Lecture #4 Cost Behaviour Chapter 10 Presented by Dr Greg Laing Prepared by Simon Lenthen University of Western Sydney

Introduction CVP analysis is concerned with the change in profits in response to changes in sales volumes, costs and prices Helps answer the following questions:- – How many units need to be sold, or services performed, to break even (for example, earn zero profit)? – What is the impact on profit of a change in the mix between fixed and variable costs? – How many units need to be sold, or services performed, to achieve a particular level of profit? – What is the impact on profit of a 15 per cent increase in costs? 2

Cost behaviour Examining cost behaviour enables us to consider – the way in which costs change, and – the main factors that influence those changes Costs can be classified as fixed, variable or mixed The nature of fixed and variable costs relates to whether such costs are likely to alter in total with changes in activity 3

Fixed, variable and mixed costs Fixed costs are those costs which remain the same in total (within a given range of activity and timeframe) irrespective of the level of activity – e.g. lease costs, depreciation charges When we consider levels of activity in terms of units of output: – total fixed costs remain the same, but – fixed costs per unit will decrease as the number of units produced increases 4

Fixed, variable and mixed costs continued 5

Variable costs change in total as the level of activity changes e.g. - costs of bricks to build a house - aviation fuel for Qantas Variable costs can be considered on either a total or unit basis 6

Fixed, variable and mixed costs continued 7

The relevant range is the range of activity over which the cost behaviour is assumed to be valid If the activity level goes outside the relevant range, then the expected behaviour of costs changes can no longer be assumed to be fixed 8

fixed, variable and mixed costs continued Mixed costs occur some costs have both fixed and variable components 9

Break-even analysis Break-even analysis relates to the calculation of the necessary levels of activity required in order to break even in a given period Break-even occurs when total revenue and total costs are equal resulting in zero profit – i.e. when 10 Revenue = FC + VC

Break-even analysis continued Break-even analysis involves the contribution margin concept Contribution margin is calculated by deducting total variable costs from total revenue Contribution margin per unit can be calculated by deducting variable cost per unit from revenue per unit 11 Contribution margin = Revenue – VC

Break-even analysis for a single product or service Example 1 Selling price$25 Purchase price$14 Fixed exhibition and trade show costs$ p.a. Fixed transport costs$ p.a. Variable demonstration costs$1 per unit Administration fixed costs$6 400 p.a. Break-even (in units) 12 FC $ = x break-even (units) CM per unit $

Break-even analysis for a single product or service continued Example 1 13 SP per unit $25 VC per unit Purchase price $14 Demonstration costs 1 15 CM per unit $10 Break-even= FC CM per unit = $( ) $10 = $ $10 = 4500 units

Break-even analysis for a single product or service continued Units to earn a desired profit Example 1 Expected profit (before tax)$ FC + Expected profit = $( ) CM per unit $10 = units FC + Expected profit = x sales units CM per unit

Break-even analysis for a single product or service continued Example 1 VC increased to $17 per unit FC reduced to $ Can also be expressed in an equation format 15 CM= $25 – $17= $8 Break-even= $32 000= 4000 units $8 s ( x ) = vc ( x ) + fc ( for break-even ) s ( x ) = vc ( x ) + fc + p ( for meeting desired profit )

Break-even analysis for a single product or service continued Graphical representation of CVP 16

Break-even analysis for multiple products Example 2 Products B101 C101 D101. Annual volume in units SP per unit $25 $30 $20 VC per unit $15 $22 $15 Annual fixed costs = $ Contribution margin $10 $8 $5 17

Break-even analysis for multiple products continued To calculate sales mix: 18 No. of sales units of product Total no. of sales units of all products For B101: units = units For C101: = For D101: =

Break-even analysis for multiple products continued To calculate weighted average CM (WACM) 19  (units CM x sales mix) For B101:$10 x 0.3= $3.00 For C101: $ 8 x 0.2= $1.60 For D101: $ 5 x 0.5= $2.50 $7.10

Break-even analysis for multiple products continued Example 2 Products B101 C101 D101. CM per unit $10 $8 $5 Sales mix WACM $3.00 $1.60 $2.50 $ Break-even= FC WACM = $ $7.10 = units

Break-even analysis for multiple products continued To determine how many of each product to sell to break-even: 21 B101: x C101: x D101: x BE units x individual sales mix

Break-even analysis for multiple products continued B101 C101 D101 Total 22 Sales volume at break-even Revenue (sales volume x SP)$ $ $ Less VC (sales volume x VC per unit)$ $ $ CM (Revenue – VC)$ $ $ $ Less FC $ Profit $0

Break-even and income taxes To calculate pre-tax profit Example 1 Expected profit (after tax)$ Pre-tax profit = $ (1 – 0.30) = $ Pre-tax profit = After-tax profit (1 – tax rate)

Break-even and income taxes continued Example 3 Average SP per box$ 4.00 Average VC per box Cost of sweets$ 2.00 Selling costs$ 0.40 Annual FC Selling$ Administration$ After-tax profit target$ Tax rate 30% 24

