1 chapter 15 allocation of support department costs, common costs, and revenues ccs: 15-29 (8%)...
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1
Chapter 15
Allocation of Support DepartmentCosts, Common Costs, and Revenues
CCs: 15-29 (8%) (new)
15-37 (10%) (=11.15-36)
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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
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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.
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Secondary Activities
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Product 1
PrimaryActivities
Product n
Attribution to cost pools of the centers; each activity has exactlyone cost driver
Usage cost driver rate
Reciprocal services
Structure of Service Department Cost Attribution
(Traceablecosts)
Operatingdepartments
Supportdepartments
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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.
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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
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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
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Direct Method
Support Departments Operating Departments
$1,700,000Assembly
$900,000Finishing
110/220
48/72
24/72
0% 0% 110/220
Maintenance$300,000
HumanResources$2,160,000
Assembly FinishingOriginal costs: $1,700,000 $ 900,000Maintenance Allocated: 150,000 150,000Human Resources Allocated: 1,440,000 720,000Total $3,290,000 $1,770,000
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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
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Overhead Allocation Sheet (Step down method)
Costs from Costs from general ledgergeneral ledger
++additionaladditional
non-out-of-non-out-of-pocket costpocket cost
S1
S2
S3
SS11 S2 S3 Sj
Primary activitiesPrimary activitiesSecondary Secondary activitiesactivities
j does not use > j j does not use > j One line for eachOne line for eachkind of input used.kind of input used.Entries in each Entries in each line sum up to the line sum up to the respective amountrespective amountin the cost in the cost recording columnrecording column
x1 x2 x3 x3
2 3 3
Sum of column j:total cost of center j
Total cost drivervolume, center j
Cost driver rate
jj = 1 = 1 jj = 2 = 2 jj = 3 = 3
1 x12 1 x13
1 =S1 /x1
2 x233 x3j
Sum of row i = Si
Start
xij = = aaijxij
usage of usage of ii by by jj
Traceable costs
Cost driver rates
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Reciprocal
M HR A FMaintenance – 12% 44% 44%Human Resources 10% – 60% 30%
Total Cost(j) = traceable cost (j) + ij × Total cost(i) all i
where ij denotes j‘s share of total i‘s service
M = 300,000 + 0.10 HRHR = 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 = 5,160,000M = 5,160.000 / 9.88 = 522,267HR = 2,160,000 + 0.12× 522,267 = 2,222,672
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Reciprocal
M HR A FBeforeallocation: $300,000 $2,160,000 $1,700,000 $ 900,000Allocation: (522,267) 62,672 229,797 229,797Allocation: 222,267 ($2,222,672) 1,333,603 666,802Total $3,263,400 $1,796,599
Total cost Assembly Department: $3,263,400Total cost Finishing Department: $1,796,599
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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:
j
jijii xayx (One equation for each secondary activity i)
(I – A)x = y
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Cost driver rates i
Activity account balance
Traceable costsTraceable costs
KKPPjj
Cost of secondary Cost of secondary activitiesactivities
Service deliveredService delivered
jj ·x ·xjj
Activity jActivity j
i iji x
jji
ijij
Pj
jjji
jijiPj
jjji
ijiPj
ax
K
xxaK
xxK
=: kkPPjj
Pj
jiijij ka
(I – AT) = k
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Example: „Fall River Company“*)
Service centers: Power Department, Water Department; Production centers: Divisions 1 und 2.
Data:
*) Kaplan/Atkinson, Advanced Management Accounting, 3rd ed. p.74-76 and 80-81. Numbers modified.
Units of service provided to:
Power Water Div.1 Div.2 Total
Power 20 70 80 70 240Units of serviceprovided from: Water 30 10 70 50 160
traceable costs $ 4.9 $ 1.25
Activity account balances:Activity account balances:
240 240 11 = 20 = 20 11 + 30 + 30 2 2 + 4.9+ 4.9 220 220 1 1 – 30 – 30 2 2 = 4.9= 4.9
160 160 22 = 70 = 70 1 1 + 10 + 10 22 + 1.25 + 1.25 – 70 – 70 1 1 + 150 + 150 22 = 1.25 = 1.25
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Calculationdirect solution matrix calculus
220 220 1 1 – 30 – 30 2 2 = 4.9 | ×5= 4.9 | ×5
– – 70 70 1 1 + 150 + 150 22 = 1.25 = 1.25
1100 1100 1 1 – 150 – 150 2 2 = 24.5= 24.5
– – 70 70 1 1 + 150 + 150 22 = 1.25 = 1.25
10301030 1 1 = 25.75= 25.75
1 1 = 0.025
2 2 = = = = 0.021.75+1.25150
+
02.0
025.0
160
25.1240
9.4
309
352
103
56103
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103
120
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309
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160
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Power and water cost:Div. 1: $3.4 mill., Div. 2: $2.75 mill.
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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.
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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) = j 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
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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.
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Interpretation of R:=(I A)-1
This means:
If you close down service center i then you can save the total reciprocal cost i 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= i xi
i.e. you may pay at most an external price of
pi = i rii
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Interpretation of RT :=(I AT)1
So we get the reciprocal cost per unit as a function of the traceable cost:
cj (kP) = i kiP rij
Similarly to the above: = rij
cj (kP) ki
P
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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
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Allocating Common Costs
Two methods for allocating common cost
1. Stand-alone cost allocation method actual cost is allocated in the ratio of stand-alone costs
2. Incremental cost allocation method a sequence of cost objects is defined each object bears the incremental cost according to the
sequence
3. 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
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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
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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
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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 UnitPrice Cost
Grammar $255 $180Translation $ 85 $ 45Composition $185 $ 95
Bundle (Suites) PriceGrammar + Translation $290Grammar + Composition $350Grammar + Translation + Composition $410
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Revenue Allocation Methods
The two main revenue allocation methods
1. The stand-alone method with alternative weightsa) Selling prices
b) Unit costs
c) Physical units
d) Stand-alone product revenues
2. The incremental method with alternative sequences
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Stand-Alone RevenueAllocation 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
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Incremental RevenueAllocation 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