MANAGERIAL ACCOUNTING 3 rd Topic FIXED AND VARIABLE COSTS, COST-VOLUME-PROFIT ANALYSIS
Structureofthelecture3 3.1 Identifying cost behaviour 3.2 CVP terminology 3.3 CVP formulas 3.4 Break-Even Analysis 3.5 Profit-volume chart 3.6 Weakness of break-even analysis 3.7 CVP analysis example(computation, grafical solution)
3.1IdentifyingCostBehaviour Successful management = planning a company s future activities, prediction of: - Volume of the activity - Cost to be incurred - Sales to be made - Profit to be received.
3.1IdentifyingCostBehaviour Cost-volume-profit (CVP) analysis helps predict how changes in costsand sales levels affect income, examines the behaviour of total revenues, total costs, and operating income as changes occur in the output level, selling price, variable costs, or fixed costs. Tool used to help answer managerial questions such: How will revenues and costs be affected - if sale will be increased? - if selling prices will be raised or lowered? - if business will be expanded into overseas markets?
3.2CVP terminology Revenues are inflows of assets received in exchange for products or services provided to customers. Revenue driver Is a factor that affects revenues (e.g. Units of output sold, selling prices, and levels of marketing costs). (Cost driver Any factor that affects cost, change in the cost driver will cause a change in the total cost of a related cost object (e.g. Units of output manufactured, number of sales visits made, and number of packages shipped)). The most detailed way of prediction: multiple revenue drivers and multiple cost drivers (general case) extensive analysis, timeconsuming. Special case of CVP: single revenue driver and single cost driver, is helpful in decisions relating to overall strategies ad long-range plans; widely used.
3.2CVP terminology CVP analysis (special case) is basedon the following assumptions: total costs can be divided into a fixedcomponents and a component that is variablewith respect to the level of output of single product or constant sale mix. The behaviour of total revenues and total costs is linear(straight-line) in relation to output units within the relevant range for short time horizont. Measure of output= number of units manufactured or units sold (e.g. Airlines passenger-miles; automobiles vehicles manufactured; hospitals patient-days; hotels room occupied; universities student credit-hours, )
3.2CVP terminology Fixed costs(fc) Remain unchanged in amount when the volume of activity varies from period to periodwithin a relevant range -fixed cost remains constant (e.g. monthly rent paid for a factory building, property taxes, office salaries, depreciation, service department costs ). While total fixed costdoes not change as the volume of the production changes (increases), the fixed cost per unit of output decreases. If the relevant range changes, the amount of fixed cost will likely change(step-wise costs).
3.2CVP terminology Fixedcosts as to thevolume ofactivity
3.2CVP terminology Fixed costs if relevatnt range changes(step-wise costs)
3.2CVP terminology Variable costs (VC) Changein proportion to changes in volume of activity, total amount of variable cost changes with the level of production. (e.g. Direct material, direct labour, sales commissions, shipping costs, and some overhead costs.) Variable cost per unitremains constant, total amount of variable cost changes with the level of production.
3.2CVP terminology Variable costs as to the volume of activity
3.2CVP terminology Totalcosts(TC) = Fixedcosts(FC) + Variablecosts(VC)
3.2CVP terminology Mixed (semi-variable; semi-fixed) costs Includes both fixed and variable cost components. (salary of sale representatives includes fixed monthly salary and variable commission based on sales). In CVP analysis, mixed costsare often separated into fixed and variable components. Curvilinear (nonlinear) costs Increases at a non-constant rate as volume increases. (total direct labour costswhen workers are paid by the hour)
3.2CVP terminology Curvilinear (nonlinear) costs the shape of the total cost function: initial steep rise, levels off, followed by a further steep rise.
