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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.

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.