Assigning Service Department Costs

Prof. Prashant Shukla

Assigning Service Department Costs

We can usually distinguish two types of departments in an organization: production

departments or operating departments which directly produce or distribute the

firm's output and service departments whose main output is to provide service

to other departments. Examples of such service departments include utilities,

maintenance, production control, stockroom, material handling, and

housekeeping and information systems. Units such as R&D or advertising that

produce company wide services may not be included in this analysis unless

their output is produced for specific departments or products.

In this chapter, we will discuss the process of attributing or allocating the costs of

service departments to operating departments and products.

Attribution and Allocations:

We will make a distinction between attribution and allocation.

Attribution is the process of assigning a cost that is associated with a particular cost

object. Such costs that can be attributed are sometimes also referred to as

separable.

Costs that cannot be attributed can be either a joint cost or common cost.

Allocation is the process of assigning a resource cost to user where a direct

measure does not exist for basis of assigning. Some surrogate (indirect

alternative) measure has to be used for defining the basis of allocation.

Rationale for allocating service costs:

There are many reasons and advantages of allocating service costs to user

departments (other service departments or production departments). These are:

1. For purposes of assessing cost of goods sold and inventory valuation needed in external financial reporting

2. To assess the performance of the service departments.

3. To ensure that the services are efficiently used by the user departments. If no costs are allocated to users for services rendered, then there may be a tendency

on the part of the users to wastefully consume more services than needed

knowing that this is got free of cost.

4. To ensure that the services are produced efficiently by comparing internal costs of the service against external costs and hence to decide whether the services

should be provided in-house or procured from external sources.


5. With a charge out system, users are made aware of the costs to them. In the absence of a charge out, the service departments may - to avoid complaints from

users, tend to provide high quality service to meet all the demands from the

users, using more resources than necessary. This will increase the cost of the

service and none will be aware of this!

By having a charge out, users will be aware of the costs and may be prepared to pay a higher

price for extra services genuinely needed. If such a situation arises and the services

department cannot cater to the full needs, then decisions on expansion of capacity may be

considered.

Measure for Cost Allocation

1. Where the service costs are of an attributable nature it is relatively easy to use a clearly

defined direct measure to charge out the service cost to the user e.g. Power consumed metered by user department on kWh measure,steam/water on acid metered

volume of consumption etc.

2. Where the services are of a varied nature then multiple measure may have to be used for

each component of the service e.g. computer charges are usually made on CPU usage time,

data storage on disks/tapes used, reports on pages printed etc.

3. The more difficult area is that of services which have no direct measure e.g. power

not metered, building maintenance, supervision etc. In such cases the service provided

is not directly related to any easily definable measure. It may not be worthwhile evolving a

measure if this is a costly exercise or the costs to be assigned are relatively small.

In such cases some indirect indicator is used as a measure, e.g. (un-metered power by

total wattage of machines installed, stores costs on space, air conditioning cost on cubic

volume or building costs on floor space etc). .

Some Common Measures Used As Basis of Allocation

COST BASE

Personnel Department No .of employees

Canteen and welfare No. of workers

Supervision Labour wages/ No. of employees

Depreciation and insurance of

buildings and equipment

Capital value/ Machine hours

Maintenance and repair Lanours hours spent/ No. of

machines

Heating and lighting Floor area

Building maintenance Cubic content

Motive Power expenses Horse power

Electric power and lighting Wattage

Store keeping expenses Weight or value of materials


Material handling Volume

Computer Total hours

Transport service expenses Mileage/ tonnage/packages/No. of

trips

Billing No. of bills

Methods of Service Cost Allocation:

There are three methods:

1. Direct method

2. Sequential (Step - ladder method)

3. Simultaneous Equations (Matrix) Method

Using numerical examples we will describe the features of each of the methods and show how

to carry out the cost allocations. Later on, we will give details of the construction of

the model used in the matrix method and highlight its many advantages as against

other methods.

Consider a simple case of three service departments S1, S2 S3 and two production

departments P1 and P2. Table below gives the details of the proportion of services rendered

by each service department to other service/ production departments, the total variable

costs of the service departments over a planned period and the number of units of

service.

In practice only the basic data on actual number of units of services given by a service

department to other users will be available, from which the proportions have to be

computed.

