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

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 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.

4. 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

5. 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.

6. 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

7. 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: , , , ,000
# of employees:

8. 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: , ,000
Human Resources Allocated: 1,440, ,000
Total $3,290,000 $1,770,000

9. 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

10. 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 = j = j = 3
p1 x p1 x13
p2 x23
Sum of row i = Si
... p3 x3j ...
S1 S S Sj
Total cost driver
volume, center j
Sum of column j:
total cost of center j
x1 x x x3
Cost driver rate
p1 =S1 /x1
p p p3
Start
Cost driver rates

11. 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
M – HR = 3,000,000
– M + HR = 2,160,000
9.88 M = 5,160,000
M = 5, / 9.88 = 522,267
HR = 2,160, × 522,267
= 2,222,672
M = , HR
HR = 2,160, M
M – 0.10 HR = ,000
– M HR = 2,160,000

12. Reciprocal M HR A F Before
allocation: $300,000 $2,160,000 $1,700,000 $ 900,000
Allocation: (522,267) , , ,797
Allocation: ,267 ($2,222,672) 1,333, ,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. (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

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

16. Calculation direct solution matrix calculus
220 p1 – 30 p2 = | ×5
– 70 p p2 = 1.25
1100 p1 – 150 p2 = 24.5
– 70 p p2 = +
1030 p = 25.75
p1 = 0.025
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 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

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 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

21. 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

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 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/( ) = 456
Cost for North Carolina client: 760 × 360/( ) = 304
Incremental method, international client first:
Cost for international client: 540
Cost for North Carolina client: 760 – 540 = 220
Shapley Value:
760/2 760/2

25. 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

26. 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 $ $ 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-alone method with alternative weights
Selling prices
Unit costs
Physical units
Stand-alone product revenues
The incremental method with alternative sequences

28. Stand-Alone Revenue Allocation Method
Consider the Grammar and Translation suite, which sells for $290 per copy.
1a) Grammar: $290× 255/( ) = $217.50
Translation: $290× 85/( ) = $72.50
1b) Grammar: $290× 180/( ) = $232
Translation: $290× 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 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