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.
Prof. Prashant Shukla
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
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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
Prof. Prashant Shukla
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.
Prof. Prashant Shukla
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.
Prof. Prashant Shukla
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.
Prof. Prashant Shukla
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.
Prof. Prashant Shukla
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).
Prof. Prashant Shukla
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.
Prof. Prashant Shukla
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
Prof. Prashant Shukla
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.
Prof. Prashant Shukla
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
Prof. Prashant Shukla
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
Unit of service 2000 2500 3000
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
Prof. Prashant Shukla
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
Prof. Prashant Shukla
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
Unit of service 5000 6000 8000
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
Prof. Prashant Shukla
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
Prof. Prashant Shukla
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.
Prof. Prashant Shukla
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.
Prof. Prashant Shukla
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.
Prof. Prashant Shukla
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.
Prof. Prashant Shukla
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
Prof. Prashant Shukla
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.
Prof. Prashant Shukla
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.