We have not shown such details here

From

To

S1 S2 S3

S1 0 10 20

(Proportion %) S2 10 0 30

S3 10 0 0

P1 50 40 30

P2 30 50 20

VariableCosts

(Rs. `000)

60 80 120

Units of Service 400 800 1000

As per above data, S1 provides services not only to production departments P1 and P2 directly

but also to service departments S2 and S3. S1 also receives services from S2 and S3.

That is to say, services are given not only to production departments directly but are also


reciprocally exchanged between service departments

It is the presence of such reciprocal exchanges that complicates the procedure of cost

allocations. We will deal with the problem when we come to the third method.

1. Direct Method

In this method it is assumed that services are rendered only to production departments

directly and none to any other service departments. Should there be exchanges of

services between service departments, these are simply ignored. The allocation

proportions are then recomputed to total to 100% deleting the proportions allocated to

service departments. These allocations can be calculated easily.

Deleting the allocations of services to service departments in the above example, the

proportions of service rendered directly to the two production departments will be re-

computed as:

From the original table we have deleted the allocation proportion to all other

service departments, leaving only the proportions to P1 and P2, and then recomputed the

proportions to total to 100% For e.g. Proportion from S1 will be P1 = 50% and P2 = 30%

totaling only 80%. Thus the revised proportion of services from S1 directly to P1 and P2

will be 50/80 = 62.5% and 30/80 = 37.5% similarly computations are done for other service

departments.

S1 S2 S3

S1 0 0 0

S2 0 0 0

S3 0 0 0

P1 62.5 44.4 60.0

P2 37.5 55.6 40.0 Revised

Proportions

The allocations of variable costs by the direct method are easily calculated as:

To P1: 0.625 (60) + 0.444(80)+ 0.60(120) =145

To P2: 0.375 (60) + 0.556(80)+ 0.40(120) =115

Observe that the total allocated costs tally with the specified total of 260.

You will observe that while this method is easy to apply, the method does not reflect the

true state of exchanges of service between service departments.


2. Sequential (Step-ladder) Method

In this method some consideration is given to the exchange of services between service

departments.

The service departments are listed in order, that is, the first which gives services to the

largest number of other service departments or the one that gives a high proportion of its

service to other service departments will be listed first. Sometimes the service

department with the largest cost is listed the first or a combination of the rules stated

above is used. Note: there will always be some doubts and arbitrariness in the order of

listing the service departments.

It is now assumed that services can flow only in one direction from a department listed

higher to others listed lower but never backward to a department listed higher.

The allocation proportions are re-adjusted eliminating the backward flows. The service

departments are now listed in the order determined.

Then, the first listed service costs are charged out to other departments listed lower as per

revised proportions. Then, the charge out of costs of next service department is taken.

But note that the costs to be allocated are now taken as the total of own cost plus the

allocated cost received from the previous departments, and the allocations made as per

revised proportions.

Thus by a sequential step by step procedure the service departments costs are

progressively carried over, some to other service departments and some to production

departments, until at the last stage all costs would have been carried over to the

production departments.

This method is better than the direct method. But it will involve some extra

computations. However, the method has the drawback: that the listing of the service

departments for the sequential allocations may not be dear-cut. Differences in listing may

produce different results.

Further certain exchanges (backward flow) are ignored which also affect the true picture.

The computations of the step method are shown below:

Since S3 gives a large proportion of its services to other service departments and it is also

the highest cost department, S3 will be listed as the first, then S1 as it services more than

one department and lastly S2, which has the least interaction.

The proportion of allocations, after the departments as decided and ignoring the

backward flows will have to be re-computed.


These are shown below:

From

To

S3 S1 S2

S1 20 0 *

Proportions

%

S2 30 11.1 0

S3 0 * 0

P1 30 55.6 44.4

P2 20 33.3 55.6

Note:

At the top of the table the departments are fisted as per order decided. ii) that certain

proportions of backward flow have been deleted indicated by a star (*) and after

deletion the remaining proportions have been re-computed to total 100%

In the first pass, cost of S3 is charged out. It gives 24 (20% of 120) to S1 and 36 (30%

of 120) to S2 and similarly to P1 and P2. Once this is done, then S3 is deleted from

consideration. The next service department listed is S1. The cost to be allocated now

is 84 (60 specified as that of S1 and 24 allocated from S3. In the second pass this total

cost of 84 will be charged out as per the revised proportions.

