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Indifference to correct classification may easily upset the
validity of comparison in this way ; and exactly similar

169



170 MANUAL OF COST ACCOUNTS

difficulties may' arise in all compilations of numerical
records.

Another example may be mentioned in the booking of
workmen's time, where some jobs are being done at piece
rates and others at day wages. It is important that the
time booked to the piece work should be stated correctly.
If the employee is left to fill his time to his jobs at the end
of the week, there is a natural tendency for him to insert
such time as will ensure his earning bonus on the piece
work, thus having a maximum amount of his time to be
paid at day rate. Production statistics prepared from
these records would then be misleading, because the
actual production per hour on the piece work jobs would
be over-stated, and that on the day work jobs under-
stated. The introduction of time clocks to stamp the time
when each job was commenced and ended would ensure
accurate records all through.

A similar position arises in striking averages. A business
man very readily assumes that if he is making 40 per cent
gross profit in one department and 20 per cent in another,
he will have an average gross profit of 30 per cent, and
that his expenses at 25 per cent will leave him with a
5 per cent profit all round ; whereas if his first department
with 40 per cent profit has only half the turnover of the
other one at 20 per cent profit, his average profit is only
26-6 per cent and his profits 1-6 per cent.

This illustration explains the distinction between an
arithmetical average of numbers and a weighted average
according to the quantities that the numbers represent.

The arithmetical average gives a true result when the
factors are correctly comparable, e.g. the weights of 50
similar cases set out on an invoice totalling l,4001b. will
average 28 Ib. per case. If some of the cases are large
cases and others half cases this result will not correctly
interpret the circumstances. The number in each group
must be obtained Assuming there are 6 large cases and
44 half cases :



STATISTICAL PRESENTATION OF RESULTS 171

Then 6x1=6

44 x = 22

28 cases 1,400 = 50 Ib. per case

f=s " and 25 Ib. per half-case.

This is an example of weighted average, the differ-
entiating weight being applied to one of the factors.

Similarly, if in a factory the cost of warehousing and
handling materials inclusive of storekeeping charges totals
for 12 months to 2,100, and the weight of material handled
amounts to 14,000 tons, the cost may be stated as 3s. per
ton ; but if there are three classes of material, and the cost
of handling is not proportionate to the weight but varies as
say



Class A Class B Class

2,000 tons with an 5,000 tons with an 7,000 tons with an
expense of ^10 expense of 8 per expense of 5 per
per ton in pro- ton in proportion ton in proportion
portion to 5 per to 5 per ton of to ^10 per ton of
ton of Class C. Class C. Class A, or 8 per

ton of Class B.

then the cost of handling, etc., in each case should be stated
as

A 2,000 x 10 = 20

B 5,000 x 8= 40 2,100 /

C 7,000 x 5 = 35 95 x 1,000



14,000 95

Class -4022105 x 10 = -22105, say, 4/6 per ton
B 022105 x 8 = -1768 3/6
C 022105 X 5 = 1105 2/3

The application of the principle is seen in detail in
framing rates of expense for the shops or departments in
a factory when the expense has to be distributed equitably
between them, and the rates proportioned to the work
done in each.

If for example the expense rates in six departments of
a factory are respectively 7s. 6d., 4s., 6s., 2s., 4s. 3d.,
Is. 9d., per hour, the oncost charged to the jobs will not be
at the average rate of 4s. 3d. per hour as would appear by

12 (1765)



172 MANUAL OF COST ACCOUNTS

taking the arithmetical average of these figures, but must
be found by taking into account the number of hours in
respect of which oncost has been charged ; so that if the
direct labour hours in the departments are respectively
10,000, 3,500, 15,000, 900, 10,000, and 2,000 the true result
will be found by taking the weighted average and is seen to
be nearly 5s. 6d. per hour ; the same averages may be
contrasted as percentages on wages amounting to 212 per
cent and 275 per cent.

The average is also spoken of as an arithmetical mean,
and a series of numbers at equal intervals represent an
arithmetical series or progression, a feature of the series
being that any two consecutive numbers differ by a common
difference.

In a series of numbers where the ratio of each term to
the next in the series is constant a geometrical progression
occurs. It is illustrated in the accumulation of compound
interest and other progressional increases, where the
increment is in constant proportion. The value of 100
at 10 per cent.

EXAMPLE (1)
in one year is ^100 X j^

in two years it will be (*IOO X j^) X (j2) or ^100 x g)'

/110\ 10

so that in ten years it will be ^100 X ( 77^ )

\1UU/

The increase occurs in geometrical progression and the
values at the end of each year form a geometrical series.
The total value at the end of the ten years is obtained most
conveniently by the use of logarithms and is shown to be
100 X 2-594 = 259 8s. Od.

