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Cost-Volume-Profit Relationships EMBA 5403 Fall 2010 Cost Estimation 1 Constant Std Err of Y Est R squared No. of Observations Degrees of Freedom X Coefficient(s) Std Err of Coef. Fall 2010 EMBA 5403 250 299.304749934466 0.944300518134715 5 3 6.75 0.9464847243 2/109 Estimation (continued) The results gives rise to the following equation: Utility Costs = £250 + (£6.75 x # of units produced) R2 = .944, or 94.4 percent of the variation in setup costs is explained by the number of setup hours variable. Fall 2010 EMBA 5403 3/109 Estimation (continued) Given: *T-value for sample size of 5 at 95% confidence level is 3.182 (two-tale test and 3 degrees of freedom) *Standard error of estimate for this sample at the 95% confidence level is 598.6 The confidence interval for 300 units is: TC = £250 + 6.75 (300) + (3.182 x £598.6) = £2275 + £1911 Fall 2010 EMBA 5403 4/109 Cost Estimation Example 2 In each month, Exclusive Billiards produces between 4 to 10 pool tables. The plant operates on 40-hr shift to produce up to seven tables. Producing more than seven tables requires the craftsmen to work overtime. Overtime work is paid at a higher hourly wage. The plant can add overtime hours and produce up to 10 tables per month. The following table contains the total cost of producing between 4 and 10 pool tables. Required: a. compute average cost per pool table for 4 to 10 tables Estimate fixed costs per month. Pool Tables Total Cost 4 62800 5 66000 6 69200 7 72400 8 75800 9 79200 10 82600 Fall 2010 EMBA 5403 5/109 Cost-Volume-Profit Analysis Examines the behavior of total revenues, total costs, and operating income as changes occur in the output level, selling price, variable costs or fixed costs helpful to understand the relationship among variable costs, fixed costs and profit Assumptions of CVP Analysis 1. revenues change in relation to production and sales 2. costs can be divided in variable and fixed categories and fixed element constant over the relevant range 3. revenues and costs behave in a linear fashion 4. costs and prices are known 5. if more than one product exists, the sales mix is constant 6. inventories stay at the same level 7. we can ignore the time value of money Fall 2010 EMBA 5403 6/109 Page 67 Contribution Margin Contribution margin is equal to the difference between total revenue and total variable costs Contribution margin per unit = Selling price - Variable cost per unit Contribution margin percentage = Contribution margin per unit / selling price per unit Per Unit Revenue Variable costs Contribution margin Fall 2010 EMBA 5403 $200 120 $80 Total for 2 units $400 240 $160 % 100% 60% 40% 7/109 Pages 68 - 69 Contribution Margin Income Statement Income statement that groups line items by cost behaviour to highlight the contribution margin 0 Revenue Packages Sold 1 2 25 40 $0 $200 $400$5,000 $8,000 Variable costs 0 120 240 3,000 4,800 Contribution margin 0 80 160 2,000 3,200 2,000 2,000 2,000 2,000 2,000 Fixed costs Operating income$(2,000)$(1,920)$(1,840) $0 $1,200 Fall 2010 EMBA 5403 8/109 Page 69 Breakeven Point Quantity of output where total revenues equal total costs Point where operating income equals zero Breakeven point in units = Fixed costs / Contribution margin per unit = $2,000 / $80 = 25 units Breakeven point in dollars = Fixed costs / contribution margin % = $2,000 / 40% = $5,000 Fall 2010 EMBA 5403 9/109 Page 71 Cost-Volume-Profit Graph $10,000 Total revenues line Breakeven Point 25 units $8,000 Total costs line $6,000 Operating income $4,000 $2,000 Operating loss $0 0 10 20 30 40 50 Units Sold Fall 2010 EMBA 5403 10/109 Page 72 Target Operating Income For most firms in the private sector, the main objective is not to breakeven Convert after-tax desired net income to its before-tax equivalent operating income Target operating income = Target net income / (1 - tax rate) Target Unit Sales = (Fixed costs + Target operating income) / Contribution margin per unit Target Dollar Sales = (Fixed