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COST VOLUME PROFIT Richard E. McDermott Ph.D. Costs Volume Profit In this chapter we study what happens to both cost and profit as volume changes. The tools we will use will be helpful in the development of flexible budgets. I am going to begin by giving you some basic definitions. I will then give you what I feel are the best formulas to use in working the problems you will be assigned. Definitions Variable Costs: Costs that vary in total, directly and proportionately, with changes in production (also called activity level). If the activity level increases by 50%, variable costs increase by 50%. Examples of Variable Costs Direct labor Direct materials Variable overhead Definitions Mixed Costs: costs that contain both a fixed and a variable element. Mixed cost change in total, but not proportionately, with changes in the activity level. An example of a mixed cost might be maintenance cost on a taxi. Maintenance costs increase as miles increase. Even if the truck is never driven, however, it is a good idea to change the oil every three months to keep it from degenerating. Separating Fixed and Variable Costs If you will look at a general ledger, you will never find accounts labeled ―variable labor‖ or ―fixed labor‖ or ―variable overhead‖ or ―fixed overhead.‖ In order to perform cost volume profit analysis, therefore, it is usually necessary to separate fixed and variable costs. There are three methods to do this: Scatter graph method The best method is the least High-low method squares method, but since Least squares method the author does not teach it we will not cover it either. Definitions Fixed Costs: Costs that do not change with increases or decreases in production volume. It is important to add, there is usually a relevant range. For example, a plant may be built to manufacture 1 to 10,000 shoes per month. Fixed costs would not change within this ―relevant range.‖ If a company wanted to manufacture 12,000 shoes per month, however, there of course would be a new relevant range and the fixed costs might increase. Examples of Fixed Costs Rent on a factory Depreciation – straight-line method Heating and air-conditioning expense Housekeeping It is important to emphasize that what might be a fixed cost in one factory, could be a variable cost in another, depending upon the way the firm does business. Other Definitions Contribution Margin: Revenue (or unit price) minus total variable costs (or unit variable costs). Example: Contribution Margin Income Statement Note that contribution Sales $100,000 margin is what Less variable costs 60,000 is left after Contribution margin $40,000 paying Less fixed costs 30,000 variable costs. Income from $10,000 operations Other Definitions Contribution Margin Income Statement After fixed costs are paid, Sales $100,000 where does the Less variable costs 60,000 contribution Contribution margin $40,000 margin go? To Less fixed costs 30,000 the bottom line! Income from $10,000 operations Notation I will use the following notation when referring to contribution margin: CMu = contribution margin per unit of produce, calculated as follows: Price – Variable Cost Per Unit = Cmu. CMt = contribution margin total calculated as follows: Total Sales – Total Variable Costs = CMt CMr = contribution margin ratio calculated as follows: CMt/Total Sales or CMu/Price. Tip for Examination In any problem where the only change is volume (i.e. variable costs per unit, and fixed costs do not change), then the impact of the change on operating income can be calculated simply by calculating the change in total contribution margin. The change in total contribution margin will equal the change in operating income. We will illustrate this in a moment. Here Are Some Formulas I Would like You to Learn PX – VX – F = P where P = unit price X = volume of units sold V = variable cost per unit F = total fixed price P = operating income or profit Breakeven Breakeven is defined as the point where the firm neither makes nor loses money. The formula for breakeven is: PX – VX – F = 0 Let us illustrate the solution for breakeven with an example. Example Morris Electronics makes calculators. The market dictates a