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 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

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

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

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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

8

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

11

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

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103

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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