S1 gives 9.3 to S2 and balance direct to P1 and P2.

In the last pass, the accumulated cost of 80+36+9.3 = 125.3 of S2 will be carried over

to the remaining departments P1 and P2. These calculations are shown in the table.

S3 S1 S2

S1 24 (84) 0

S2 36 9.3 (125.3)

S3 (120) 0 0

P1 36.0 46.7 55.6 =138.3

P2 24.0 28.0 69.7 =121.7

Costs as

given

120 60 80 260.0

Check the accuracy of computations by tallying the ultimate total of costs allocated

to production departments with the total of the costs specified for the service

departments.


3. Simultaneous Linear Equations (Matrix) Method

Basically what is done in this method is that the service department costs are first

adjusted for reciprocal exchange of services between the service departments (so to say),

by crediting each department for the services it has rendered to other departments and

debiting it for services availed of from other departments. By doing so all service

exchange between them are accounted for and what remains is to charge out the adjusted

costs directly to the production departments.

We show below how the equations are generated with the help of the numerical data of

the Example used earlier.

Let X1, X2, X3 denote the adjusted costs of the service departments S1, S2 and S3

respectively. Then the adjusted costs can be expressed as under incorporating terms for

services given and taken from other departments.

X1=60+0.0X1+0.1X2+0.2X3

X2=80+0.1X1+0.0X2+0.3X3

X3= 120+0.1X1 +0-0 X2+0.0X3

Consider the first equation. What this represents is that the adjusted cost (X1) of the first

department S1 is 60 of its own and 0% of own cost, 0.1 (10%) of costs received from S2

and 0.2 (20%) received from S3. Similarly for the other two departments.

The equations can now be re - written (merging coefficients of the variables) as under:

(1-0)X1 - 0.1 X2 - 0.2X3 = 60

-0.1X1 + (1-0) X2 - 0.3X3 = 80

-0.1X1 - 0X2 + (1-0) X3 = 120

Which can be written in matrix format as under:

1 - 0.1 -0.2 X1 60

-0.1 1 -0.3 * X2 = 80

-0.1 0 1 X3 120

Or as (I -A) X = b

The solution to such simultaneous equations (in real problems there will be many such

equations) is obtained by inverting the matrix of the coefficients. The solution for X can

be expressed as:

X = (I-A)-1

b -

That is, by pre-multiplying b by (I - A)-1

the inverse of the coefficient matrix.


For the numerical problem the (3 by 3) matrix can be easily inverted manually giving

the following result

1 0.10 0.23 60 98.862

1 0.13 0.98 0.32 80 = 128.852

0.967 0.10 0.01 0.99 120 129.886

The adjusted costs of the services are as given in the last column. Note that at this

stage, the total of the adjusted cost does not tally with the total costs as specified.

This apparent anomaly will disappear during the carry over of adjusted costs to

the production departments.

Now the next step is to carry over the adjusted costs to the production

departments. This again is done as a matrix multiplication:

98.862

Z1 0.5 0.4 0.3 139.938

= 128.852 =

Z2 0.3 0.5 0.2 120.062

129.886

Truth the allocated service costs to P1 is Rs. 139,938 and to P2 is Rs. 120,062.

Note that the total of these tally with Rs. 260,000 which is same as the total of the

costs specified (60 + 80 + 120 = 260 thousand)

Special Feature of the Matrix Method

In addition to providing a correct method of allocating service cost under

reciprocal exchange of services, the method has some additional features:

The adjusted costs Xj give the effective cost of service department. Dividing this

by the number of units of service the correct unit cost can be computed. This

information will be very useful in comparing own costs against external costs of

the service.

In the event of dose down of a service center the number of units of service that

should be acquired externally can be easily determined. This is calculated by

dividing the number of units produced internally by the diagonal element of the

concerned service in the inverse of the matrix (I - A).

We will present another example to demonstrate these features:

For example consider a textile mill located in a backward area, which has its own

internal service departments for supply of water (S\V), Steam (SS) and Power

(SP).


Part of the water is converted into steam using own power and part of the steam is

used to generate power.

