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Chapter

Chapter 8

Decision-Making − Cost Behaviour

8.1 Introduction 107 8.2 Cost Behaviour 108 8.3 Breakeven Analysis 111 8.4 Decision-Making 114 8.5 Summary 117

Learning Objectives

After completing the study of this unit you should be able to:

• explain the nature of cost behaviour

• define and calculate the breakeven position

• calculate target profits

• make key business decisions.

8.1 Introduction

Decision-making is a vital part of every manager’s job. To ensure the best options are selected, the manager needs accurate information about the alternatives available. Whatever decision is being made, the financial aspects of the problem will invariably be required and such aspects often hinge on the relationship between costs, volume and profit. Knowledge of this relationship greatly assists, in particular, the short-term planning process. See worked example 8.1.

Worked example 8.1

You have been asked by the captain of the golf club to organise this year’s dinner-dance at which all the prizes for this year’s events will be handed out. The local hotel has given you the following quotation.

1. Hire of room £300

2. Hire of band £120

3. Hire of disco £80

And for each person attending:

4. Food £20

5. Champagne cocktail £4

6. Party hats and crackers £6

You have been told to set the ticket price at £50 each. How many people do you need to attend to cover your costs?

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Solution

If you have deduced the correct answer of 25 people then you are well on your way to understanding the basic features of cost behaviour. The costs of the room, the band and the disco are costs that you will have to incur regardless of how many people you can persuade to attend the function − they are your fixed costs. The costs of food, champagne and the party hats are costs which will increase as the number of people attending increase − they are your variable costs.

If charging £50 a ticket, you know that the first £30 will be used to pay for the food, the champagne and the party hats (i.e. the variable costs). This leaves £20 per person that you can use to help to pay for your fixed costs. If you can persuade 25 people to come then they will each contribute £20 towards meeting those fixed costs, raising a total of £500 − exactly the amount you need to cover your fixed costs. Therefore, in order to breakeven, your ticket sales need to be 25.

A lot of the accounting terms that are part of everyday business life were used in the example above. Knowledge of how costs behave is essential for the tasks of budgeting, planning, control and decision-making and you need to develop this knowledge.

8.2 Cost Behaviour

The basic principle of cost behaviour is that as the level (or volume) of activity rises, costs will usually rise. For good decision-making you must determine in what way costs will rise and by how much. Such knowledge will help in answering the following questions.

• What should our minimum output be for next year?

• What do we need to sell to meet our required profit levels?

• If we reduce our selling prices how will this affect output?

It is normal to simplify cost behaviour by assuming costs are either fixed, variable or semi- variable.

8.2.1 Fixed Costs

Fixed costs are those which are unaffected by increases or decreases in the volume of output, but which remain constant, at least for a specified period of time. Examples of fixed costs include:

• depreciation of machinery

• the salary of the managing director

• the rent and rates of the warehouse building

• leasing costs for the salespeople’s company cars.

Fixed costs can also be shown graphically.

You can see from Figure 8.1 that the total fixed costs are constant for all levels of activity. However, unit fixed costs decrease proportionally with the level of activity. If your factory rent bill is £20,000 and your output is 100 units then each of your units of output has to absorb a £200 share of this fixed cost. However, if you double your output to 200 units then the respective share of fixed costs will halve to £100 per unit (£20,000/200 units).

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Decision-Making − Cost Behaviour

Figure 8.1 Fixed costs

8.2.2 Variable Costs

As their name suggests, variable costs vary in direct proportion to the volume of output. If output doubles then the total variable cost will double. Examples of variable costs could include:

• raw materials

• direct labour

• sales commission.

Variable costs are shown graphically in Figure 8.2.

Figure 8.2 Variable costs

You should note that although total variable costs increase with output, the unit variable cost will remain constant.

8.2.3 Semi-variable Costs

Semi-variable costs are those that include both a fixed and a variable element. Maintenance could be an example of a semi-variable cost to your business because you might carry out planned maintenance regardless of the level of activity (a fixed element) as well as incur maintenance because of the level of activity (the variable element). Other examples might be:

• equipment charges

• power costs

• a telephone bill.

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Semi-variable costs are shown graphically in Figure 8.3.

Figure 8.3 Semi-variable costs

To assist in decision-making you need some means of splitting the semi-variable costs into their respective elements. A common method used is the high-low method, which compares the two extreme points on the range of values, as shown in worked example 8.2.

Worked example 8.2

The total annual costs incurred at various output levels for a department in a company have been measured as follows.