price of $30 for a model with their particular features. Variable costs per unit are $16, total fixed costs are $200,000. What is the breakeven point in units for sales of the calculators? Solution PX - VX – F = 0 Income statement 30X – 16X – 200,000 Sales $428,571 =0 Variable cost 228,571 14X = 200,000 Contribution $200,000 margin X = 14,285.714286 Fixed cost 200,000 calculators Operating $0 income Note that at breakeven, contribution margin equals fixed costs. New Problem Most companies are not in the business to breakeven. Assume that Morris Electronics wants to make $50,000. How many calculators will they have to sell to achieve that objective? We are solving for ―target sales‖ Solution PX - VX – F = P 30X – 16X – 200,000 = 50,000 14X = 250,000 X = 17,857.14285 calculators What if we want to know the sales dollar volume to break even? 17,857.14285 x 30 = $535,714 Deriving an Alternate Formula PX – VX – F = P Simplifying the equation X(P – V) – F = P But we know that price per units minus variable cost per unit equals the contribution margin Since (P – V) = CMu (CMu)(X) = F + P X = (F + P)/CMu when we want to know target sales in units for a specific level of profits If we are solving for target sales at breakeven, P = 0 so X = F/CMu Formulas for target sales with a profit and no profit (breakeven) Example Problem Let us use the same data from Morris Electronics, where the company wants to earn a $50,000 profit. X = (F + P)/CMu X = (200,000 + 50,000)/14 X = 250,000/14 X = 17,857.142858 units breakeven Or Sale at breakeven = 17,857.142858 x 30 = $535,714 Now Finding Breakeven Sales Dollar Volume We can either multiply 17,857.142858 times the sales price of $30, or use this formula S = (F + P)/CMr where S = sales dollars, CMr stands for contribution margin ratio, and the contribution margin ratio is defined thus: CMr = Total Contribution Margin/Sales Or CMr = Unit Contribution Margin/Price CMr in this problem is 14/30 = .466667 So sales in dollars = (200,000 + 50,000)/.466667 = $535,714 Therefore the Formula For Breakeven Would Be: S = (F + P)/CMr Or S = (F + 0)/CMr Or S = F/CMr Two formulas to get the same answers! To get breakeven in dollars use F/CMr where CMr is the contribution margin ration (contribution margin divided by sales). Let Us Solve Another Problem Assume that Morris Electronics can only manufacture 15,000 units a year. The variable cost is $16 per unit, and fixed costs are $200,000 per year. Assuming that they want to earn $50,000 per year, what must the price be to obtain their net profit objective? Solution PX – VX – F = P(15,000) – 16(15,000) – 200,000 = 50,000 15,000P – 240,000 – 200,000 = 50,000 15,000P = 490,000 P = $32.6667 To check: $490,000 – 240,000 – 200,000 = $50,000 Alternate Formulas We could have used: X = (F + )/CMu to solve for breakeven in units where of course is 0 Or S = (F + )/CMr to solve for breakeven in sales dollars to get the same results (again at breakeven is 0). In this case, S is of course sales dollars. Income Statements Traditional income statement CVP Income Statement Sales $xxx Sales $xxx Cost of Goods Sold xxx Variable Costs xxx Gross Margin xxx Contribution Margin xxx Administrative and xxx Fixed Costs xxx Selling Expense Income xx Income xx A better income statement to use for internal reporting, especially when management wants to do CVP analysis, is the CVP income statement shown above. Income Statements It is better, because it gives us the figures needed for CVP analysis. FASB still requires the traditional income statement for external reporting, however. One More Concept . . . Margin of Safety: The difference between actual or expected sales and sales at the break even point. The formula is: Actual (expected) sales – breakeven sales = margin of safety in dollars. Problem Johnson Foundry currently sells $1,500,000 of product a year. Their breakeven point is $1,250,000. What is their margin of safety? $1,500,000 – $1,250,000 = $250,000 Separating Fixed and Variable Costs One method (a very inaccurate method) of separating fixed and variable costs is the high-low method. The method is inaccurate because it depends upon only two data points, a high and low point. The small sample size, plus the fact