The service departments provide services to two production departments of

spinning (PS) and Weaving (PW)

The data on proportions of service exchanges, the variable costs and the number

of units of services are given below:

From

To

SW SS SP

SW 0 0 20

% SS 50 0 0

SP 0 40 0

PS 30 25 35

PW 20 35 45

Variable

Costs

(Rs.000)

30 120 150

Water consumption is 600,000 litres, Steam 240,000 cubic metres and Power 500,000 Kwh.

The matrix equation to be solved will be:

1 0 -0.2 X1 30 30

-0.5 1 0 X2 120 = 120

0 -0.4 1 X3 150

Solving by matrix inversion

1 0.08 0.2 30 72.50

1 0.5 1 0.1 120 = 156.25

0.96 0.2 0.4 1 150 212.50

That is X1 = 72.5, X2 = 156.25, X3 = 212.50, totaling 441.25

The allocations to production departments will be:

0.30 0.25 0.35

0.20 0.35 0.45

75.50

135.187

156.25 = =

164.813

212.50

Thus the allocation costs are: To Spinning PS = Rs. 135,187 and to weaving

PW = Rs. 164,813 totaling 300,000 tallying with the total service cost specified.


Comments on additional features:

Suppose that an external agency can supply power at a cost of 35 paise per Kwh. Should

the mill avail of this offer and if so what will be the consequences?

Power can be purchased from the agency only if it is cheaper than the cost of

own production.

Suppose power department SP is dosed. Then all the variable cost of SP will be saved.

Now

observe that 40% of the steam used to generate power can be reduced. Since presently

50% of the water is used for total steam production, there will be a 20% (40% of 50%)

reduction in water consumption. Thus water usage will be at 80% of current level. Of the

total 500,000 kWh of power, 80% i.e. 400,000 kWh required for production and the

balance 100,000kwh is used to heat water.

When water consumption reduces to 80% level the power consumption will be 80% of

100,000 i.e.80,000 kWh.

Thus the total power to be purchased externally will be 400,000 + 80,000 = 480,000 kWh.

Now consider the saving that will accrue as a result of dose down of the power

department.

Rs

100/16 saving of the variable cost of SP = 150,000

40% saving of the variable cost of SS = 48,000

20% saving of the variable cost of SW = 6,000

Total Savings 204,000

The cost of buying 480,000 kWh of power at a price of 35 paise will amount to Rs.

168,000.Comparing this with the cost savings of Rs. 204,000 there will be net savings of

Rs. 36,000 to the mill. Hence, the mill should close down the power department and buy

power from the external agency at a price of 35 paise/kWh.

In the above example we have traced the savings and the power to be bought by a round

about analysis of cause - effect reasoning.

Even in this simple example where the number of service departments and the

interactions are few the computations have been enormous. For a real-life problem

with a larger number of service departments and complex interactions between the

departments this type of cause - effect analysis will be very difficult and almost


impossible to be done.

It is in this context that the matrix method provides all the required

information in a straight forward simple way.

The actual cost of generating power internally is

= Adjusted cost of power department / number of units of power

= 212500 / 500000

= 42.5 paise per kWh

As the purchase price of 35 paise is lower than the internal cost of 42.5 paise,

the mill should buy power from the agency.

The amount of power to be bought is

= current usage / diagonal element in the inverse matrix

corresponding to the column of the power department = 500000 /1.04166667

= 480,000

The cost of water and steam can be computed in a similar manner.

For water: 72500 / 600000 = 12.08 paise per litre

For steam: 156250 / 240000 = 65.1 paise per cubic metre.


Problems

Problems for Practice:

1. A small factory has three-service department S1, S2, S3 providing services to two

production departments P1 and P2. Table below gives the service exchanges between the

departments the annual variable costs and the number of units of services.

User Department Source of Services

S1 S2 S3

S1 10% 10 0

S2 20 0 30

S3 0 20 10

P1 40 30 25

P2 30 40 35

Variables cost

Rs.000

120 160 200

Unit of service 1600 2400 2600

a. Compute the service costs after reciprocal exchanges and compute the allocations to the two

production departments.

b. An external agency offers the services of S1 at a unit price of Rs. 80/- and services S2 at

a unit price of Rs. 100. Would it be worthwhile availing of these offers? If only one of the services

can be purchased which would Variable costs can be saved if a service department is closed down.