costs + Target operating income) / Contribution margin % Fall 2010 EMBA 5403 11/109 Pages 73 - 75 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 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? sensitivity analysis broadens management’s perspectives about possible outcomes Fall 2010 EMBA 5403 12/109 Pages 76 - 77 Alternative Cost Structures CVP helps managers assess the risks and potential benefits of adopting alternative cost structures Example: Alternative rental arrangements Option 2 $1,400 Fixed Fee + 5% Commission Option 1 $2,000 Fixed Fee Rev $ Rev $ Cost Units Breakeven = 25 units Fall 2010 EMBA 5403 Option 3 20% Commission Rev $ Cost Cost Units Units Breakeven = 20 units Breakeven = 0 units 13/109 Pages 77 - 78 Basics of Cost-Volume-Profit Analysis Fall 2010 EMBA 5403 CM is used first to cover fixed expenses. Any remaining CM contributes to net operating income. 14/109 The Contribution Approach Sales, variable expenses, and contribution margin can also be expressed on a per unit basis. If Racing sells an additional bicycle, $200 additional CM will be generated to cover fixed expenses and profit. Fall 2010 EMBA 5403 15/109 The Contribution Approach Each month Racing must generate at least $80,000 in total CM to break even. Fall 2010 EMBA 5403 16/109 The Contribution Approach If Racing sells 400 units in a month, it will be operating at the break-even point. Fall 2010 EMBA 5403 17/109 The Contribution Approach If Racing sells one more bike (401 bikes), net operating income will increase by $200. Fall 2010 EMBA 5403 18/109 The Contribution Approach We do not need to prepare an income statement to estimate profits at a particular sales volume. Simply multiply the number of units sold above break-even by the contribution margin per unit. If Racing sells 430 bikes, its net income will be $6,000. Fall 2010 EMBA 5403 19/109 CVP Relationships in Graphic Form The relationship among revenue, cost, profit and volume can be expressed graphically by preparing a CVP graph. Racing developed contribution margin income statements at 300, 400, and 500 units sold. We will use this information to prepare the CVP graph. Income 300 units Sales $ 150,000 Less: variable expenses 90,000 Contribution margin $ 60,000 Less: fixed expenses 80,000 Net operating income $ (20,000) Fall 2010 EMBA 5403 Income 400 units $ 200,000 120,000 $ 80,000 80,000 $ - Income 500 units $ 250,000 150,000 $ 100,000 80,000 $ 20,000 20/109 CVP Graph 450.000 400.000 350.000 300.000 250.000 In a CVP graph, unit volume is usually represented on the horizontal (X) axis and dollars on the vertical (Y) axis. 200.000 150.000 100.000 50.000 - 100 200 300 400 500 600 700 800 Units Fall 2010 EMBA 5403 21/109 CVP Graph 450.000 400.000 350.000 300.000 250.000 200.000 Fixed Expenses 150.000 100.000 50.000 - 100 200 300 400 500 600 700 800 Units Fall 2010 EMBA 5403 22/109 CVP Graph 450.000 400.000 350.000 300.000 250.000 Total Expenses 200.000 Fixed Expenses 150.000 100.000 50.000 - 100 200 300 400 500 600 700 800 Units Fall 2010 EMBA 5403 23/109 CVP Graph 450.000 400.000 Total Sales 350.000 300.000 250.000 Total Expenses 200.000 Fixed Expenses 150.000 100.000 50.000 - 100 200 300 400 500 600 700 800 Units Fall 2010 EMBA 5403 24/109 CVP Graph 450.000 Break-even point (400 units or $200,000 in sales) 400.000 350.000 300.000 250.000 200.000 150.000 100.000 50.000 - 100 200 300 400 500 600 700 800 Units Fall 2010 EMBA 5403 25/109 Contribution Margin Ratio The contribution margin ratio is: CM Ratio = Total CM Total sales For Racing Bicycle Company the ratio is: $80,000 = 40% $200,000 Each $1.00 increase in sales results in a total contribution margin increase of 40¢. Fall 2010 EMBA 5403 26/109 Contribution Margin Ratio Or, in terms of units, the contribution margin ratio is: CM Ratio = Unit CM Unit selling price For Racing Bicycle Company the ratio is: $200 = 40% $500 Fall 2010 EMBA 5403 27/109 Contribution Margin Ratio 400 Bikes Sales $ 200,000 Less: variable expenses 120,000 Contribution margin 80,000 