Cost and cost behaviour L2 Student Slides PDF

Learning area 3 Chapter 3: Cost behaviour: Analysis and Use Specific Outcomes: After studying this learning area, you should be able to: 1. Explain the effect of a change in activity on both total variable costs & per unit variable costs. 2. Explain the effect of a change in activity on both tot...

Learning area 3 Chapter 3: Cost behaviour: Analysis and Use Specific Outcomes: After studying this learning area, you should be able to: 1. Explain the effect of a change in activity on both total variable costs & per unit variable costs. 2. Explain the effect of a change in activity on both total fixed costs & fixed costs expressed on a per unit basis. 3. Use a cost formula to predict costs at a new level of activity. 4. Analyse a mixed cost using the high-low method. 5. Explain the least-squares regression method of analysing a mixed cost. 6. Prepare an income statement using the contribution format. Types of Cost behaviour Patterns Recall the summary of our cost behaviour discussion from Chapter 2.  Activity Base To plan and control variable costs, a manager must be well acquainted with various activity bases within the firm. An activity base is a measure of whatever causes the incurrence of variable cost—also referred to as a cost driver. Some cost drivers are direct labour hours, machine hours, units produced or sold.  The Activity Base Units Machine produced hours A measure of the event causing the incurrence of a variable cost – a cost driver Kilometers Labour driven hours  Cost Behaviour Examples of normally variable costs Merchandisers Service Organisations Cost of Goods Sold Supplies and travel Manufacturers Merchandisers and Direct Material, Direct Manufacturers labour, and Variable Sales commissions and Manufacturing Overhead shipping costs Examples of normally fixed costs Merchandisers, manufacturers, and service organisations Real estate taxes, Insurance, Sales salaries Depreciation, Advertising  Total Variable Cost Example Your total potato cost is based on how many packets of chips are made Total Potato Cost Number of chips packets  Variable Cost Per Unit Example The cost per packet of chips is constant. For example, R2 per packet. Cost per packet Potatos used  Direct materials is a true or proportionately variable cost because the amount used during a period will vary in direct proportion to the level of True production activity. variable costs Moreover, any amounts purchased but not used can be stored and carried forward to the next period as inventory.  Step variable costs Step variable costs are a type of cost in business that change with production volume but in a more segmented manner than variable costs. Unlike variable costs, which change in direct proportion to the level of production, step variable costs remain fixed within certain ranges of production output but jump to a higher level when production exceeds certain thresholds.  Step variable costs cont… Fixed within Range: Within a certain range of production levels, step variable costs stay constant. For example, if you need one supervisor for every 10 employees, and you have between 1 and 10 employees, the cost for that supervisor is fixed. If you hire more than 10 employees, you’ll need another supervisor, which increases the cost in a step-like fashion.  Discrete Jumps: The cost increases in discrete steps rather than continuously. So, instead of a gradual increase with every additional unit produced, the cost remains steady within certain production Step ranges and jumps up when moving to a new range. variable costs Common examples include the costs of additional supervisory staff, equipment, cont… or facilities.  A factory operates efficiently with one set of machinery, producing up to 10,000 units per month at a cost of $50,000. However, if production exceeds 10,000 units, the factory Step needs to invest in additional machinery. variable Production between 10,001 and cost… 15,000 units per month, the factory invests an additional $30,000 in machinery, raising the total cost to $80,000.  For production between 15,001 and 20,000 units per month, another investment of $40,000 is required, increasing the total cost to $120,000. Step variable Understanding step variable cost… costs is crucial for budgeting and financial planning, as it helps in predicting how costs will behave as production levels change.  Step-Variable Costs Total cost remains constant within a narrow range of activity. Cost Volume  Step-Variable Costs Total cost increases to a new higher cost for the next higher range of activity. Cost Volume  Purpose: establish if there is a relationship between two variables. Specifically, establish if there is a Linear statistically significant relationship between the two concept Examples: Income and spending, wage and gender, student height and exam scores, election results and unemployment.  Linearity concept A linear relationship is one where the relationship between two variables can be described by a straight line on a graph, indicating a constant rate of change and proportional effects. The graph of a linear relationship is a straight line. If the relationship is positive, the line slopes upwards from left to right. If the relationship is negative, the line slopes downwards.  