Note: The required inverse matrix is given below:

0.84 0.09 0.03

1

0.738 0.18 0.81 0.27

0. 04 0.18 0.88


2. A small factory has three service departments S1, S2, S3 and two production departments P1, P2.

Table below gives the proportion of services exchanges and relevant costs and volume of Services.

S1 S2 S3

S1 10% 20% 10%

S2 0 0 20%

S3 20% 30% 0

P1 30% 25% 50% P2 40% 25% 20%

Variables cost Rs.

`000

130 170 230


a. Find the adjusted costs of the service departments and the total cost of allocations to

each of the production departments.

b. An external agency can offer the services of S2 at a unit price of Rs. 70/- and of S3 at a

unit price of Rs. 95. Would it be worthwhile to by these services externally?

The factory cannot close down both S2 and S3 as this will lead to labour problems. Thus

if only one of the two departments can be closed down, determine which should be

closed and the saving the workshop will derive

Note: The inverse of the required matrix given below may be used in calculations.

1 0.94 0.23 0.14

0.818 0.04 0.88 0.18

0.20 0.31 0.90


3. A small factory has three service departments, S1, S2, S3providing services to

two production departments P1 and P2. Data on the proportion of services to be

provided, the costs and the number of units of services are given below:

S1 S2 S3

Sl 10% -- 20%

S2 -- 10% --

S3 20% 40% --

P1 40% 20% 50%

P2 30% 30% 30%

Variables cost Rs.

`000

80 100 120

Fixed cost 60 80 100

Units 3000 2000 4000

a. Develop the equations from which the reciprocally adjusted costs can be allocated to

the production department.

b. Compute the allocated costs to the production departments, separately for the variable

and fixed parts.

c. For technical reasons it is decided to close down the service department S3 and

purchase the required services externally. What should be the maximum price that can

be offered so as not to incur any more cost than now and how many units of this service

will have to be bought?

Note: The required inverse matrix is given below

1 0.90 0.08 0.18

0.774 0.00 0.86 0.00

0.18 0.36 0.81


4. A small factory has two production departments Pl and P2 which are serviced by

three service departments Si, S2 and S3. Data on proportion of services exchanged

between the departments, annual variable costs and number of services to be

produced are detailed below:

S1 S2 S3

S1 10% 10% 15%

S2 -- -- 10% S3 20% 15% --

P1 30% 50% 45%

P2 40% 25% 30% Variables cost

Rs.`000

800 1000 1200


a .Develop an appropriate matrix equation that will enable computation of the adjusted

costs of the services.

b. Using the data given above, compute the adjusted costs of the services and the

allocated costs to each of the production departments. (Show the figures of allocations

from the each services and the total).

c. An external agency offers the services of S2 and S3 at unit prices. of Rs. 160/- and Rs.

180/- which offer will be more beneficial and the annual savings there from.

d. After computing the allocations a revision had to be made on the output levels of two

production departments - PI output to be increased by .20% and P2 output to be decreased

by 20%. Determine how many units of the services SI, S2, S3 will be needed to support this

revised activity level.

Note: The inverse of the relevant matrix given below may be used in your computations.

1 0.985 0.1225 0.16

0.8545 0.020 0.87 0.09

0.200 0.155 0.09


5. A small firm has three services departments (S1, S2, S3) and two operating departments (O1

and O2).the services produced are reciprocally exchanged between the services department and

also allocated to the operating departments.

Data on the proportion of such exchanges, variable costs of the service departments for a

planning period and the number of units of services produces are given.

Sources

User Department S1 S2 S3

S1 10% 20 -

S2 25 - 10

S3 15 20 5

O1 30% 20 50

O2 20 40 35

Variable Cost (Rs. 000) 80 100 120

Units 2000 3000 6000

a. Compute the reciprocally adjusted costs of the services and the allocated costs to the operating

departments.

b.An external agency is prepared to offer the service currently produces by S3 at a unit price of

Rs.25. should the firm avail of this offer and close down the service department S3 ? If so, how

many units of service will have to be purchased externally and how much savings can be

achieved?