Less: fixed expenses 80,000 Net operating income $ - 500 Bikes $ 250,000 150,000 100,000 80,000 $ 20,000 A $50,000 increase in sales revenue results in a $20,000 increase in CM. ($50,000 × 40% = $20,000) Fall 2010 EMBA 5403 28/109 CONTRIBUTION MARGIN RATIO CMR= CONTRIBUTION MARGIN RATIO = CM / SALES OR cmu/p VCR = VARIABLE COST RATIO = VC/SALES OR vcu/p CMR +VCR= 1 EFFECT OF CHANGE IN FIXED COSTS? EFFECT OF CHANGE IN VARIABLE COSTS? EFFECT OF CHANGE IN SELLING PRICE? Fall 2010 EMBA 5403 29/109 Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the CM Ratio for Coffee Klatch? a. 1.319 b. 0.758 c. 0.242 d. 4.139 Fall 2010 EMBA 5403 30/109 Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the CM Ratio for Coffee Klatch? a. 1.319 b. 0.758 Unit contribution margin CM Ratio = Unit selling price c. 0.242 d. 4.139 ($1.49-$0.36) = = Fall 2010 EMBA 5403 $1.49 $1.13 = 0.758 $1.49 31/109 Changes in Fixed Costs and Sales Volume What is the profit impact if Racing can increase unit sales from 500 to 540 by increasing the monthly advertising budget by $10,000? Fall 2010 EMBA 5403 32/109 Changes in Fixed Costs and Sales $80,000 + $10,000 advertising = $90,000 Volume Sales increased by $20,000, but net operating Fall 2010 33/109 income decreased by $2,000. EMBA 5403 Changes in Fixed Costs and Sales Volume The Shortcut Solution Increase in CM (40 units X $200) Increase in advertising expenses Decrease in net operating income Fall 2010 EMBA 5403 $ 8,000 10,000 $ (2,000) 34/109 Change in Variable Costs and Sales Volume What is the profit impact if Racing can use higher quality raw materials, thus increasing variable costs per unit by $10, to generate an increase in unit sales from 500 to 580? Fall 2010 EMBA 5403 35/109 Change in Variable Costs and Sales Volume 580 units × $310 variable cost/unit = $179,800 Sales increase by $40,000, and net operating income Fall 2010 36/109 increases by $10,200. EMBA 5403 Change in Fixed Cost, Sales Price and Volume What is the profit impact if Racing (1) cuts its selling price $20 per unit, (2) increases its advertising budget by $15,000 per month, and (3) increases unit sales from 500 to 650 units per month? Fall 2010 EMBA 5403 37/109 Change in Fixed Cost, Sales Price and Volume Sales increase by $62,000, fixed costs increase by $15,000, and net operating income increases by $2,000. Fall 2010 38/109 EMBA 5403 Change in Variable Cost, Fixed Cost and Sales Volume What is the profit impact if Racing (1) pays a $15 sales commission per bike sold instead of paying salespersons flat salaries that currently total $6,000 per month, and (2) increases unit sales from 500 to 575 bikes? Fall 2010 EMBA 5403 39/109 Change in Variable Cost, Fixed Cost and Sales Volume Sales increase by $37,500, variable costs increase by $31,125, but fixed expenses decrease by $6,000.40/109 Fall 2010 EMBA 5403 Change in Regular Sales Price If Racing has an opportunity to sell 150 bikes to a wholesaler without disturbing sales to other customers or fixed expenses, what price would it quote to the wholesaler if it wants to increase monthly profits by $3,000? Fall 2010 EMBA 5403 41/109 Change in Regular Sales Price $ 3,000 ÷ 150 bikes = Variable cost per bike = Selling price required = $ 20 per bike 300 per bike $ 320 per bike 150 bikes × $320 per bike = $ 48,000 Total variable costs = 45,000 Increase in net income = $ 3,000 Fall 2010 EMBA 5403 42/109 Break-Even Analysis Break-even analysis can be approached in two ways: 1.Equation method 2.Contribution margin method Fall 2010 EMBA 5403 43/109 Equation Method Profits = (Sales – Variable expenses) – Fixed expenses OR Sales = Variable expenses + Fixed expenses + Profits At the break-even point profits equal zero Fall 2010 EMBA 5403 44/109 Break-Even Analysis Here is the information from Racing Bicycle Company: Total Sales (500 bikes) $ 250,000 Less: variable expenses 150,000 Contribution margin $ 100,000 Less: fixed expenses 80,000 Net operating income $ 20,000 Fall 2010 EMBA 5403 Per Unit $ 500 300 $ 200 Percent 100% 60% 