that high and/or low points are often outliers caused by inaccurate readings make it inadvisable to use in the real world. Nevertheless, since the book teaches it, so will I (sigh). Steps Use the following formula to determine variable costs. (high costs low costs) variable costs per unit (high activity low activity ) Steps Calculate total variable cost and total costs at high or low activity. Subtract total variable costs from total costs (at high or low activity) to determine total fixed costs. Example Community Hospital’s controller has provided you with the following information. Using the high-low method, divide payroll into fixed and variable costs. Chest Labor X-rays Dollars January 1,200 16,400 February 1,400 18,800 High March 900 12,800 April 875 12,500 Low May 1,300 17,600 June 1,350 18,200 Solution 1. Calculate variable costs using this formula. (high costs low costs) variable costs per unit high activity low activity $18,800 $12,500 $12 / xray 1, 400 875 Solution 2. Calculate variable costs at high or low (we will use high here). $12 variable cost per x-ray x 875 x-rays = $10,500 3. Subtract variable costs at high or low (we will use low here) from total costs to get fixed costs. $12,500 total costs – 10,500 variable costs = $2,000 fixed costs Summary: variable costs = $12 per unit and fixed costs = $2,000 per period (per month in this case) Question Given this data what would be the total cost at 1,145 x-rays? Variable costs = $12 x 1,145 = $13,740 Fixed costs = $2,000 Total costs at 1,145 x-rays = $15,740 The best method, the least squares method can be worked using Excel or a financial calculator. If you want to learn how to do it on a financial calculator, look in the hp 10bII instruction book under ―regression). Brief Exercise 5-1 Monthly costs for two levels of production are given below. From this information determine which costs are variable, fixed, and mixed, and give the reason for each answer. Cost 3000 units 6000 units Indirect labor $10,000 $20,000 Supervisory salaries $5,000 $5,000 Maintenance 4,000 7,000 Brief Exercise 5-1 Cost 3000 units 6000 units Indirect labor $10,000 $20,000 Supervisory salaries $5,000 $5,000 Maintenance 4,000 7,000 Indirect labor is obviously variable, as it varies proportionally with volume. When volume doubles, costs double. Brief Exercise 5-1 Cost 3000 units 6000 units Indirect labor $10,000 $20,000 Supervisory salaries $5,000 $5,000 Maintenance 4,000 7,000 Supervisory salaries are obviously fixed, since they stay the same At different levels of production. Brief Exercise 5-1 Cost 3000 units 6000 units Indirect labor $10,000 $20,000 Supervisory salaries $5,000 $5,000 Maintenance 4,000 7,000 Maintenance salaries are mixed, since they increase, but not proportional to increase in production volume. Brief Exercise 5-2 For Loder Company, the relevant range of production is 40% to 80% of capacity. At 40% of capacity, variable cost is $4000 and fixed cost $6,000. Diagram the behavior of each costs within the relevant range assuming the behavior is linear. Brief Exercise 5-2 To create these graphs I used Excel. Brief Exercise 5-3 For Hunt Company, a mixed cost is $20,000 plus $16 per direct labor hour. Diagram the behavior of the cost using increments of 500 hours up to 2,500 hours on the horizontal access, and increments of $20,000 up to $80,000 on the vertical axis Note to students: I think the question would have been clearer if the author had said “fixed cost is $20,000 plus $16 per direct labor hour.” Brief Exercise 5-3 Exercise 5-2 Kozy Enterprises is considering manufacturing a new product. It projects the costs of direct materials and rents for a range of output as shown on the following slide. Output in Units Rent Expense Direct Materials 1000 5000 4000 2000 5000 6000 3000 5000 7800 4000 7000 8000 5000 7000 10,000 6000 7000 12,000 7000 7000 14,000 8000 7000 16,000 9000 7000 18,000 10,000 10,000 23,000 11,000 10,000 28,000 12,000 10,000 36,000 Exercise 5-2 Relevant Range Exercise 5-2 Relevant Range Exercise 5-2 The relevant range is 4,000 – 9,000 units of output since a straight-line relationship exists for both direct materials and rent within this range. Exercise 5-4 Identify each of the following