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 £ 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..

. 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 £ 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 £ 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--£2 800 Fuel and Oil--£1 200 Servicing--£ 500 Taxation and Insurance --£1 250 Depreciation--£950

Making reasonable assumptions where appropriate, calculate: 1)The overall cost per mile, regarding ALL costs as just being mileage-dependent and assuming 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 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 watches and the receipts from selling them are expected to be £ Each watch will therefore sell for £( /20 000) = £25.

If we sell n watches, therefore, we expect to receive £25n.

Making the watches will cost us £ regardless of how many we make, plus an amount per watch made totalling £ if we make watches as planned.

This must be £ / = £15 per watch, or £15n in all if, as before, we sell n watches.

Our total cost will therefore be £( n).

(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= n

This means that 25n= n andn= /10 = watches.

(b) Actually we intend to sell watches , or 33.3%, more than breakeven - - and this is the Margin of Safety.

(c) If we only sell watches, we will receive x £25 = £ from selling them...

but making them will cost us £ £15 x = £ We will therefore make a LOSS of £

(d) Here is the graph.

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 watches, it is quite simple -- we will sell them all !

Making them will cost (15n ) = £ , whilst we will sell them for £25n = £ We will therefore make £ profit.

If we make watches, it will cost us £ We will sell them all 95% of the time for £25 x = £

but 5 % of the time we will only sell for £ as we calculated above.

We now use the probabilities to calculate our expected sales receipts: 0.95 x x = £

Our expected profit is therefore £ £ = £

We will now do the one for watches made (‘Over to you’ will feature and !)

Cost = £ x 15 = £ Receipts if we sell them all: £25 x = £ (prob. 20 %) Receipts if we sell : £25 x = £ (prob. 20 %)

Receipts if we sell : £25 x = £ (prob. 35 %) Receipts if we sell : £25 x = £ (prob. 20 %) Receipts if we sell : £25 x = £ (prob. 5 %)

For the ‘expected’ outcome, we multiply the sales figure by the probability of its occurrence and add up the results.

x x = £

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 !)