Introduction to revenue, cost and profit terms Variable and fixed costs, cost-volume-profit analysis Pia Nylinder Pia.nylinder@lnu.se

Organization of the presentation Variable cost Fixed cost Cost volume profit (CVP) analysis Decision-making Opportunity costs Sunk costs

Variable and fixed costs

Principles of cost division Cost terms and concepts Activity level Variable and fixed costs Cost assignment Direct and indirect costs Decision making Relevant and irrelevant costs Variable and fixed cost can be used in different situations Cost volume profit analysis Budgeting Product costing

Activity level Activity (volume) level = Activity (output) of an organization measured in quantity, time or value Units of production or sales, hours worked, miles traveled Industry Measure of activity Airlines Passenger-kilometers Automobiles Vehicles manufactured Hospitals Patient-days Hotels Rooms occupied Consultancy firm Hours debited Sales company Sales value/Number of customers

Variable costs Variable Cost = A cost that varies in total when the volume of activity changes Linearity of variable costs Nonlinearity of variable costs (two types of nonlinierity)

Linearity of variable costs Linear variable costs = Costs that in total vary in direct proportion to changes in the activity level Total variable cost = Unit variable cost x Activity level Unit variable cost = Total variable cost/Activity level For example: Material cost in a manufacturing company, petrol in a transport company and sales commission in a sales company Total variable cost Cost per unit Activity level Activity level

Nonlinearity of variable costs 1. Nonlinear variable costs = Costs that in total decreases when the activity level increases For example: Discount when purchasing material Total variable cost Cost per unit Activity level Activity level

Nonlinearity of variable costs 2. Nonlinear variable costs = Costs that in total increases when the activity level increases For example: Overtime compensation Total variable cost Cost per unit Activity level Activity level

Fixed costs Fixed costs Step fixed costs (Semi-fixed)

Fixed costs Fixed costs = A cost that remains constant in total when the level of activity changes for a specified time period Unit fixed cost = Total fixed cost/Activity level For example: Supervisors’ salaries, leasing charges for cars, rent for premises Total fixed cost Unit fixed cost Activity level Activity level

Fixed costs Two important assumptions Relevant range Time span An output range of activity level that the firm expects to be operating within period of time Time span A cost is only fixed for a short period of time, for instance a month or a year

Activity level (Volume in Units) Relevant Range 160 000 – 120 000 – 80 000 – 40 000 – Fixed Costs Relevant Range 0 5 000 10 000 15 000 20 000 25 000 Activity level (Volume in Units)

Step fixed costs Step fixed costs = A cost that is fixed within specified activity levels but that eventually increases or decreases by a constant amount at various critical activity levels Unit fixed cost = Total fixed cost/Activity level For example: Supervisors’ salaries, equipment costs, rent for premises Total fixed costs Unit fixed costs Activity level Activity level

Mixed costs (Semi-variable costs) Mixed costs = A cost that include both a fixed and a variable component. Fixed cost that remains constant and variable cost when the activity level changes Unit variable and fixed costs = Total variable and fixed costs/Activity level For example: Electric utility charge (fixed service fee and variable charge per kilowatt hour used), car rental cost, commission cost Total cost Unit cost Total variable cost Total fixed cost Activity level Activity level

What happen when the volume increase (decrease)? To conclude… What happen when the volume increase (decrease)? Total cost Cost per unit Fixed costs Unchanged Decreases (increases) Variable costs Increase (decreases) Unchanged BRYGGA: Vad gör verksamhetsvolymen? Driver rörliga och därmed totala kostnader.

Cost volume profit (CVP) relationship

CVP-relationship Examines what will happen to the financial results if a specific level of activity fluctuates Study interrelationships of prices activity levels (volumes) fixed and variable costs profits Vital information in decisions about e.g. price, market mix and product mix Very simple and usable method

CVP-relationship Sensitivity analysis Sensitivity analysis is a “what-if” technique that examines how a result will change if the original predicted data are not achieved or if an underlying assumption changes A CVP-analysis can answer a lot of questions What will happen to operating income if volume declines by 5%? What will happen to operating income if variable costs increase by 10% per unit? What operating income is expected when sales are 10 000 units? Suppose that fixed costs increased by $30,000. What are the new fixed costs? What is the new breakeven point?