Break-even and income taxes continued To calculate target pre-tax profit (in units): 25 Pre-tax profit target = $ = $ (1 – 0.30) CM= SP of $4 – VC per box of $2.40 = $1.60 Target pre-tax profit= FC + pre-tax profit target CM per box = $ $ $1.60 = boxes

CVP assumptions The behaviour of costs can be classified as fixed or variable Cost behaviour is linear Fixed costs remain ‘fixed’ over the time period and/or a given range of activity (often referred to as the relevant range) Unit price and cost data remain constant over the time period and relevant range For multi-product entities, the sales mix between the products is constant 26

Contribution margin ratio The contribution margin ratio can be express in 2 ways – The percentage by which revenue exceeds VC – The CM expressed as a percentage of revenue 27 Total CM = x % Total sales CM per unit = x % SP per unit

Contribution margin ratio continued Example 1 28 Break-even= $45 000= $ in sales 0.40 CM ratio= $25 – $15= 0.40 or 40% $25 SP = $25 100% 1.00 VC = $15 60% 0.60 CM = $10 40% 0.40

Using break-even data Identifying the number of products or services required to be sold to meet break-even or profit targets Planning products and allocating resources by focusing on those products that contribute more to profitability Determining the impact on profit of changes in the mix of fixed and variable costs Pricing products 29

Margin of safety and operating leverage The margin of safety provides an indication of how much revenue (sales in units) can decrease before reaching the break-even point 30 Margin of safety = actual or estimated – units at break-even in units units of activitypoint Margin of safety = actual or estimated – revenue at break-even revenues revenuepoint

Margin of safety and operating leverage continued Operating leverage is the mix between FC and VC in the cost structure of an entity It provides an understanding of the impact of changes in revenue on profit Greater proportion of FC in a firm  more highly leveraged  more risky because fluctuations in sales  higher fluctuations in profit 31

Margin of safety (example) Modclean uses casual labour to demonstrate their product. – Variable cost $1 per unit Human resource manager proposes to hire a part-time permanent employee – Fixed cost $10,000 If this proposal goes ahead – Variable costs drop by $1.00 – Fixed Costs increase by $10,000 32

Is it worthwhile? – Determine level of sales at which profit would be the same... – $10,000/$1 = 10,000 units – At this point we are indifferent because profit is same. Margin of safety (example, cont) 33 Fixed Costs/Variable costs

Margin of safety (example, cont) Contribution margin under part time employee $25 – 14 = $11 Contribution Margin under casual employee $25 – 15 = $10 Therefore if sales fall below 10,000 units they should use casual labour because profit reduces at a slower rate and if sales rise above 10,000 units they should use part-time labour because profit increases at a faster rate 34

Contribution margin per limiting factor Contribution margin per limiting factor is the contribution margin per unit of limited resource Example 2 Products B101 C101 D101. Budgeted sales next year SP per unit $25 $30 $20 VC per unit $15 $22 $15 CM per unit $10 $8 $5 Labour time per unit 1 hr 4 hrs 1.5 hrs Total labour hrs required hrs hrs hrs 35

Contribution margin per limiting factor continued By summing the required hours, we find that the firm needs a total of hours BUT only hours are available for production Firm wants to know which product it should promote This means we need to determine the most profitable product To do this need to find CM per hour because time is the limiting factor 36

Contribution margin per limiting factor continued B101 C101 D101 CM per unit $10 $8 $5 Labour time per unit 1 hr 4 hrs 1.5 hrs Total labour hrs required hrs hrs hrs CM per hour $10 p.h. $2.00 p.h. $3.33 p.h. This analysis shows that –C101 is most profitable per unit –But B101 will maximise profit by providing more CM per hour (60,000 x $10) 37

May and buy (outsourcing) and special order decision To make sure decisions are based on the right information, the following must be identified where relevant: – Relevant costs and relevant income – Incremental costs and incremental income – Opportunity cost – Avoidable costs and unavoidable costs 38

May and buy (outsourcing) and special order decision continued A make or buy decision requires an entity to choose whether – To make or buy a product or service OR – To outsource the production of that product or service Such a decision will involve both quantitative and qualitative factors 39

May and buy (outsourcing) and special order decision continued A special order is a one-off request from a customer that is different from the orders usually received by the entity The incremental FC must be considered These will be dependant on whether the entity is operating at full capacity, or has idle capacity (or available capacity) 40

Summary CVP analysis is an important part of the planning process and serves as a useful decision-making tool An understanding of fixed, variable and mixed costs is necessary to execute break-even analysis Break-even analysis can be conducted for single-product/service entities and multi- product/service entities 41

Summary continued The concepts of margin of safety and operating leverage provide businesses with useful extensions to the basic CVP analysis and break-even calculations Special attention needs to be given to limited resources Entities use relevant income/costs to analyse make or buy and special order decisions 42

Homework Ch 10: CQ 10.11, EX 10.19, 10.24, Due in Tutorial Next Week. 43