Simple Costing

It is necessary if we are organising the production of manufactured articles or the

provision of services to be able to answer questions such as:

At what price should we sensibly sell each product (or will we make a profit if we use the price the Marketingfolk suggest ?)

At what price should we sensibly sell each product (or will we make a profit if we use the price the Marketingfolk suggest ?)Will we make a profit, and if so how much ?

At what price should we sensibly sell each product (or will we make a profit if we use the price the Marketingfolk suggest ?)Will we make a profit, and if so how much ?How many products must we sell before we break even ?

We are not sure how many we can sell, but we have

some statistical market info. How can we use it to

determine how many to make ?

The demand from our customers is greater than we can supply. Will it be a paying

proposition to work some overtime to make more

products ?

Someone comes along from Outer Mongolia or somewhere prepared to buy quite a lot of

our products but cannot afford to pay the full price -- will it

pay us to reduce it to persuade him/her to buy ?

To answer such questions, it is likely to be beneficial to

construct a simple Mathematical Model as

follows.

The term suggests a good-looking lad or lass who is good at sums, but it does not mean that ! For what it does mean,

read on ...

We start with the (usually reasonable) assumption that our total costs of production

partly depend on time and , if we further assume for the

moment that we only make one type of article, partly depend on

the number of articles we make.

It is also probable that we must make a (largish) one-off

payment initially to buy the machinery etc. that we need

to make the article ...

… but it is possible to budget that cost as part of the time

cost by taking the view that we are paying it off over the

anticipated total time that we are manufacturing the articles.

A simple first scenario:

It costs us £70 000 to buy our equipment in the first

place. We sell each article for £100 and the materials to make it cost £30 per item.

We make 20 articles per week. Ignoring interest charges and other like

complications, how long will it be before we begin to

make a profit ? (This is called Breakeven Analysis).

The answer proceeds by commonsense.

.

The answer proceeds by commonsense.

.

Each item is sold for £100 - £30 = £70 more than it cost to buy the materials for it, so

each one contributes £70 towards the £70000 the

equipment cost..

We must therefore sell 70000/70 = 1000 articles, so

it will take 1000/20 = 50 weeks.

Have we ignored anything likely to be significant in practice ?

Have we ignored anything likely to be significant in practice ?

I think we probably have -- what about heating and lighting our factory, the rates, tax etc? Is

"Jones the Bank" likely to charge us interest if we borrow the £100

000 from her/him? (Yes!)

Things are often more complicated than they seem but the following approach is

often helpful.

Many firms base their strategy on the following headings:

Fixed Time Cost (incurred, for example, per week regardless of whether production is taking place or not) -- capital charges, rates, some of the power bills, usually wages for the normal working week for employees.

Variable Time Cost (incurred whenever production is taking place but regardless of how

much is actually being made) -- overtime and contract wages and more of the power bills. It is often possible to incorporate

this cost in with the ...

Unit Cost -- what it costs per article produced -- materials

and the remainder of the power bill.

We will apply this idea to the simple scenario and we will

now also assume that the £70 000 was borrowed originally

and it is to be paid off over five years at a rate of £800 per

week including the interest ...

… (actually a high rate of interest -- a loan shark must

have got in on the act). With the cost information we

have at the moment, we have:

Fixed Time Cost = £800 per week

Variable Time Cost = zero

Unit Cost = £30 per unit

This tells us that, at our previous production rate of 20 articles per week, our weekly costs will be £800 + £30 x 20

= £1 400 per week.

Our weekly surplus is therefore £600 .. but there are a number of things we have not allowed

for.

Rent? Heating ?

Lighting ? Rates ?

Maintenance of our equipment ?

A Simple Example for you (based on one in ‘Essential Elements of Management

Accounting’ by Jill and Roger Hussey)

A taxi business has the following costs per quarter (13

weeks).Driver’s Pay -- £2 800Fuel and Oil -- £1 200

Servicing -- £ 500Taxation and Insurance

-- £1 250Depreciation -- £950

Making reasonable assumptions where appropriate, calculate:

1) The overall cost per mile, regarding ALL costs as just being mileage-dependent and assuming 15 000 mile/quarter. This cost is

known as the Absorption Cost per mile.

2) The Time Cost and the Unit Cost (assumed as cost/mile)

again assuming 15 000 mile/quarter.