3.2CVP terminology Curvilinear variable cost function
3.3CVP formulasi. Total costs= fixed costs + variable costs TC = VC + FC TC = v u *Q + FC Averageunit cost= totalcost/ quantity c u = TC / Q c u = FC / Q + v u Income = Total revenues (sales) total costs = total revenue variable costs fixed costs I = S TC I = S VC -FC
3.4Break-EvenAnalysis, formulasii. Break-even analysis is a special case of CVP analysis Break-even point (BEP) is the sales level at which a company neither earns a profit nor incurs a loss. It is the moment when sales cover total costs. Sales = fixed costs + variable costs S = FC + VC s u *Q = FC + v u *Q Q BEP = FC / (s u v u )
3.4Break-EvenAnalysis Linear CVP relationships(special case of CVP) 1. Constant variable cost and selling price is assumed. 2. Only one break-even point,and profit increases as volume increases. 3. The diagram is not intended to provide an accurate representation for all levels of output.the objective is to provide an accurate representation of cost and revenue behaviour only within the relevant range of output.
3.4Break-EvenAnalysis Break-even chart (linear CVP)
3.4Break-EvenAnalysis, formulasiii. Contribution margin per unitis the difference between selling price per unit and variable cost per unit. Used for decision on optimal structure of the production. cm u = s u v u then BEP in output units = fixed costsdivided by contribution margin per unit Q BEP = FC / cm u Q BEP = FC / (s u v u ) Total contribution margin: CM = S VC CM = cm u *Q
3.4Break-EvenAnalysis, formulasiv. Contribution margin ratio (contribution to sales; profit-volume ratio) is the proportion of sales available to cover fixed costs and provide for profit, which is defined as contribution margin per unit divided by unit selling price. cmr u = cm u /s u - using either unit or total figures. - Usage: when given estimate of total sales revenue, it is possible to estimate total contribution. BEP in monetary units = fixed costsdivided by contribution margin ratio BEP = FC / cmr u Margin of safety is the amount by which sales may decrease before a loss occurs. MoS= (Expected sales BEP) / Expected sales
3.4Break-EvenAnalysis, formulasv. Quantification of the income I = S VC FC I = s u *Q v u *Q FC I = cm u *Q FC, Also: I = S VC FC I = cmr u *S FC I + FC = cmr u *S and,wheni=0,thenbep=fc/cmr u
3.5Profit-volume charts Profit-volume chart variant of break-even chart, shows the impact on income of changes in the output level. PV chart is obtained by plotting loss or profit against volume of activity. The slope of the graph is equal to the contribution per unit each additional unit sold decreases the loss, or increases the profit. At zero activity there are no contributions, so there will be a loss equal to the total fixed costs.
3.5Profit-volume chart
3.6 Weaknessofbreak-evenanalysis 1. Non-straight-line relationships We assumes strictly straight-line relationships between sales revenues, variable costs and volume of activity what usually is not in real life. 2. Stepped fixed costs Most fixed costs are not fixed over all volumes of activity, they tend to be stepped. 3. Multi-product businesses. We assume effect of additional sales of one product (or service); problem of identifying the fixed costs of one particular activity
3. 7 CVP analysis: non-graphical computations Example 1 Fixed costs per annum 60,000 Unit selling price 20 Unit variable cost 10 Relevant range 4,000 12,000 units Question 1: Break even point? Question 2: How many units to be sold to obtain 30,000 profit? Question 3: How much is total contribution when we estimate total sales 200,000?
3. 7 CVP analysis: non-graphical computations Example 1 Question 1: Break-even point (in units; ) _ Fixed costs = 60,000/ 10 = 6,000 units Contribution per unit 6,000 units * 20 = 120,000 Question 2:Units to be sold to obtain a 30,000 profit: Fixed costs + desired profit = 90,000/ 10 = 9,000 units Contribution per unit Question 3: Total contribution by sales 200,000 Cmr u = cm u /S u = 10 / 20 = 0.5 CM = S * cmr u = 200,000 * 0.5 = 100,000 (I = CM FC = 100,000 60,000 = 40,000; when I = 0, then BEP = FC / cmr u = 60,000 / 0.5 = 120,000)
3. 7 CVP analysis:break-evenchart
3. 7 CVP analysis:contributionchart
3. 7 CVP analysis:profit-volume chart
Break-evenchart forexerise3.1 Decision making: purchase of new machine?
Break-evenchart forexerise3.1 Decision making