CVP – Different approaches Two main approaches to CVP-analysis: Total revenue function Contribution function Both approaches can be performed with: Equation method Graph method

Total revenue function Unit selling price x Units sold = Total revenue Costs Unit variable cost x Units sold = Total variable costs Total variable cost + Total fixed costs = Total costs Result Total revenue – Total costs = Operating profit Total revenue – Total variable costs – Total fixed costs = Operating profit Unit selling price x Units sold - Unit variable cost x Units sold - Fixed costs = Operating profit

Total revenue function Kr Total revenue Total cost Profit Variable costs Loss Fixed costs Units sold

Total revenue function – Break- even point The break-even point states in units sold and total sales where the profit is equal to zero Total revenue – Total variable costs – Fixed costs = zero operating profit Kr Break-even point in revenue (sales) Total revenue Break-even point Total cost Variable costs Fixed costs Break-even point in units Units sold

Total revenue function – Safety of margin Indicates by how much sales may decrease before a loss occurs Can be expressed in actual units and actual sales Margin of safety percentage

Total revenue function – Break- even point The break-even point states in units sold and total sales where the profit is equal to zero Total revenue – Total variable costs – Fixed costs = 0 kr Kr Break-even point in revenue (sales) Total revenue Total cost Margin of safety Variable costs Fixed costs Margin of safety Break-even point in units Units sold

Total revenue function – Break- even point The break-even point states in units sold and total sales where the profit is equal to zero Total revenue – Total variable costs – Fixed costs = 0 kr Kr Break-even point in revenue (sales) Total revenue Total cost Margin of safety Fixed costs Variable costs Margin of safety Break-even point in units Units sold

Total revenue function – Safety of margin Units Actual units - break-even units Total sales Actual total sales - break-even sales Percentage (Actual units – Break-even units)/Actual units (Actual total sales – break-even sales)/Actual sales

CVP-relationship - Assumptions Important assumptions of CVP-analysis Change in costs varies in relation to one cost driver, i.e. activity level (sales volume) Revenue per unit remains constant Variable costs per unit remain constant Total fixed costs remain constant Costs can be divided in variable and fixed categories Sales volume = Production volume The behavior of total revenues and total costs is linear in relation to output units within the relevant range Note: CVP-analysis can be used in companies with multiple products Unit contribution margin is replaced with contribution margin for a composite unit A composite unit is composed of specific numbers of each product in proportion to the product sales mix Sales mix is the ratio of the volumes of the various products

Cost volume profit analysis – Example A company has recently developed a new product. The new product is a book about management accounting and it will revolutionize the area. It contains new terms and concepts. The company is particularly interested in adopting the cost volume profit approach to decision-making. The accountant at the company has prepared the following information about price, costs and volume for one year: Price per unit $40 Variable cost per unit $20 Fixed costs $600 000 Sales volume 40 000 units

Cost volume profit analysis – Example What will the operating profit be if 40 000 units are sold? What will the operating profit be if the company spends an additional $100 000 on a marketing campaign. They assume that the campaign will increase the sales volume with 10 000 units. If the company desire a profit of $300 000, how many units would have to be sold? Determine the annual break-even point in units. Suppose that the variable cost increases by 10 %. Compute the new break-even point. Determine the margin of safety in units at a sales volume of 40 000 units.

Cost volume profit analysis – Example Sales volume Units 20 000 30 000 40 000 50 000 Sales price per unit $ 40 40 40 40 Variable cost per unit $ 20 20 20 20 Fixed cost per unit $ 30 20 15 12 Total cost per unit $ 50 40 35 32 Total revenue $ 800 000 1 200 000 1 600 000 2 000 000 Total variable costs $ -400 000 -600 000 -800 000 -1 000 000 Total fixed costs $ -600 000 -600 000 -600 000 -600 000 Operating profit $ -200 000 0 200 000 400 000 (Total costs 1 000 000 1 200 000 1 400 000 1 600 000)

CVP-graph - Exemple Kr 1 600 000 kr 1 400 000 kr 30 000 * 40 = Number of units sold 30 000 40 000 Margin of safety = 40 000 – 30 000 = 10 000 units

Contribution & Contribution per unit Sales – variable costs= contribution Revenue Unit selling price x Units sold = Total revenue Costs Unit variable cost x Units sold = Total variable costs Contribution Total revenue – Total variable costs= Total contribution Unit selling price x Units sold - Unit variable cost x Units sold = Total contribution Unit selling price - Unit variable cost = Contribution per unit

