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## Lecture #4 Cost Behaviour Chapter 10

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**Lecture #4**Cost Behaviour Chapter 10 Presented by Dr Greg Laing http://www.youtube.com/watch?v=DaavRAV8a0A Prepared by Simon LenthenUniversity 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?**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 totalwith changes in activity**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**Fixed, variable and mixed costs continued**• 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**Fixed, variable and mixed costs continued**• 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**fixed, variable and mixed costs continued**• Mixed costs occur some costs have both fixed and variable components**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 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 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 $28 000 p.a. Fixed transport costs $10 600 p.a. Variable demonstration costs $1 per unit Administration fixed costs $6 400 p.a. • Break-even (in units) FC $ = x break-even (units) CM per unit $**Break-even analysis for a single product or service**continued • SP per unit $25 • VC per unit • Purchase price $14 • Demonstration costs 115 • CM per unit $10 Example 1 • Break-even = FC CM per unit • = $(28 000 + 10 600 + 6 400) $10 • = $45 000 $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) $50 000 FC + Expected profit = x sales units CM per unit FC + Expected profit = $(45 000 + 50 000) CM per unit $10 = 9 500 units**Break-even analysis for a single product or service**continued Example 1 VC increased to $17 per unit FC reduced to $32 000 • Can also be expressed in an equation format • 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**Break-even analysis for multiple products**Example 2 Products B101 C101 D101 . Annual volume in units 60 000 40 000 100 000 SP per unit $25 $30 $20 VC per unit $15 $22 $15 Annual fixed costs = $355 000 Contribution margin $10 $8 $5**Break-even analysis for multiple products continued**• To calculate sales mix: No. of sales units of product Total no. of sales units of all products For B101: 60 000 units = 0.3 200 000 units For C101: 40 000 = 0.2 200 000 For D101: 100 000 = 0.5 200 000**Break-even analysis for multiple products continued**• To calculate weighted average CM (WACM) (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 0.3 0.2 0.5 WACM $3.00 $1.60 $2.50 $7.10 Break-even = FC WACM = $355 000 $7.10 = 50 000 units**Break-even analysis for multiple products continued**• To determine how many of each product to sell to break-even: BE units x individual sales mix B101: 50 000 x 0.3 15 000 C101: 50 000 x 0.2 10 000 D101: 50 000 x 0.5 25 000 50 000**Break-even analysis for multiple products continued**B101 C101 D101 Total Sales volume at break-even 15 000 10 000 25 000 Revenue (sales volume x SP) $375 000 $300 000 $500 000 Less VC (sales volume x VC per unit) $225 000 $220 000 $375 000 CM (Revenue – VC) $150 000 $ 80 000 $125 000 $355 000 Less FC $355 000 Profit $0**Break-even and income taxes**• To calculate pre-tax profit Example 1 Expected profit (after tax) $50 000 Pre-tax profit = After-tax profit (1 – tax rate) Pre-tax profit = $50 000 (1 – 0.30) = $71 428**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 $160 000 Administration $280 000 After-tax profit target $100 400 Tax rate 30%**Break-even and income taxes continued**• To calculate target pre-tax profit (in units): Pre-tax profit target = $100 400 = $143 428 (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 = $440 000 + $143 428 $1.60 = 364 642 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**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 CM per unit = x % SP per unit Total CM = x % Total sales**Contribution margin ratio continued**Example 1 • CM ratio = $25 – $15 = 0.40 or 40% $25 • SP = $25 100% 1.00 • VC = $15 60% 0.60 • CM = $10 40% 0.40 • Break-even = $45 000 = $112 500 in sales 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**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 Margin of safety = actual or estimated – units at break-even in units units of activity point Margin of safety = actual or estimated – revenue at break-even revenues revenue point**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 becausefluctuations in sales higher fluctuations in profit**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**Margin of safety (example, cont)**• 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. • 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**Contribution margin per limiting factor**• Contribution margin per limiting factor is the contribution margin per unit of limited resource Example 2Products B101 C101 D101 . Budgeted sales next year 60 000 40 000 100 000 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 60 000 hrs 160 000 hrs 150 000 hrs**Contribution margin per limiting factor continued**• By summing the required hours, we find that the firm needs a total of 370 000 hours • BUT only 250 000 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**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 60 000 hrs 160 000 hrs 150 000 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)**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 andrelevant income • Incremental costs and incremental income • Opportunity cost • Avoidable costs andunavoidable costs**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**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)**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**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**Homework**Ch 10: CQ 10.11, 10.12 EX 10.19, 10.24, 10.32 Due in Tutorial Next Week.