Output Total cost (£s)

1,000 3,000

3,000 8,000

5,000 11,000

7,000 12,000

9,000 12,000

11,000 13,000

The high-low method divides the difference in total cost between the two points by the corresponding difference in output, thereby calculating the variable cost per unit of output.

Variable cost per annum = Change in total cost / Change in output = (£13,000 − £3,000) / (11,000 units − 1,000 units) = £10,000 / 10,000 units = £1 per unit

The fixed cost may now be estimated using either the upper or the lower total cost as the starting point.

Fixed cost per annum = Total cost − (Variable cost per unit × Number of units) = £13,000 − £1 × 11,000 units) = £2,000

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Knowledge of your fixed and variable costs would enable you to plot your total costs graphically (see Figure 8.4).

Figure 8.4 Total costs

8.3 Breakeven Analysis

One of the main reasons for distinguishing between different cost behaviours is to allow managers to estimate the contribution that each unit of output makes towards the com- pany’s fixed costs. This separation of fixed and variable costs helps to provide more relevant information about costs for decision-making.

8.3.1 Contribution

To obtain a contribution per unit for your product, you simply deduct the variable costs per unit from your selling price per unit. The surplus that is (hopefully) left then makes a contribution towards meeting all those fixed costs that you are committed to, regardless of your level of activity. The more units you sell, the greater the total contribution will be, and if total contribution exceeds your fixed costs then you will have made a profit.

Selling price per unit x

less: Variable costs per unit x

equals: Contribution per unit x

Contribution per unit × Number of units = Total contribution Total contribution less fixed costs = Profit

What has been done above is often referred to in textbooks as marginal costing. Marginal costing (sometimes known as CVP analysis) is concerned with the relationship that exists between sales, variable costs, fixed costs, volume and profit.

We saw in Units 2 and 3 how an income statement for financial accounting purposes highlights the costs by function as per the example below.

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Income statement for Braid Ltd

Year ended 31st December 20x8

£000s

Sales 5,000

Cost of sales 3,000

Gross profit 2,000

Selling/distribution costs 800

Administration costs 700

Net profit 500

However, for management accounting purposes, highlighting the costs by their behaviour rather than their function might better show the same information, particularly for decision-making purposes.

Income statement for Braid Ltd

Year ended 31st December 20x8

£000s

Sales 5,000

Variable costs 2,000

Contribution 3,000

Fixed costs 2,500

Net profit 500

If the company only manufactured and sold one product, then knowledge of their sales volume would enable you to calculate the selling price, variable cost and, most importantly, contribution per unit.

If, for example, you knew that Braid Ltd had manufactured and sold 50,000 units then you know that

• the selling price per unit was £100 (£5,000,000/50,000 units)

• the variable cost per unit was £40 (£2,000,000/50,000 units)

• the contribution per unit was £60 (£3,000,000/50,000 units).

Note: The £60 contribution per unit would be a constant figure regardless of the level of activity and is the key determinant of making good business decisions.

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Worked example 8.3

Returning to the golf club dinner we discussed in worked example 8.1:

Selling price per unit £50

Variable costs per unit £30

Contribution per unit £20

Twenty-five people attending the dinner dance multiplied by the £20 contribution per unit gives you a total contribution of £500. Deducting the fixed costs of £500 leaves you with neither a profit nor a loss.

8.3.2 Breakeven Point

Breakeven analysis shows the level of activity at which a company will make neither a profit nor a loss and can be calculated using the following formula.

Breakeven point in units = Fixed costs

Contribution per unit

Therefore, the breakeven number for the golf club dinner needs to be 25 (£500/£20).

You can further expand the use of the mathematical formula above if, in addition to wanting to know your breakeven point, you would like to establish how many units to sell to enable you to achieve some desired profit target.

Units sold for desired target = Fixed costs + Desired profit

Contribution per unit

You can see the formula above being used in worked example 8.4.

Worked example 8.4

The captain of the golf club sees the annual dinner-dance as an opportunity to raise much needed funds for some replacement machinery required by the greenkeeper. He has set you a target of £1,000 profit to be raised. Given all the previously quoted costs and selling prices, how many people do you now need to attend the function?

Solution

To achieve your target will require 75 people to attend the function. The first 25 people will contribute sufficient funds to meet your fixed costs and therefore breakeven. Each additional person will contribute £20 directly to profit. Therefore, 50 people contributing £20 each will give you your profit target of £1,000.