Hours Studied and Exam Scores Positive Description: Generally, as the number of hours a student studies increases, their exam relationship scores tend to increase as well. Example: If a student studies for 2 hours, they might score 70% on an exam. If they study for 5 hours, their score might rise to 85%. The more they study, the higher their score tends to be.  Air Temperature and Heating Costs Negative Description: As the air temperature increases, the cost of heating a home generally decreases. relationship Example: If the outside temperature is 0°C, heating costs might be £150 per month. If the temperature rises to 10°C, heating costs might drop to £90 per month. As the temperature goes up, the expense for heating the home decreases.  Finance: Linear relationships are used in financial models to predict costs, revenues, and other metrics where the relationship between Linear variables is proportional. concept cont… Economics: Linear models help in understanding and forecasting economic relationships like supply and demand.  The linearity assumption is a fundamental concept in finance and economics. It assumes that relationships Linearity between variables are linear, meaning they can be represented Assumption as straight lines on a graph. Commonly used in financial modelling and forecasting.  In dealing with variable costs, we have assumed a strictly linear relationship between cost and Linearity volume. concept and Although many costs are not strictly relevant linear when plotted as a function of volume, a curvilinear cost can be range satisfactorily approximated with a straight line within a narrow band known as “relevant range.”  The Linearity Assumption and the Relevant Range Economist’s Curvilinear Cost Function Total Cost Volume  Importance of Linearity Simplifies complex relationships between variables. Linearity Makes it easier to use Assumption mathematical tools for analysis. Helps in predicting future values and understanding trends.  The relevant range is that range of activity within which the assumptions made about cost behaviour are valid. Relevant range is the span of values The over which the linearity assumption Relevant holds true. Range Outside this range, relationships may no longer be linear. Concept Crucial for accurate financial forecasting and budgeting.  Example: Cost behaviour analysis in a company. Linearity and Fixed costs are constant within a relevant range. Relevant Range Variable costs change linearly with production levels within that range.  The Linearity Assumption and the Relevant Range Economist’s Curvilinear Cost Function Total Cost Accountant’s Straight-Line Approximation (constant unit variable cost) Volume  The Linearity Assumption and the Relevant Range The straight Economist’s line closely Curvilinear Cost approximates Function the curvilinear variable cost Relevant line. However, only within the Total Cost Range relevant range. Accountant’s Straight-Line Approximation (constant unit variable cost) Volume  Budgeting and Forecasting: Accurate predictions within the relevant range. Investment Analysis: Financial Assessing risk and returns Applications based on linear assumptions. Valuation Models: Simplifying complex financial models.  Total Fixed Cost Example Your monthly factory rent probably does not change when you make more chips. Number of Packet of Chips Number of Packet of Chips  Fixed Cost Per Unit Example The average cost per packet of chips decreases as more chips are made. Monthly Basic Factory Rent per chips packet Number of Chips packets  Types of Fixed Costs Fixed Costs Committed Discretionary Long-term, cannot be May be altered in the reduced in the short short-term by current term. managerial decisions Examples Examples Depreciation on Advertising and Buildings and Research and Equipment Development  Trend Toward Fixed Costs Increased automation. Increase in salaried knowledge workers who are difficult to train and replace. Implications Managers are more ‘locked-in’ with fewer decision alternatives. Planning becomes more crucial because fixed costs are difficult to change with current operating decisions.  Fixed Costs and Relevant Range Example: Office space is available at a rental rate of £30,000 per year in increments of 1,000 square metres. As the business grows more space is rented, increasing the total cost. Continue  Fixed Costs and Relevant Range 90 Thousands of pounds Total cost doesn’t Relevant change for a wide Rent Cost in 60 range of activity, Range and then jumps to a new higher cost for 30 the next higher range of activity. 00 1,000 2,000 3,000 Rented Area (Square metres)  Fixed Costs and Relevant Range Step-variable costs can be adjusted more How does this type quickly and... of fixed cost differ The width of the from a step-variable activity steps is much cost? wider for the fixed cost.  