40% 45/109 Equation Method We calculate the break-even point as follows: Sales = Variable expenses + Fixed expenses + Profits $500Q = $300Q + $80,000 + $0 Where: Q = Number of bikes sold $500 = Unit selling price $300 = Unit variable expense $80,000 = Total fixed expense Fall 2010 EMBA 5403 46/109 Equation Method We calculate the break-even point as follows: Sales = Variable expenses + Fixed expenses + Profits $500Q = $300Q + $80,000 + $0 $200Q = $80,000 Q = $80,000 ÷ $200 per bike Q = 400 bikes Fall 2010 EMBA 5403 47/109 Equation Method The equation can be modified to calculate the break-even point in sales dollars. Sales = Variable expenses + Fixed expenses + Profits X = 0.60X + $80,000 + $0 Where: X = Total sales dollars 0.60 = Variable expenses as a % of sales $80,000 = Total fixed expenses Fall 2010 EMBA 5403 48/109 Equation Method The equation can be modified to calculate the break-even point in sales dollars. Sales = Variable expenses + Fixed expenses + Profits X = 0.60X + $80,000 + $0 0.40X = $80,000 X = $80,000 ÷ 0.40 X = $200,000 Fall 2010 EMBA 5403 49/109 Contribution Margin Method The contribution margin method has two key equations. Break-even point = in units sold Break-even point in total sales dollars = Fall 2010 EMBA 5403 Fixed expenses Unit contribution margin Fixed expenses CM ratio 50/109 Contribution Margin Method Let’s use the contribution margin method to calculate the break-even point in total sales dollars at Racing. Break-even point in total sales dollars = Fixed expenses CM ratio $80,000 = $200,000 break-even sales 40% Fall 2010 EMBA 5403 51/109 Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the break-even sales in units? a. 872 cups b. 3,611 cups c. 1,200 cups d. 1,150 cups Fall 2010 52/109 EMBA 5403 Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the break-even sales in Fixed expenses Break-even Unit CM units? = $1,300 a. 872 cups = $1.49/cup - $0.36/cup b. 3,611 cups $1,300 = $1.13/cup c. 1,200 cups = 1,150 cups d. 1,150 cups Fall 2010 53/109 EMBA 5403 Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the break-even sales in dollars? a. $1,300 b. $1,715 c. $1,788 d. $3,129 Fall 2010 54/109 EMBA 5403 Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the break-even sales in dollars? Fixed expenses Break-even = a. $1,300 CM Ratio sales $1,300 b. $1,715 = 0.758 c. $1,788 = $1,715 d. $3,129 Fall 2010 55/109 EMBA 5403 DERIVATION OF EQUATIONS SALES= VARIABLE COSTS+FIXED COSTS + PROFIT p*q= vcu *q + FC + ¶ AT BREAKEVEN PROFIT = 0 p*q=vcu *q +FC q * (p-vcu) = FC q= FC / (p - vcu) OR q=FC/ cmu CM= SALES - TOTAL VC VC= SALES - CM= INCLUDE VARIABLE PRODUCTION AND SELLING EXPENSES cmu=CONTRIBUTION MARGIN PER UNIT= p - vcu=CM/q vcu= VARIABLE COST PER UNIT= VC/ q q number of units Fall 2010 EMBA 5403 56/109 PROFIT ANALYSIS AT BREAKEVEN PROFIT = 0 BEFORE BREAKEVEN LOSS; AFTER BREAKEVEN PROFIT CM COVERS FIXED COST UPTO BREAKEVEN POINT AFTER BREAKEVEN POINT INCREASE IN CM WILL INCREASE NET INCOME CM = FC + INCOME BEFORE TAX Fall 2010 EMBA 5403 57/109 Target Profit Analysis The equation and contribution margin methods can be used to determine the sales volume needed to achieve a target profit. Suppose Racing Bicycle Company wants to know how many bikes must be sold to earn a profit of $100,000. Fall 2010 EMBA 5403 58/109 The CVP Equation Method Sales = Variable expenses + Fixed expenses + Profits $500Q = $300Q + $80,000 + $100,000 $200Q = $180,000 Q = 900 bikes Fall 2010 EMBA 5403 59/109 The Contribution Margin Approach The contribution margin method can be used to determine that 900 bikes must be sold to earn the target profit of $100,000. Unit sales to attain = the target profit Fixed expenses + Target profit Unit contribution margin $80,000 + $100,000 = 900 bikes $200/bike Fall 2010 EMBA 5403 60/109 Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. How many cups of coffee would have to be sold to attain target profits of $2,500 per month? a. 3,363 cups b. 2,212 cups c. 1,150 cups d. 4,200 cups Fall 2010 61/109 EMBA 5403 Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. How many cups of coffee would have to be sold to attain target profits of $2,500 per month? a. 3,363 cups b. 2,212 cups c. 1,150 cups d. 4,200 cups Fall 2010 62/109 EMBA 5403 Unit breakeven Unit sales Fixed expenses + Target profit to attain = Unit CM target profit $1,300 + $2,500 = $1.49 - $0.36 = $3,800 $1.13 = 3,363 cups Fall 2010 EMBA 5403 63/109 The Margin of Safety The margin of safety is the excess of budgeted (or actual) sales over the break-even volume of sales. Margin of safety = Total sales - Break-even sales Let’s look at Racing Bicycle Company and determine the margin of safety. Fall 2010 EMBA 5403 64/109 The Margin of Safety If we assume that Racing Bicycle Company has actual sales of $250,000, given that we have already determined the break-even sales to be $200,000, the margin of safety is $50,000 as shown Break-even sales 400 units Sales $ 200,000 Less: variable expenses 120,000 Contribution margin 80,000 Less: fixed expenses 80,000 Net operating income $ Fall 2010 EMBA 5403 Actual sales 500 units $ 250,000 150,000 100,000 80,000 $ 20,000 65/109 The Margin of Safety The margin of safety can be expressed as 20% of sales. ($50,000 ÷ $250,000) Break-even sales 400 units Sales $ 200,000 Less: variable expenses 120,000 Contribution margin 80,000 Less: fixed expenses 80,000 Net operating income $ Fall 2010 EMBA 5403 Actual sales 500 units $ 250,000 150,000 100,000 80,000 $ 20,000 66/109 The Margin of Safety The margin of safety can be expressed in terms of the number of units sold. The margin of safety at Racing is $50,000, and each bike sells for $500. Margin of $50,000 = = 100 bikes Safety in units $500 Fall 2010 EMBA 5403 67/109 MARGIN OF SAFETY EXCESS OF SALES (EITHER ACTUAL OR FORECASTED ) OVER THE BREAKEVEN SALES I.E., THE BUFFER AMOUNT MoS $= ACTUAL OR BUDGETED SALES - BREAKEVEN SALES $ MoS % = MoS $ / ACTUAL OR BUDGETED SALES BREAKEVEN SALES IN SINGLE PRODUCT SETTING SALES $ = VC$ + FC$ WHERE VCR= x% *SALES THEN 1-x% = CMR SALES $ = x% *SALES +FC (1-x)* SALES $ = FC THAT IS CMR*SALES = FC SALES $ AT BREAKEVEN = FC/ CMR Fall 2010 EMBA 5403 68/109 Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the margin of safety? a. 3,250 cups b. 950 cups c. 1,150 cups d. 2,100 cups Fall 2010 EMBA 5403 69/109 Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the margin of safety? a. 3,250 cups b. 950 cups c. 1,150 cups d. 2,100 cups Fall 2010 EMBA 5403 70/109 Margin of Safety Margin of safety = Total sales – Break-even sales = 2,100 cups – 1,150 cups = 950 cups or 950 cups Margin of safety = 2,100 cups = 45% percentage Fall 2010 EMBA 5403 71/109 Cost Structure and Profit Stability Cost structure refers to the relative proportion of fixed and variable costs in an organization. Managers often have some latitude in determining their organization’s cost structure. Fall 2010 EMBA 5403 72/109 Cost Structure and Profit Stability There are advantages and disadvantages to high fixed cost (or low variable cost) and low fixed cost (or high variable cost) structures. An advantage of a high fixed cost structure is that income will be higher in good years compared to companies A disadvantage of a high fixed with lower proportion of cost structure is that income fixed costs. will be lower in bad years compared to companies with lower proportion of Fall 2010 73/109 fixed costs. EMBA 5403 Operating Leverage A measure of how sensitive net operating income is to percentage changes in sales. Degree of Contribution margin = operating leverage Net operating income Fall 2010 EMBA 5403 74/109 Operating Leverage At Racing, the degree of operating leverage is 5. Actual sales 500 Bikes Sales $ 250,000 Less: variable expenses 150,000 Contribution margin 100,000 Less: fixed expenses 80,000 Net income $ 20,000 Fall 2010 EMBA 5403 $100,000 = 5 $20,000 75/109 Operating Leverage With an operating leverage of 5, if Racing increases its sales by 10%, net operating income would increase by 50%. Percent increase in sales Degree of operating leverage Percent increase in profits × 10% 5 50% Here’s the verification! Fall 2010 EMBA 5403 76/109 Operating Leverage Actual sales (500) Sales $ 250,000 Less variable expenses 150,000 Contribution margin 100,000 Less fixed expenses 80,000 Net operating income $ 20,000 Increased sales (550) $ 275,000 165,000 110,000 80,000 $ 30,000 10% increase in sales from $250,000 to $275,000 . . . Fall 2010 EMBA 5403 . . . results in a 50% increase in 77/109 income from $20,000 to $30,000. Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the operating leverage? a. 2.21 b. 0.45 c. 0.34 d. 2.92 Fall 2010 EMBA 5403 78/109 Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the operating leverage? a. 2.21 b. 0.45 Operating Contribution margin c. 0.34 leverage = Net operating income d. 2.92 $2,373 = $1,073 = 2.21 Fall 2010 EMBA 5403 79/109 Con’t Actual sales 2,100 cups Sales $ 3,129 Less: Variable expenses 756 Contribution margin 2,373 Less: Fixed expenses 1,300 Net operating income $ 1,073 Fall 2010 EMBA 5403 80/109 Quick Check At Coffee Klatch the average selling price of a cup of coffee is $1.49, the average variable expense per cup is $0.36, and the average fixed expense per month is $1,300. 2,100 cups are sold each month on average. If sales increase by 20%, by how much should net operating income increase? a. 30.0% b. 20.0% c. 22.1% d. 44.2% Fall 2010 EMBA 5403 81/109 Quick Check At Coffee Klatch the average selling price of a cup of coffee is $1.49, the average variable expense per cup is $0.36, and the average fixed expense per month is $1,300. 2,100 cups are sold each month on average. If sales increase by 20%, by how much should net operating income increase? a. 30.0% Percent increase in sales 20.0% b. 20.0% × Degree of operating leverage 2.21 c. 22.1% Percent increase in profit 44.20% d. 44.2% Fall 2010 EMBA 5403 82/109 Cost Structure and Operating Leverage Operating leverage is greatest in companies that have a high proportion of fixed costs in relation to variable costs. Sales Variable Expense CM Fixed Expenses Net Income Operating Leverage Factor Fall 2010 EMBA 5403 Company A $ 500.000 300.000 200.000 150.000 $ 50.000 Company B $ 500.000 50.000 450.000 400.000 $ 50.000 200.000 50.000 4 450.000 50.000 9 83/109 Operating Leverage Factor A measure of how a percentage change in sales will affect profits. Operating leverage factor = Contribution margin Net income The greater the operating leverage, the greater the sensitivity of its profit to changes in volume. Fall 2010 EMBA 5403 84/109 Operating Leverage Factor If Company A and B increases its sales by 10%, which company will have the greatest change in net income and why? Fall 2010 EMBA 5403 85/109 COST STRUCTURE AND PROFITABILITY HIGH VARIABLE COSTS LEAD TO LOWER CM AND LESS VULNERABLE IN CRISIS TIME HIGH FIXED COSTS CAUSE HIGHER BREAKEVEN POINT; AFTER THE BREAKEVEN POINT PROFITS INCREASE FASTER THAN THE HIGH VARIABLE COST COMPANY DEGREE OF OPERATING LEVERAGE: CONTRIBUTION MARGIN / NET INCOME FOR A GIVEN % CHANGE IN SALES, INCOME WILL INCREASE BY (% INCREASE IN SALES *DEGREE OF OPERATING LEVERAGE) DEGREE OF OPERATING LEVERAGE DECREASES AS THE SALES MOVE AWAY FROM THE BREAKEVEN POINT IF VARIABLE COSTS ARE HIGH DEGREE OF OPERATING LEVERAGE LOW; AND VICE VERSA Fall 2010 EMBA 5403 86/109 Verify Increase in Profit Actual sales 2,100 cups Sales $ 3,129 Less: Variable expenses 756 Contribution margin 2,373 Less: Fixed expenses 1,300 Net operating income $ 1,073 % change in sales % change in net operating income Fall 2010 EMBA 5403 Increased sales 2,520 cups $ 3,755 907 2,848 1,300 $ 1,548 20.0% 44.2% 87/109 Structuring Sales Commissions Companies generally compensate salespeople by paying them either a commission based on sales or a salary plus a sales commission. Commissions based on sales dollars can lead to lower profits in a company. Let’s look at an example. Fall 2010 EMBA 5403 88/109 Structuring Sales Commissions Pipeline Unlimited produces two types of surfboards, the XR7 and the Turbo. The XR7 