Note: The inverse of the matrix required in the computation is given below for ready use:

1 * 0.93 0.19 0.02

0.7865 0.2525 0.855 0.09

0.20 0.21 0.85

6. A factory has three service departments S1, S2, and S3 giving services to three production

departments O1, O2 and O3.For a budgeted period the following services have been provided:

To

From

S1 S2 S3 O1 O2 O3 Total

S1 0 0 0 20 40 0 60

S2 20 0 30 70 50 60 230

S3 110 90 0 350 250 0 800

The variable costs of the service departments for the same period are:

S1=Rs.40000

S2=Rs.80000

S3=Rs.30000


a. Allocated the service department costs to the production departments.

b.What is the maximum price payable per unit for any one of the services to be purchased from

outside so as not to incur costs more than the current own service? Calculator for each of the

services.

c.How many units of service will have to be purchased from outside under closure of each of the

service departments?

7. A cotton mill has its own internal service departments for supply of water (S,), steam (S),

and power (S,). A portion of water is converted into steam using own power and a

portion of steam is used to generate steam is used to generate steam. The service

departments render services to two production departments, i.e. spinning (P) and weaving

(P).

The proportions of service exchanges, the variable costs and the number of units of services

are given below:

From S1 S2 S3

To S1 10% 20 0

S2 25 0 10

S3 15 20 5

P1 30% 20 50

P2 20 40 35

Variable costs ('000) 60 120 160

Water consumption is 8,00,000 liters, steam 3,00,000 cubic meters and power 6,00,000 kwh.

a.. Determine the allocated costs to production departments.

b. If an external agency can supply power at a cost of 30 p/ kWh, should the mill buy it?

c.If the mill buys it, what amount of power it will buy.

d. Find also the cost/unit of water and steam.

8. The following transition matrix T shows that brand 1 retains 70% of its

customers but loses 30% to brand 2; brand 2 retains 80% of its customers and

loses 20% of its customers to brand 1.

0.70 0.30

T = 0.20 0.80

These are the only two brands available in the market. During the last period brand I had

30% and brand 2 had 70% in the market. Find the expected market shares in the next

period.


9. Modern Manufacturers Ltd. Have three production departments P1, P2, P3 and two

service departments S1 and S2 the details pertaining to which are as under:

P1 P2 P3 S1 S2

Direct wages (Rs.) 3000 2000 3000 1500 195

Working Hours 3070 4475 2419 -- --

Value of machines (Rs.) 60000 80000 100000 5000 5000

H.P.of machines 60 30 50 10 --

Light points 10 15 20 10 5

Floor space (sq. ft.) 2000 2500 3000 2000 500

The following figures extracted from the accounting records are relevant.

Rs.

Rent and Rates 5000

General lighting 600

Indirect wages 1939

Power 1500

Depreciation on machines 10000

Sundries 9695

The expenses of the service departments are allocated as under.

P1 P2 P3 S1 S2

S1 20% 30% 40% -- 10%

S2 40% 20% 30% 10% --

You are required to calculate the overhead absorption rate per hour in respect of the three

production departments using matrix method.

Find out the total cost of product X which is processed for manufacture in departments P1,

P2, and P3 for 4,5 and 3 hours respectively, given that its direct material cost is Rs.50 and

direct labour cost Rs.30.


10. Defex Company manufactures a number of components for household electrical

gadgets. It has two service departments S1 and S2 and two production departments P1 and

P2. The estimated overhead costs for a period and interdepartmental relationship matrix

are given below:

Service provided

by

Service provided to

S1 S2 P1 P2

S1 0 10% 40% 50%

S2 20% 0 50% 30%

Total estimated

Overhead

costs(Rs-)

9000 4000 3500 3000

The total estimated overhead costs = Rs. 19,500.

You are required to calculate the overhead costs for P1 and P2 using:

a.Direct allocation method;

b. Step method of allocation,

i) allocating S1 costs first and

ii) allocating S2 costs first

c. Matrix method of allocation.

11. You are the accountant of a small factory of RTC Ltd. It has three service departments

S1, S2 and S3 and three production departments P1, P2 and P3. For the budgeted period 1998-

99, the services provided are as stated under in percentages:

To S1 S2 S3 P1 P2 P3 Total

From

S1 0 0 0 0.20 0.80 0 1.00

S2 0.08 0 0.12 0.32 0.24 0.24 1.00

S3 0.15 0.10 0 0.45 0.30 0 1.00

The variable costs of the service departments for the budgeted period are:

S1 = Rs. 36,000 for 70 units.