costs as variable, fixed, or mixed. Wood used in production of furniture—variable Fuel used in delivery trucks– variable Straight-line depreciation on factory buildings– fixed Screws used in production of furniture– variable Sales staff salaries– fixed Sales commissions– variable Property taxes– fixed Exercise 5-4 Insurance on buildings– fixed Hourly wages of furniture craftsman– fixed Salaries of factory supervisor– fixed Utilities expense– mixed Telephone bill– mixed Brief Exercise 5-8 Larisa Company has a unit selling price of $520, variable costs per unit of $286, and fixed cost of $187,200. Compute the breakeven in units using the mathematical equation and contribution margin per unit. Mathematical Equation PX – VX – F = 520X – 286X – 187,200 = 0 234X = 187,200 X = 800 Contribution Margin Per Unit Breakeven = F/CMu 187,200/(520 – 286) 187,200/234 X = 800 units Brief Exercise 5-9 Turgro Corp. had total variable cost of $180,000 total fixed costs of $160,000, and total revenues of $300,000. Compute the required sales in dollars to break even. Brief Exercise 5-9 We know that at breakeven, fixed costs = contribution margin. Since fixed costs are $160,000 then the contribution margin must be $160,000 We know that CMr is CMt/Sales (CMt = total contribution margin from income statement) From the data given in the problem we know the CMr is (300,000 – 180,000)/300,000 = 40% So when CMt is $160,000, then sales must be $160,000/.40 = $400,000 Brief Exercise 5-10 For MeriDen Company, variable costs are 60% of sales and fixed costs are $195,000. Management’s net income goal is $75,000. Compute the required sales in dollars needed to achieve management’s target net income if $75,000. Use the contribution margin approach. Brief Exercise 5-10 S (target sales) = (F + )/CMr S = (195,000 + 75,000)/.40 How did I get .40 for CMr? One trick to remember is that contribution margin ratio is (1 – variable expense ratio) Thus CMr is 1 - .60 = .40 S = $270,000/.40 S = $675,000 Exercise 5-8 Green with Envy provides environmentally friendly lawn services for homeowners. Its operating costs are as follows: Depreciation = $1,500/month Advertising = $200/month Insurance = $2,000/month Weed and feed materials = $13/lawn Direct labor = $12/lawn Fuel = $2/lawn Compute breakeven in units and dollars. Exercise 5-8 Fixed costs are $1,500 + $200 + $2,000 = $3,700 per month Variable costs are $13 + $12 + $2 = $27 per lawn PX - VX - F = 0 60X – 27X – 3,700 = 0 33X = 112.12 lawns Breakeven sales dollars = 112.12 x 60 = $6,727.27 Exercise 5-10 (Not assigned) During the month of March, New Day Spa services 570 clients at an average price of $120. During the month, fixed costs were $21,000 and variable costs were 65% of sales. What was the contribution margin . . . Indollars Per unit And as a ratio? Contribution Margin In dollars . . . Sales (570 x $120) $68,400 Variable costs (.65 x $68,400) 44,460 Contribution margin $23,940 Per unit . . . $23,940/570= $42 As a ratio . . . 42/120 = .35 Breakeven Point Breakeven in $ = F/CMr Breakeven in $ = $21,000/.35 = $60,000 Breakeven in Units = F/CMu Breakeven in Units = $21,000/$42 Breakeven in Units = 500 Exercise 5-14 Lynn Company had $150,000 of net income in 2008 when selling price per unit was $150. Variable costs were $90. Fixed costs were $570,000. Management expects per-unit data and total fixed cost to remain the same in 2009. Management is under pressure to increase net income by $60,000 in 2009. Exercise 5-14 Compute the number of units sold in 2008 PX – VX – F = P 150X – 90X – 570,000 = 150,000 60X = 720,000 X = 12,000 units Exercise 5-14 Question: How many units would have had to have been sold in 2009 to reach the stockholder’s desired profit level? Target sales in units = P PX – VX – F = P 150X – 90X - $570,000 = ($150,000 + $60,000) 60X = $570,000 + $150,000 + $60,000 60X = $780,000 X = 13,000 units Exercise 5-14 Assume Lynn Company sells he same number of units in 2009 as it did in 2008. What would the selling price have to be in order to reach the stockholder’s desired profit level? PX – VX – F = P 12,000P – (90)(12,000) – 570,000 = 210,000 12,000P = 1,860,000 P = $155 The End!

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