sells for $100 and generates a contribution margin per unit of $25. The Turbo sells for $150 and earns a contribution margin per unit of $18. The sales force at Pipeline Unlimited is compensated based on sales commissions. Fall 2010 EMBA 5403 89/109 Structuring Sales Commissions If you were on the sales force at Pipeline, you would push hard to sell the Turbo even though the XR7 earns a higher contribution margin per unit. To eliminate this type of conflict, commissions can be based on contribution margin rather than on selling price alone. Fall 2010 EMBA 5403 90/109 The Concept of Sales Mix Sales mix is the relative proportion in which a company’s products are sold. Different products have different selling prices, cost structures, and contribution margins. Let’s assume Racing Bicycle Company sells bikes and carts and that the sales mix between the two products remains the same. Fall 2010 EMBA 5403 91/109 Revenue Mix Revenue mix (or sales mix) is the relative combination of quantities of products or services that make up total revenue Fall 2010 EMBA 5403 92/109 Pages 73 - 75 Multi-product break-even analysis Racing Bicycle Co. provides the following information: Fall 2010 EMBA 5403 $265,000 93/109 = 48.2% (rounded) $550,000 Multi-product break-even Break-even Fixed expenses = analysis sales CM Ratio $170,000 = 48.2% = $352,697 Fall 2010 EMBA 5403 94/109 SALES MIX= % OF TOTAL SALES FOR EVERY PRODUCT THREE PRODUCTS A , B, C % SALES OF a, b , c where a= sales of product a / total sales etc. CMa = CM OF PRODUCT A, B OR C WEIGHTED CMR= a * CMR of product A + b * CMR of product B + c * CMR of product C BREAKEVEN IN MULTIPLE PRODUCT S= FC/ WEIGHTED CMR •TO FIND HOW MANY UNITS MUST BE SOLD AT BREAKEVEN (OR FOR TARGET INCOME): 1.FIND BREAKEVEN IN MULTIPLE PRODUCTS 2.COMPUTE EACH PRODUCTS SALES AMOUNT BY MULTIPLYING THE SALES RATIO * BREAKEVEN SALES 3.FIND THE BREAKEVEN SALE SHARE OF EACH PRODUCT; 4.DIVIDE EACH PRODUCTS SHARE OF BREAKEVEN SALES BY THE UNIT PRICE OF EACH PRODUCT TO GET THE NUMBER OF UNITS TO BE SOLD OF EACH PRODUCT IN ORDER TO BREAKEVEN OR FOR TARGET INCOME Fall 2010 EMBA 5403 95/109 Key Assumptions of CVP Analysis Selling price is constant. Costs are linear. In multi-product companies, the sales mix is constant. In manufacturing companies, inventories do not change (units produced = units sold). Fall 2010 EMBA 5403 96/109 Multiple Cost Drivers In many cases there may be multiple cost drivers Do-All Software Example Variable costs: $40 per software package sold $15 per invoice issued Operating income = Revenue – ($40 x packages sold) – ($15 x invoices issued) – Fixed costs In cases where there are multiple cost drivers there are multiple breakeven points Fall 2010 EMBA 5403 97/109 Examples Please do the exercises before the next session. Fall 2010 EMBA 5403 98/109 Contribution Margin & Gross Margin Merchandising Sector Gross Margin Format Contribution Margin Format Revenues Variable costs: Cost of goods sold Other variable Contribution margin Fixed costs: Cost of goods sold $200 $120 43 5 163 37 Other fixed 19 24 Operating income $13 Fall 2010 EMBA 5403 Revenues $200 Cost of goods sold (120+5) 125 Gross margin 75 Operating costs (43+19) 62 Operating income $13 99/109 Pages 82 - 83 Example 1: equation approach • • • • • Movie theater: $48,000 monthly fixed costs $8 ticket price. $2 variable cost per ticket. $6 contribution margin per ticket; 75% cont. margin ratio Give breakeven units and revenue BEunits = $48,000/($8 - $2) BEunits = 8,000 tickets. BErevenue = $64,000 Fall 2010 EMBA 5403 100/109 $000 (per month) 40 30 Profit 20 Break-even point: 8,000 tickets 10 Profit area 0 -10 -20 Loss 2,000 4,000 6,000 Loss area -30 8,000 10,000 Volume of tickets sold in one month -40 -50 Fall 2010 EMBA 5403 Fixed expenses = $48,000 101/109 Example 1 Cont’d • Suppose practical capacity per month is 12,000 tickets and that the movie theater has operated at 60% capacity during December. It is now December 30. • Has the theater made money in December? • If they could