Using the formula above: Fixed costs (£500) + Desired profit (£1,000)

Contribution per unit (£20) = 75 people

It is common to show this information in a graphical form, which gives an immediate visual display of:

• the breakeven point

• how much output needs to be sold to make a profit

• the likelihood of making a loss

• outcomes should the costs or revenues vary.

A typical breakeven graph is shown in Figure 8.5.

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Figure 8.5 Breakeven point

8.4 Decision-Making

When deciding which products are to be marketed, consideration should be given to their comparative contributions. See worked example 8.5.

Worked example 8.5

Smithy plc manufactures three different products, the details of which are as follows.

Products Bee Cee Dee

Details per unit £ £ £

Selling price 100 75 200

less variable costs:

Direct materials 30 15 40

Direct labour 15 20 55

Variable overheads 35 25 75

80 60 170

Contribution per unit 20 15 30

By analysing the information down to the contribution per unit level, you can see that it is in the interests of Smithy plc to sell as many of the Dee product as possible (assuming no capacity constraints exist) because it offers the highest contribution per unit. Their second choice would be Bee, which offers a slightly higher contribution per unit than the final product Cee. But the important thing is that all three products do make a contribution towards covering the fixed costs. If your variable costs per unit exceed your selling price per unit then you have a negative contribution − in other words you are already losing money on the product before you even consider your fixed costs. From a financial viewpoint, there is absolutely no point in manufacturing such a product.

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Also, with this contribution per unit analysis you can fairly easily see the effect on contribution that a change in sales revenue or variable costs would have. For example, if you had to drop the selling price of Dee by £20 then suddenly it would become the least attractive to sell in terms of contribution (which would fall to £10). For another example of this concept, see worked example 8.6.

Worked example 8.6

Cramb Construction Ltd has the capacity to produce 5,000 radios per month but is currently only operating at 60% capacity. Annual fixed costs are £400,000 and the following unit information is available.

Variable overheads £10

Direct material £15

Selling price £50

Direct labour £13

Required

The managing director has asked you as the management accountant to provide the following information, which will be discussed at next week’s board meeting.

a. The current contribution per radio.

b. The annual profit (or loss) at the current level of operation.

c. The level of output at which Cramb Construction will breakeven.

d. Profit at 100% capacity.

e. The quantity needed to sell to retain the profit level in point b) above, if the selling price dropped by 6%, the variable overheads increased by 10% and the fixed costs increased by 15%.

f. Does the answer for e) pose any problems for the company?

Solution

£ £

Selling price 50

less variable costs:

Direct materials 15

Direct labour 13

Variable overheads 10

Contribution per radio 12

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Contribution per radio £12

Sales volume:

5,000 radios × 12 months × 60% 36,000 radios

Total contribution £432,000

less fixed expenditure £400,000

Profit £32,000

Fixed costs Contribution per unit

= £400,000

£12 = 33,334 radios

Contribution per radio £12

Sales volume:

5,000 radios × 12 months 60,000 radios

Total contribution £720,000

less fixed expenditure £400,000

Profit £320,000

£ £

Selling price (£50 − 6% thereof) 47

less variable costs:

Direct materials 15

Direct labour 13

Variable overheads 11

Contribution per radio 8

Fixed costs + Desired profit Contribution per unit

= £460,000 + £32,000

£8 = 61,500 radios

Note that the fixed costs of £460,000 = £400,000 + 15% thereof.

f. The answer to e) poses a capacity problem, because the current manufacturing limit is 5,000 radios per month, which equates to 60,000 per annum.

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8.5 Summary

In this unit, you have studied the basic principles of cost behaviour and seen how an under- standing of the relationship between costs, volume and profit can greatly assist key short-term business planning.

You should now be aware of cost behaviour, which categorises costs as:

• fixed (if the cost is unaffected by movements of output)

• variable (if the cost varies with activity)

• semi-variable (if the costs include a fixed and variable element).

A company with a good knowledge of its cost behaviour has given itself the best opportunity to make the correct business decisions. It will be in a position to calculate some or all of the following:

• contribution per product

• breakeven points

• profit at various capacity levels.

The following questions can all be answered by using the techniques discussed throughout the unit.

• What products should be manufactured, on a financial basis?

• What quantities should be manufactured?

• What product lines should be closed down?

• What selling prices are appropriate?

Application of cost-behaviour analysis and decision-making techniques should ensure that companies stay on track in their quest to meet both their short- and long-term company objectives.