(2) Similarly, if a sum of 100 is to be paid in five years
in repayment of a present loan of 50 the yearly rate of
compound interest will be the ratio of the geometrical
series at yearly intervals. The series for the five years



STATISTICAL PRESENTATION OF RESULTS 173

is found by taking the fifth root of the ratio between the

first and last terms of the series, that is / which will

M 50

give the ratio of the terms of the series ; so that the rate
per cent of the annual increase at compound interest
is

Yl2? x 100- 100
V 50

= 1-48 X 100-100

= 14-8 per cent per annum.

(3) A Sinking Fund is required to amount to 10,000
in 10 years, the annual instalment and interest being
invested at 5 per cent per annum. If the yearly sum to be
provided is represented by X, then the summation of the
geometrical progression shows that



X ((*)"- ,)



100



. 4,0.000



X x (1-629- 1) = 10,000 x -05

= 795 nearly

(4) It is required to find the value of a Plant costing
100,000 in 20 years if 4 per cent per annum is adopted
as a yearly rate of depreciation on the diminishing
value.

96

In the series of yearly values 100,000 : 100,000 X 77^ : 100,000



X f Yoo ) '



term at the end f the 20th year



100,000 x



= 100,000 X -4426
= 44,260



The geometric mean of two quantities is found by taking



174 MANUAL OF COST ACCOUNTS

the square root of their product. The insertion of a series
of geometric means between two quantities is shown in
the above example (2) by the finding of the common ratio
according to the number of terms required.

The geometric mean is always less than the arithmetical
mean for the same numbers and so may be more con-
veniently adopted for contrasting tables of averages
where the extremes are widely divergent.

Another form of variation in a series of statistical data
is that of harmonic progression which occurs in the accelera-
tion of velocity or regular variation of motion. It may be
illustrated by an example of a motorist, who, in travelling
a distance, covers the first part of the journey at 10 miles
per hour, the second part at 20 miles per hour, the third
part at 30 miles per hour, and the fourth part at 40 miles
per hour. The average rate of travelling is not 25 miles
per hour, but 19*2 miles. To find the harmonic mean of
10, 20, 30, 40, forming an arithmetical progression, the

harmonic scale TTT + T^ + ^r + ^is used and - of this
1 u 2i\j oU 4U 4

total gives So that 19-2 is the harmonic mean of the

series. Harmonic variation also occurs in vibrations of
sound waves.

Other expressions which are used in connection with
the tabulation of statistical data are

(1) The Mode is the group in a series which contains
the most numerous examples. It is not a specific example
which is exactly determinable like an arithmetical average,
but is the group as a whole into which the largest number
of examples fall.

(2) The Median is again not the arithmetical average
but is the example in the series which occurs at the centre
point midway between the two extremes. It is thus
different from the mode and to find it the centre point
of the series must first be determined and then the



STATISTICAL PRESENTATION OF RESULTS 175

example occurring at that point must be found or
estimated.

In a similar way to the determination of the Median, the
Quartiles are placed at points midway between the Median
and the extremes of the series and are similarly found :
other terms in a series are referred to as variates.
These points are particularly useful in dealing with large
numbers such as statistics of population, employment,
wages, etc.

In the tabulation of records dealing with the purely
statistical side of a business, it is no less important to handle
the figures so that they will present a correct view of
affairs. The same applies to curves and diagrams when
used for illustration purposes. These may give an exag-
gerated impression if faultily drawn in the setting out of
the scale or in the methods adopted.

It is essential that the horizontal and vertical scales
should be measured in equal gradations from the start to
the finish of each scale, and for the purposes of comparison
it is preferable to arrange the scales so that several series
can be tabulated rather than to show independent diagrams,
when different scales render comparison difficult. The
records should progress across the diagram upwards and
from left to right. Where the figures to be tabulated are
not in respect of equal periods in each case, the periods over
which the figures are tabulated must be proportioned
accordingly so that an equal period of time (e.g. in the
case of fluctuations of business or population, etc.) is
represented by a similar space at any portion of the
diagram.

Diagrams may be drawn to represent not only fluctua-
tions between individual groups, but to show the cumula-
tive effect of fluctuations as the period progresses ; or the
object of the diagram may be to show the trend of the
statistics, and in that event a better presentation is made
by averaging several periods to obtain each point on the
diagram and a smoother curve results.