Break-even, margin of safety and analysis Break-even is where; Total revenue = Total costs Break even point (in units) = Fixed costs Contribution per unit Break even point (in sales value)= Break-even point (in units) * selling price per unit

Break-even Analysis Fixed Costs = 50,000 Skr Price per unit = 5 Skr Variable Cost = 3 Skr Contribution = Breakeven Volume = Breakeven Skr = Break-even point (in units) = Fixed costs Contribution Break-even point (in sales) = Break-even point (in units) x Selling price per unit

Break-even Analysis Fixed Costs = 50,000 Skr Price per unit = 5 Skr Variable Cost = 3 Skr Contribution = Breakeven Volume = Breakeven Skr = Break-even point (in units) = Fixed costs Contribution Break-even point (in sales) = Break-even point (in units) x Selling price per unit

Relevant costs for decision-making are: Future expenditures unique to the decision alternatives under consideration. Expected to occur in the future Differ among marketing alternatives being considered In general, opportunity costs are considered relevant costs

Sunk costs for decision-making are: The direct opposite of relevant costs. Past expenditures for a given activity Typically irrelevant in whole or in part to future decisions Examples of sunk costs: Past marketing research and development expenditures Last year’s advertising expense

When opportunity costs are relevant, an example: The oportunity cost represent ”by the forgone potential benefit from the best rejected cource of action” + Selling price Variable cost Opportunity cost = Operational profit or loss Sid 178

Limiting factors Avalable capacity Limited capacity

Decision-making when there is avalable capacity Golvad AB incoming orders are decreasing. One day however, they get a offer from a man who want their help to instal hardwoodfloor in his house. The most he can pay is 7000 SKr (excluding VAT) for the work, including material, labor and travelexpeses. Should Golvad AB accept the offer? Costing (Golvad´s own calculation) +Labor (350 Skr * 10 h) 35oo Skr +Material cost 5000 Skr +Travelling costs 300 Skr +Profit margin 15% * 3 500 Skr 525 Skr Priduction cost 9 325 Skr

Decision-making when there is avalable capacity Golvad AB incoming orders are decreasing. One day however, they get a offer from a man who want their help to instal hardwoodfloor in his house. The most he can pay is 7000 SKr (excluding VAT) for the work, including material, labor and travelexpeses. Should Golvad AB accept the offer? Costing (Golvad´s own calculation) +Labor (350 Skr * 10 h) 35oo Skr +Material cost 5000 Skr +Travelling costs 300 Skr +Profit margin 15% * 3 500 Skr 525 Skr Priduction cost 9 325 Skr

Decision-making when there is limited capacity In a company is labour the limiting factor. The company have tro decide of they should concentrate their producton on product A or B. Contribution per unit A is 1200 SKr and for B 1500 Skr. The number of labour hours used for A is 30 minutes and for B 40 minutes. Which product should the company concentrate the production on in order to maximise their profit?

Decision-making when there is limited capacity In a company is labour the limiting factor. The company have tro decide of they should concentrate their producton on product A or B. Contribution per unit A is 1200 SKr and for B 1500 Skr. The number of labour hours used for A is 30 minutes and for B 40 minutes. Which product should the company concentrate the production on in order to maximise their profit?

Decision-making when there is limited capacity In a company is labour the limiting factor. The company have tro decide of they should concentrate their producton on product A or B. Contribution per unit A is 1200 SKr and for B 1500 Skr. The number of labour hours used for A is 30 minutes and for B 40 minutes. Which product should the company concentrate the production on in order to maximise their profit? Product A Product B The company should choose to procuce A. The contribution comes out ahead because it produces the highes contribution per scarce labour resourses.

Limiting factors (cont.) We continue with the company in the last example. We know the contribution per limiting factor (labour hours). In order to count the total contribution we need to know how many units which can be produced. Suppose the capacity is 4000 labour hours = 240 000 minutes (4000 hours * 60 minutes). The maximum products of A that can be produced is 240 000 minutes / 30 minutes per unit = 8000 units. Product B can produce 240 000 minutes/40 minutes per unit = 6 000 units. Which product gives the best profit? The total contribution is counted as: Product A 1200 SKr * 8000 units = 9600 000 SKr Product B 1500 SKr * 6000 units = 9 000 000 Skr The calculation shows that we should choose product A because it gives the best profit.