Chapter 15 Allocation of Support Department Costs, Common Costs, and Revenues CCs: 15-29 (8%) (new) 15-37 (10%) (=11.15-36) 1 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 2 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. 3 from general ledger Additional cost not out of pocket Directly attributable Structure of Service Department Cost Attribution (Traceable costs) Support departments Secondary Activities Attribution to cost pools of the centers; each activity has exactly one cost driver Usage cost driver rate Reciprocal services Operating departments Primary Activities Product 1 Product n 4 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. 5 Allocating Support Departments Costs Direct method: Step-down (sequential allocation) method: Allocates support department costs to operating departments only. 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 6 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 Budgeted costs before allocations: $300,000 Square feet: 5,000 # of employees: 8 Human Resources $2,160,000 30,000 15 Assembly Finishing $1,700,000 110,000 48 $900,000 110,000 27 7 Direct Method Support Departments Maintenance $300,000 0% Operating Departments 110/220 $1,700,000 Assembly 24/72 $900,000 Finishing 0% Human Resources $2,160,000 Original costs: Maintenance Allocated: Human Resources Allocated: Total Assembly $1,700,000 150,000 1,440,000 $3,290,000 Finishing $ 900,000 150,000 720,000 $1,770,000 8 Step-Down Method Which support department should be allocated first? Maintenance to Human Resources: 12% × $300,000 = $36,000 Maintenance provides 12% of its services to Human Resources. Human Resources provides 10% of its services to Maintenance. Maintenance to Assembly: Maintenance to Finishing: 44% × $300,000 = $132,000 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 9 xij = aijxij Overhead Allocation Sheet (Step down method) Traceable costs Secondary activities j does not use > j j=1 j=2 j=3 p1 x12 p1 x13 p2 x23 usage of i by j Primary activities Costs from general ledger + additional non-out-ofpocket cost S1 S2 S3 Total cost driver volume, center j Cost driver rate ... p3 x3j ... S1 S2 S3 Sj x1 x2 x3 x3 p1 =S1 /x1 p2 p3 p3 Cost driver rates One line for each kind of input used. Entries in each line sum up to the respective amount in the cost recording column Sum of row i = Si Sum of column j: total cost of center j Start 10 Reciprocal M Maintenance – Human Resources 10% HR 12% – A 44% 60% Sa × Total cost(i) Total Cost(j) = traceable cost (j) + all i ij F 44% 30% where aij denotes j‘s share of total i‘s service 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 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 11 Reciprocal Before allocation: Allocation: Allocation: Total M HR $300,000 (522,267) 222,267 $2,160,000 62,672 ($2,222,672) A $1,700,000 229,797 1,333,603 $3,263,400 F $ 900,000 229,797 666,802 $1,796,599 Total cost Assembly Department: $3,263,400 Total cost Finishing Department: $1,796,599 12 Budgeting requirements (cont‘d) Then the total volumes of cost drivers are determined by the system of equations xi yi aij x j j (One equation for each secondary activity i) The same system can be written as a matrix equation: (I – A)x = y 13 Cost driver rates pi Activity account balance Activity j Traceable costs KPj Service delivered Cost of secondary activities pj ·xj p i i K Pj p i xij p j x j i j xij K Pj p i aij x j p j x j i j p j p i aij k i j (I – AT)p = k P j K P j xj p i aij p j i j =: kPj 14 Example: „Fall River Company“*) Service centers: Power Department, Water Department; Production centers: Divisions 1 und 2. Data: Units of service provided to: Units of service provided from: Power Water Power 20 Water traceable costs Div.1 Div.2 Total 70 80 70 240 30 10 70 50 160 $ 4.9 $ 1.25 Activity account balances: 240 p1 = 20 p1 + 30 p2 + 4.9 160 p2 = 70 p1 + 10 p2 + 1.25 220 p1 – 30 p2 = 4.9 – 70 p1 + 150 p2 = 1.25 *) Kaplan/Atkinson, Advanced Management Accounting, 3rd ed. p.74-76 and 80-81. Numbers modified. 15 Calculation direct solution matrix calculus 220 p1 – 30 p2 = 4.9 – 70 p1 + 150 p2 = 1.25 | ×5 1100 p1 – 150 p2 = 24.5 + – 70 p1 + 150 p2 = 1.25 1030 p1 = 25.75 p1 = 0.025 p2 = 1.75+1.25 150 = 0.02 Power and water cost: Div. 1: $3.4 mill., Div. 2: $2.75 mill. x11 x A 1 x21 x 1 x12 20 70 x2 240 160 x22 30 10 x2 240 160 220 30 T 240 240 (I A ) 70 150 160 160 120 16 T 1 ( I A ) 103 103 56 352 103 309 120 16 4.9 0.025 T 1 P 103 103 240 (I A ) k 56 352 1 . 25 0.02 103 309 160 16 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. 17 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: xi (y) yj = 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) 18 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 procurement 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. 19 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 20 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 cj (kP) Similarly to the above: k P = rij i 21 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 22 Allocating Common Costs 1. Two methods for allocating common cost Stand-alone cost allocation method 2. Incremental cost allocation method 3. actual cost is allocated in the ratio of stand-alone costs 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 23 Example A consultant in Tampa is planning to go to Chicago and meet with an international client. The consultant is also planning to attend a business meeting with a North Carolina client in Durham. The round-trip Tampa/Chicago/Tampa airfare costs $540. 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: Cost for North Carolina client: 760 × 540/(540 + 360) = 456 760 × 360/(540 + 360) = 304 Incremental method, international client first: Cost for international client: Cost for North Carolina client: Shapley Value: 540 360 220 400 760/2 760/2 540 760 – 540 = 220 24 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 Checking Safety deposit boxes Investment advisory Hotels Lodging Food and beverage services Recreation Tours Transportation Lodging Guides 25 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) Grammar + Translation Grammar + Composition Grammar + Translation + Composition Price $290 $350 $410 26 Revenue Allocation Methods 1. The two main revenue allocation methods The stand-alone method with alternative weights a) b) c) d) 2. Selling prices Unit costs Physical units Stand-alone product revenues The incremental method with alternative sequences 27 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: Translation: $734,400 ÷ $816,000 = 0.90, $290 × 0.90 = $261 $81,600 ÷ $816,000 = 0.10, $290 × 0.10 = $29 28 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 29