176 MANUAL OF COST ACCOUNTS

Another very common source of error is the readiness
with which many business men accept " special tests "
of work done as a safe basis for calculating results. So
many factors enter into the problem in a case like the
making of a special test of work in a factory, that even
if frequently done, these will often be entirely unreliable
owing to the prevalence, at the time, of necessarily
unrepresentative conditions not applying to the factory as
a whole ; for example, in respect of such matters as time
lost between jobs ; time fixing or preparing machines ;
occasional faulty material and other similar causes. Thus,
it is essential, in building up an approximation of the
whole from a few selected factors, to have all the conditions
fairly represented in the factors ; any faults being magni-
fied in proportion to the degree to which the conclusion is
expanded.



Weekly Summary.

In most businesses a weekly summary is found useful
showing

(a) Sales in each department for the week and the
corresponding week of the previous year ;

(b) Total sales for the quarter to date, with similar
comparisons of previous years ;

(c) Statistics of quantities in detail of each product
turned out, where these can be produced ;

(d) Departmental cost and profit summaries, if obtainable,
week by week ;

(e) Statement of Sundry Book Debts, showing in an
aggregate account the balance at the commencement
of the week, sales debited for the week, cash and
discounts and other credits for the week and aggregate
balance ,1

(/) Similar statements of Bank Account and Sundry
Creditors ;

(g) Accruing liabilities.



178



MANUAL OF COST ACCOUNTS



Use of Diagrams.

Diagrams should be made use of to emphasize
(1) Comparisons between groups ; e.g. Areas propor-
tioned to -Population and shaded to show Trade done.

A.





COMPARISONS OF Two AREAS CANVASSED BY SALESMEN.

A. Having Population, 50,000; Weekly Sales Value, 1,000;
2 per 100 Population.

B. Having Population, 100,000; Weekly Sales Value, 1,800;
1 16s. per 100 Population.

(2) The composition of a group or similar groups ; e.g.
Character and Proportion of Trade done in an Area
comparing different Periods.




JANUARY. FEBRUARY.

PER 100 SALES.

Diagram showing composition of Trade done in January and
February.

(3) The variations in a series of similar records at
successive dates ; e.g. Wages and Expenses ; with Expense
fluctuations expressed as percentage on Wages.



STATISTICAL PRESENTATION OF RESULTS



179



Wages
Expenses .
Percentage


.Jan.


Feb.


Mar.


April.


May.


June.


July.


Aug.


Sep.


Oct.


Nov.


Dec.


550
110


600
600
100


A

650
118


600
92


700
116


750
107


A

750
115


7 lo

700
93


700
800
114


800
850
106


950
850
89


sfo

800
94



*] ()r\o


v\. Fe


b. Me


ir A|


IT. Mi


iy. Ju


ne. Ji


ly. Ai


Se


pt, a


:t. N


DV. De


900




















^


^^


800










Fvni








..


-^._


-^


700










&




'""l?^




^x^










_, -


*"*V^


>^^*




*-


s^










500


~^f^


*"*.


*>r




















120%

no%

100%
90%
80%


























/"


\
\


/


Sj^


^*f






^






^>s


/


\


/


^




\


/


"*^


s.








\


/






\






N


^^

























(4) The variations between two or more series ; e.g.
Sales during different periods.

Jan. Feb. Mar. Apl. May. June. July. Aug. Sept Oct. Nov. Dec



0,000
19,000
18,000
17,000
16,000
15,000
14,000
13,000
12,000
:f 1 1 nnn








1920


















^s


^-"^
















1919^,


19ZO,.


S












**>







*'










/'












1919








/'/'






-s.


V




m,'


"" -


-^^




"* ^


s








^N

x_


^^.*-


s






^^


jr
















1918

**


^- "*


.


















'






,^.


^^^


-.




k ^-*^.






1917


1917^,


.
















U ^-^.


r """



(5) Comparisons in three relations which can be com-
bined geometrically, e.g. Sales per traveller per 1,000
population in different areas.



180



MANUAL OF COST ACCOUNTS




COMPARISON OF Two AREAS CANVASSED BY SALESMEN TO SHOW
SALES PER TRAVELLER PER 1,000 POPULATION.

A. Population, 50,000; Sales, 1,000 j Travellers, 10 5 Sales
per Traveller, 100.

B. Population, 100,000; Sales, 1,800; Travellers, 15; Sales
per Traveller, 120.

A. Sales per 1,000 Population, 20 ; Sales per Traveller per
1,000, 2.

B. Sales per 1,000 Population. f.\ 8 ; Sales per Traveller per
1,000, 1 4s.



CHAPTER XVII

EXAMINATION QUESTIONS

Institute of Chartered Accountants

(1) WHEN closing the accounts of a manufacturing business
how should the value of " work-in-progress " be arrived
at ? Briefly describe a type of business with which you
are familiar and state how the value of this asset is ascer-
tained. When the valuation has been made how would
you require it to be dealt with in the accounts you are
asked to audit ?