Labour cost may be fixed or variable Is It depends on labour contracts, Labour regulations and custom Variable In some countries it is fixed while or Fixed in others there is much greater latitude Cost? It is generally agreed that, until otherwise stated, direct labour is regarded as a variable cost  Mixed Costs A mixed cost has both fixed and variable components. Consider the following electric utility example. Total Utility Cost Mixed Costs Variable Utility Charge Fixed Monthly Utility Charge Activity (Kilowatt Hours)  Mixed Costs The total mixed cost line can be expressed as an equation: Y = a + bX Where: Y = the total mixed cost a = the total fixed cost (the vertical intercept of the line) b = the variable cost per unit of Total Utility Cost activity (the slope of the line) X = the level of activity Variable Utility Charge Fixed Monthly Utility Charge Activity (Kilowatt Hours) Total Utility Cost Mixed Costs Variable bX Utility Charge Fixed Monthly a Utility Charge Activity (Kilowatt Hours) The Analysis of Mixed Costs Account Analysis Engineering Approach High-Low Method Scattergraph Method Least-Square Regression Method  The High-Low Method WiseCo recorded the following production activity and maintenance costs for two months: Units Cost High activity level 9,000 £ 9,700 Low activity level 5,000 6,100 Change 4,000 £ 3,600 Using these two levels of activity, compute:  the variable cost per unit;  the fixed cost; and then  express the costs in equation form Y = a + bX.  The High-Low Method Units Cost High activity level 9,000 £ 9,700 Low activity level 5,000 6,100 Change 4,000 £ 3,600 Changein cost  Unit variable cost = Change in units  The High-Low Method Units Cost High activity level 9,000 £ 9,700 Low activity level 5,000 6,100 Change 4,000 £ 3,600  Unit variable cost = £3,600 ÷ 4,000 units = £0.90 per unit  The High-Low Method Units Cost High activity level 9,000 £ 9,700 Low activity level 5,000 6,100 Change 4,000 £ 3,600 1. Unit variable cost = £3,600 ÷ 4,000 units = £0.90 per unit 2. Fixed cost = Total cost – Total variable cost Fixed cost = £9,700 – (£0.90 per unit × 9,000 units) Fixed cost = £9,700 – £8,100 = £1,600  The High-Low Method Units Cost High activity level 9,000 £ 9,700 Low activity level 5,000 6,100 Change 4,000 £ 3,600 1. Unit variable cost = £3,600 ÷ 4,000 units = £0.90 per unit 2. Fixed cost = Total cost – Total variable cost Fixed cost = £9,700 – (£0.90 per unit × 9,000 units) Fixed cost = £9,700 – £8,100 = £1,600 3. Total cost = Fixed cost + Variable cost (Y = a + bX) Y = £1,600 + £0.90X  The High-Low Method If sales salaries and commissions are £10,000 when 80,000 units are sold and £14,000 when 120,000 units are sold, what is the variable portion of sales salaries and commission? a. £0.08 per unit b. £0.10 per unit c. £0.12 per unit d. £0.125 per unit  The High-Low Method If sales salaries and commissions are £10,000 when 80,000 units are sold and £14,000 when 120,000 units are sold, what is the variable portion of sales salaries and commission? a. £0.08 per unit Units Cost b. £0.10 per unit High level 120,000 £ 14,000 c. £0.12 per unit Low level 80,000 10,000 Change 40,000 £ 4,000 d. £0.125 per unit £4,000 ÷ 40,000 units = £0.10 per unit  The High-Low Method If sales salaries and commissions are £10,000 when 80,000 units are sold and £14,000 when 120,000 units are sold, what is the fixed portion of sales salaries and commissions? a. £ 2,000 b. £ 4,000 c. £10,000 d. £12,000  The High-Low Method If sales salaries and commissions are £10,000 when 80,000 units are sold and £14,000 when 120,000 units are sold, what is the fixed portion of sales salaries and commissions? a. £ 2,000 Total cost = Total fixed cost + Total variable cost b. £ 4,000 £ 14,000 = Total fixed cost + c. £10,000 (£0.10 × 120,000 units) d. £12,000 Total fixed cost = £14,000 - £12,000 Total fixed cost = £ 2,000  Least-Squares Regression Method Accountants and managers may use computer software to fit a regression line through the data points. The cost analysis objective is the same: Y = a + bx Least-squares regression also provides a statistic, called the adjusted R2, that is a measure of the goodness of fit of the regression line to the data points. Least-Squares Regression Method Least-Squares Regression Method The adjusted R2 is the percentage of the variation in total cost explained by variation in the activity. Y 20 * ** * * * ** Total Cost 10 * * 2 R for this relationship is near 100% since the data points are very close to the regression line. 0 X 0 1 2 3 4 Activity  In some situations, there may be more than one causal factor driving the variable cost element. Multiple Regression Multiple regression is an Analysis analytical method that is used when the dependent variable (i.e., cost) is caused by more than one factor. The Contribution Format Let’s put our knowledge of cost behaviour to work by preparing a contribution format profit statement.  The traditional approach to the profit and loss statement is organized in A New a ‘functional’ format. Statement of Profit Internally, the manager or Loss needs cost data organized Format in a format that will facilitate planning, control and decision making.  The Contribution Format The contribution margin format emphasises cost behaviour. Contribution margin covers fixed costs and provides for profit.  The Contribution Format Used primarily for Used primarily by external reporting. management.