tampa/Durham/Tampa airfare costs $360. The consultant decides to combine the two trips into a Tampa/Durham/Chicago/Tampa itinerary 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: 540 360 220 400 760/2 760/2

Revenues and Bundled Products A bundled product is a package of two or more products (or services) sold for a single price. Bundled product sales are also referred to as “suite sales.” The individual components of the bundle also may be sold as separate items at their own “stand-alone” prices. Examples Banks Hotels Tours Checking Safety deposit boxes Investment advisory Lodging Food and beverage services Recreation Transportation Lodging Guides

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

Revenue Allocation Methods The two main revenue allocation methods The stand-alone method with alternative weights Selling prices Unit costs Physical units Stand-alone product revenues The incremental method with alternative sequences

Stand-Alone Revenue Allocation Method Consider the Grammar and Translation suite, 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

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