S2 = Rs. 84,000 for 250 units.

S3 = Rs. 25,000 for 800 units.


Your Assistant was asked to workout the following:

a. The allocate on of the service costs to the production departments. b. If anyone of the services is to be purchased externally, then the maximum price that can

be paid per unit so as to incur any additional costs than what is current on own service.

This has to be determined for each of the three services.

c. The number of units of service that will have to be purchased externally under closure of each of the service departments.

The said Assistant took the job in right earnest but has fallen ill after working up to the stage

stated below:

1 -0.08 -0.15

(I-A) = 0 1 -0.10

0 -0.12 1

He also correctly worked out the determinant to be 0.988. Complete the exercises as

enumerated above under (a), (b) and (c).

12. A company has three Production Departments A, B and C and two Service

Departments X and Y. The expenses incurred by them during a month are:

A Rs. 80,000

B Rs. 70,000

C Rs.50,000

X Rs.23,400

Y Rs. 30,000

The expenses of Service Department are apportioned to the Production Departments on

the following basis:

Expenses of A B C X Y

X 20% 40% 30% -- 10%

Y 40% 20% 20% 20% --

Show clearly using matrix method how the expenses of X and Y Departments would be

apportioned to A, B and C Departments.


13. A company reapportions the costs incurred by two service cost centres, materials

handling and inspection, to the three production cost centres of matching, finishing and

assembly.

The following are the overhead costs which have been allocated and apportioned to the

five cost centres:

Rs. ('000)

Matching 400

Finishing 200

Assembly 100

Materials handling 100

Inspection 50

Estimates of the benefits received by each cost centre are as follows:

Matching% Finishing% Assembly% Handling% Inspection

%

Material

handling

30 25 35 0 10

Inspection 20 30 45 5 0

You are required to calculate the charge for overhead to each of the three production

cost centres, including the amount reapportioned from the two service centres, using

matrix method.

14.The new Enterprises Ltd. has three Production Departments A, B and C and two

service departments D & E . The following figures are extracted from the records of

the company.

Rs.

Rent & Taxes 5000

General Lighting 600

Indirect Wages 1500

Power 1500

Depreciation on machinery 10000

Sundries 10000


The Following further details are available.

Total A B C D E

Floor Space(sq. ft) 10000 2000 2500 3000 2000 500

Light Points 60 10 15 20 10 5

Direct Wages (Rs.) 10000 3000 2000 3000 1500 500

H.P.of Machines 150 60 30 50 10 --

Value of machinery

(Rs.)

250000 60000 80000 100000 5000 5000

Working hours -- 6226 4028 4066 -- --

The expenses of D & E are allocated as follows

A B C D E

D 20% 30% 40% -- 10%

E 40% 20% 30% 10% --

You are required to calculate the overhead absorption rate per hour in respect of the three

production departments using matrix method.

What is the total cost of an article if its raw material cost is Rs. 50, labour cost is Rs. 30 and

it passes through Departments A,B,and C for 4,5 and 3 hours respectively.

15. The space Production Company manufactures components for radio and television

satellites using two service departments and two service departments. The inter-

departmental relations and estimated overhead costs are given below.

Percentage of services provided to:

From Maintenance Scheduling Mouldings Assembly

Maintenance -- 10% 40% 50%

Scheduling 20% -- 50% 30%

Total

overhead

costs (Rs.)

750000 400000 378000 276000

Required:

a. Using the direct method, shoe the amount of scheduling Department costs to be allocated to Assembly Department.

b. Repeat (i) using the step method and allocating the maintenance first.

c. Repeat (i) using matrix method.


16. A Company has three production cost centres A,B and C and two service cost centre X

and Y. Costs allocated to service centres are required to be appointed to the production

centres to find out cost of production of different products.

It is found that benefit of service cost centres is also received by each other along with the

production cost centres. Overhead costs as allocated to the five cost centres and estimates of

benefit of service cost centres received by each of them are as under:

Cost Centres Overhead costs as

aloocated (Rs.)

Estimates of benefits received from service

centres (%)

X Y

A 80000 20 20

B 40000 30 25

C 20000 40 50

X 20000 -- 5

Y 10000 10 --

You are required to find the final overhead costs of each of the production departments including

reappointed cost of service centres using matrix method.

Documents

Assigning Service Department Costs