(2) From the following information prepare Pig Iron
Production Account showing the cost per ton of each class
of expenditure and of the pig iron produced

Sundry Stores on hand 1st July, 1918 Coal, 4,720; Coke;
3580- Limestone, 1,450 ; Ironstone, 3,930 ; Sundries, 2,700.

Purchased during the year Coal, 21,880; Coke, 29,470;
Limestone, 5,080 ; Ironstone, 18,690 ; Sundries, 7,810.

Sales of Slag, 10,000 ; General Works Charges, 4,400 ; Wages,
17,600 ; Production of Pig Iron, 32,000 tons.

Stocks on hand June, 1919 Coal, 3,800 ; Coke, 2,650 ; Lime-
stone, 1,730 ; Ironstone, 3,420 ; Sundries, 2,910.

(3) A client of yours who manufactures small machine
parts asks you to initiate a system of Cost Accounts in
his works, and to conduct a half-yearly audit of the costing
books.

What books other than the ordinary financial books of
account should you recommend your client to adopt ?
Detail briefly the audit you would carry out.

(4) Draw up a system of Cost Accounts for a building
contractor and show how they would be co-ordinated
with the financial accounts of the business.

(5) You are asked to consider and report upon the
costing system employed by a manufacturer of cycle
accessories ; more particularly as to whether the interest

181



182



MANUAL OF COST ACCOUNTS



upon capital and loans should be taken into account in
arriving at costing results.

Report briefly upon the latter point.

(6) A pencil manufacturer makes two types of pencils
" Black " and " Coloured." They undergo two processes,
factory and finishing. Raw materials used in the factory
and general expenses are apportioned in the ratio of output
of each class ; the output in 1918 was 24,000 gross Black
and 8,400 gross Coloured ; the actual cost of labour for
each process is ascertained ; " other charges " for each
processes are apportioned in the same ratio as labour for
that process ; finishing materials are apportioned in the
ratio of finishing labour. From the following particulars
prepare a statement of the cost per gross, in shillings and
pence of each item and each process in the cost of manu-
facture ; and the profit per gross if the selling prices are
1 and 19s. respectively.



Factory Raw Materials, Opening Stock
Purchases .
Closing Stock
Wages, Black

,, Coloured
Charges

Fin shing Wages, Black .
,, Coloured

Raw Materials, Opening Stock
Purchases .

Closing Stock

Charges ....
General Expenses ....



3,680

10,710

4,940

4,200

1,365

3,710

2,000

560

720

3,370

890

1,920

3,645



(7) A, who commenced business on 1st July, 1918, as
a piano manufacturer places before you the following
information and asks you to prepare a statement showing
the profit per piano sold (charging labour and material at
actual cost, works oncost at 100 per cent on labour and
office oncost at 25 per cent on works cost), and statement
showing a reconciliation between the profit, as shown by
the Cost Account and the profit as shown by the Profit
and Loss Account for the year ended 30th June, 1919.

Two grades of pianos are manufactured and are known



EXAMINATION QUESTIONS



183



as No. 1 and No. 2. There were no pianos in stock or in
course of manufacture on 30th June, 1919.

fo

8
19



Average Cost of Materials, per Piano No. 1

No. 2



,, ,, of Labour

Finished Pianos Sold, No. 1
No. 2

Sale Price of Pianos, No. 1
No. 2

The Works Expenses were
The Office Expenses were



No. 1
No. 2



118

205



14



75
55

5,240
3,166



You are required to prepare the necessary statements,
showing the actual profit for the year.

(8) The Paper Products Company, Ltd.,' owns
A paper mill, all the output of which is sold to the

factory at 10 per cent above mill cost price.
The factory which sells all its output to the selling

department at 10 per cent above factory cost price.
The selling department.

From the following figures calculate (a) the factory cost
of output, showing the proportion " paper " bears to
" other goods, wages and charges " ; (b) the profit made
by the company in the year ; allowing for (c) the reserve
required to eliminate the unrealized profit on increase in
stocks in the year, assuming that the selling department
increase is in the same proportions as in (a).



FACTORY

Opening Stock on Hand, Paper

Other Goods

Paper Purchases from Mill

Other Goods, Wages, Charges, etc.