Which of these costs would be the better guide to (a) how much per mile we should

charge in normal taxi operation ...

...and (b) whether we could charge less on occasion to

secure, for example, a booking to Heathrow Airport, and still

make a profit ?

Here is a more complicated example, taken from a past

exam paper.

Quality Ltd. is a manufacturer who produces a single model

of wrist-watch.

A Profit and Loss Budget has been prepared for the coming financial year which is based on an anticipated sales level

of 20,000 watches per annum.

Required:

(a) Calculate the break-even point in terms of both

number of watches sold and sales revenue. (b) Calculate the "margin of safety" in terms of watches sold and as a percentage.

(c) Calculate the profit or loss if the forecast sales is changed to 10,000 watches per year. You can assume

that the variable cost per unit and total fixed costs remain the same.

(d) Illustrate the answers of (a), (b) and (c) with a suitable graph/chart.

The Answer

We will assume that the Variable Costs are all directly proportional to the number of

watches sold.

We are first told that the annual sales are expected to be 20 000 watches and the receipts from

selling them are expected to be £500 000. Each watch will therefore

sell for £(500 000/20 000) = £25.

If we sell n watches, therefore, we expect to

receive £25n.

Making the watches will cost us £150 000 regardless of how

many we make, plus an amount per watch made

totalling £300 000 if we make 20 000 watches as planned.

This must be £300 000/20 000 = £15 per watch, or £15n in all

if, as before, we sell n watches.

Our total cost will therefore be £(150 000 + 15n).

(a) The Break-Even point is reached when we receive the same total sum from selling our watches as it costs us to

make them.

This means that 25n =150000 + 15n

This means that 25n =150000 + 15n

and n = 150 000/10= 15 000 watches.

(b) Actually we intend to sell 20 000 watches -- 5 000, or

33.3%, more than breakeven -- and this is the Margin of

Safety.

(c) If we only sell 10 000 watches, we will receive 10 000 x £25 = £250 000 from

selling them ...

but making them will cost us £150 000 + £15 x 10000 =

£300 000.

We will therefore make a LOSS of £50 000.

(d) Here is the graph.

0 0.5 1 1.5 2 2.5 3 3.5 40

1

2

3

4

5

6

7

8

9

10

Watches sold per annum, x 10 000

Cost and sales, £ per annum (x 100 000)

Cost

Sales receipts

What if things are not certain ?

Problems can arise if we are not sure how many items

produced we can sell. If we do not make enough, we lose the opportunity of making profits on the ones we could have sold ... but if we make too

many, we have incurred costs unnecessarily.

It is often possible, through experience or market research,

to establish probabilities regarding likely demand for the

product.

We will revert to the watch example and discover from

sales and our market research department that our wholesalers

order in multiples of 2000 and our sales probabilities are

expected to be:

If we make 16 000 watches, it is quite simple -- we will sell

them all !

Making them will cost (15n + 150 000) = £390 000,

whilst we will sell them for £25n = £400 000.

We will therefore make £10 000 profit.

If we make 18 000 watches, it will cost us £420 000. We will sell them all 95% of the time

for £25 x 18 000 = £450 000 ...

but 5 % of the time we will only sell 16 000 ...

for £400 000 as we calculated above.

We now use the probabilities to calculate our expected sales

receipts:0.95 x 450 000 + 0.05 x 400

000 = £447 500.

Our expected profit is therefore

£447 500 - £420 000

= £27 500.

We will now do the one for 24 000 watches made

(‘Over to you’ will feature 20 000 and 22 000 !)

Cost = £150 000 + 24 000 x 15 = £510 000

Receipts if we sell them all: £25 x 24 000 = £600 000

(prob. 20 %)Receipts if we sell 22 000: £25 x 22 000 = £550 000

(prob. 20 %)

Receipts if we sell 20 000:£25 x 20 000 = £500 000

(prob. 35 %)Receipts if we sell 18 000: £25 x 18 000 = £450 000

(prob. 20 %)Receipts if we sell 16 000: £25 x 16 000 = £400 000

(prob. 5 %)

For the ‘expected’ outcome, we multiply the sales figure by

the probability of its occurrence and add up the

results.

600 000 x .2 + 550 000 x .2 +

..... = £515 000

So we now expect a profit of only £5 000, though it is

interesting to note that a loss will result 60 % of the time ....

Over to you ....

(Do please come to your “practice session” this week !)