Closing Stocks on Hand, Paper

Other Goods
SELLING DEPARTMENT

Opening Stocks on Hand

Sales

Wages, Charges, etc.

Closing Stocks on Hand



18,700
14,800
73,300
43,900
24,200
13,500

27.400

148,000

16,400

37,300



(9) What are the principles of Process Cost Accounts ?
Illustrate your answer by means of pro forma accounts of
a manufacturing business to which Process Cost Accounts
could apply with advantage.



184 MANUAL OF COST ACCOUNTS



From the point of view of Cost Accounts discuss
and compare the practice of paying wages

(a) On the piece-work system ;

(b) On the day-work basis ;

(c) On the bonus or premium system.

(11) A company desires to inaugurate an efficient system
of Cost Accounts in connection with the manufacture of
several distinct kinds of goods. You are required to
select a business, and to explain how the costing system
should be constructed, mentioning three items which you
would include amongst the Oncost charges, and stating
how you would apportion such charges between the
different departments.

(12) A business is carried on in three separate depart-
ments. Expenses not directly chargeable to any one
department are apportioned, one-half to A, three-tenths
to B, and one-fifth to C. From the following particulars
prepare Trading and Profit and Loss Accounts of the three
departments (in columnar form), showing the gross and net
profits and the percentages thereof, and of the totals,
to turnover, exclusive of inter-departmental transactions.

Stocks on Hand, 1st January, 1918

A Department, 1,782; B, 560; C, 125.
Stocks on Hand, 31st December, 1918

A Department, 1,936 ; B, 471 ; C, 316.
Outside Sales for the Year

A Department, 11,174 ; B, 5,613 ; C, 4,851.
Inter-Departmental Sales

A to B, 904 ; A to C, 482 ; B to A, 1,126 ; B to C, 219 ;

C to A,, 348.
Wages

A Department, 2,470 } B, 1,328 ; C, 915.
Outside Purchases

A Department, 4,041 ; B, 1,537 ; C, 1,526.
Salaries

A Department, 945 ; B, 572 ; C, 416.
Management Salaries, 1,200 ; Rent, Rates, and Taxes, 1460 ;

Insurance, 210 ; Horses, Vans, etc., Expenses, 870 ;

Postages and Telegrams, 110; Bad Debts, A, 276, B,



143, C, 224 ; Sundry Expenses, 530j^ Depreciations

off, 740 ; St
Advertising, 450.



written off, 740 ; Stationery and Printing, 260 ;



(13) You are Auditor to a Limited Company which
manufactures and repairs motor cycles. The directors



EXAMINATION QUESTIONS



185



have instructed you to extend your audit to the costing
records.

Upon attending at the Stores Department you find

(a) That invoices representing goods purchased are
handed to the storekeeper when the goods arrive.

(b) That particulars of goods received and issued are
entered by the storekeeper in a " Stores Book," no
other record being kept.

(c) That stores are issued to foremen upon verbal
request.

(d) That the storekeeper is allowed to order goods
direct if under 10 in value.

(e) That stores " left over " from jobs are replaced in
the store-room bins by the foreman concerned.

If you do not approve of the system of store keeping
described above, make suggestions for its improvement.

(14) A Company carrying out large contracts, kept
separate accounts for each Contract in its Contract Ledger.
This Ledger showed the following expenditure in connection
with Contract No. B497, as on 31st July, 1920 :

Materials Purchased . 47 > 952

,, from Store
Plant from other Contracts

,, Purchased
Wages .
Direct Expenses
Proportion of Establishment Charges



8,674
12,520

3,619
63,524

1,915

7,619



145,823

The Contract, which was commenced on 1st February,
1920, was for 295,000, and cash had been received amount-
ing to 110,950, which was the full amount certified, less
20 per cent retention money. The work was certified to
31st July, 1910, when it was half completed, and materials
on the site were valued at 8,747.

A Contracting Plant Ledger was kept in which deprecia-
tion was dealt with monthly, the total amount of which
was 1,419 in respect of Plant on Contract No. B497.

You are* required to prepare an account showing the



186 MANUAL OF COST ACCOUNTS

profit, if any, to date ; and to state what amount should,
in your opinion, be taken into consideration in the
Company's accounts for the year to 31st July, 1920.

(15) A manufacturer of matches desires you to devise
a system of Cost Accounts for his factory, and thereafter
to audit them.

Assume that the power employed is electricity, and briefly
describe the various items which it would be necessary to
deal with.

Classify these elements of cost in the groups into which
you would divide them, and state the sources from which
you would derive the necessary details.


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