capture 1,000 customers by lowering the ticket price to $7 for New Year’s Eve, should they do it? Fall 2010 EMBA 5403 102/109 Example 1 con’t practical capacity operating at contribution fixed costs loss 12000 tickets 60% =60% *12000*6= 43200 48000 -4800 7-2 add'l contribution Fall 2010 EMBA 5403 1000 5 5000 > 200 net income yes, they should 4800 103/109 Example 2 Data: The Doral Company manufactures and sells pens. Present sales output is 5,000,000 per year at a selling price of $.50 per unit. Fixed costs are $900,000 per year. Variable costs are $.30 per unit. What is the current yearly operating income? What is the current breakeven point in sales dollars? Fall 2010 EMBA 5403 104/109 Example 2 Cont’d –answer part 1 Contribution margin ratio = total contribution margin = Fixed Cost operating income Breakeven Sales = Fall 2010 EMBA 5403 $.20/$.50= $1,000,000 $900,000 $100,000 40% 900,000/60%= $2,250,000 105/109 Example 2 Cont’d – question part 2 Compute the new operating income if . . . 1. A $.04 per-unit increase in variable costs. 2. A 20% decrease in fixed costs, a 20% decrease in selling price, a 10% decrease in variable costs, and a 40% increase in units sold. Fall 2010 EMBA 5403 106/109 Example 2 Cont’d –answer part 2 1. $0.04 increase in variable costs new variable cost 0.34 new cont. margin per pen 0.16 total sales 5,000,000 pens total cont. margin = $800,000 Fixed costs $900,000 operating income ($100,000) 2. A 20% decrease in fixed costs, a 20% decrease in selling price, a 10% decrease in variable costs, and a 40% increase in units sold. new selling price new variable costs new units sold total cont. margin = Fixed costs operating income Fall 2010 EMBA 5403 $0.40 $0.27 7,000,000 pens $1,890,000 $900,000 $990,000 107/109 Example 2 Cont’d-questions part 3 Compute the new breakeven point in units for each of the following changes. A 10% increase in fixed costs: A 10% increase in selling price and a $20,000 increase in fixed costs. Fall 2010 EMBA 5403 108/109 Example 2 Cont’d –answer part 3 new BE units if fixed cost increase by 10% new fixed costs contribution margin per pen New BE units $990,000 $0.20 4,950,000 pens new BE units if selling price increase by 10% and fixed cost increase by $20.000. $0.55 per pen new selling price $920,000 new fixed costs $0.25 per pen new contribution margin 3,680,000 pens New BE units Fall 2010 EMBA 5403 109/109 Example 3 The Rapid Meal has two restaurants that are open 24 hours per day. Fixed costs for the two restaurants together total $450,000 per year. Service varies from a cup of coffee to full meals. The average sales check for each customer is $8.00. The average cost of food and other variable costs for each customer is $3.20. The income tax rate is 30%. Target net income is $105,000. Fall 2010 EMBA 5403 110/109 Example 3 Cont’d Compute the total dollar sales needed to obtain the target net income. How many sales checks are needed to break even? Compute net income if the number of sales checks is 150,000 Fall 2010 EMBA 5403 111/109 Example 3 - answers Compute the total dollar sales needed to obtain the target net income before tax income= 105000/0.7= $150,000 approach 1; sales = vc +fc+before tax profit sales = average sales check x no of customers variable cost= vc per cust x no of customers average check per customer = 8 variable cost per customer = 3.2 approach 2: contribution margin per customer = 4.8 contribution margin ratio = 0.6 fixed costs = $450,000 fixed cost + target income = $600,000 Sales to reach target income = $1,000,000 (600.000 /0.60) Fall 2010 EMBA 5403 112/109 Example 3 - answers How many sales checks are needed to break even? fixed cost + target income = contribution margin per customer = number check (customers) to reach target income $600,000 $4.80 125000 Compute net income if the number of sales checks is 150,000 contribution margin per customer = number of sales checks (customers)= total contribution margin fixed costs = income before tax income tax net income Fall 2010 EMBA 5403 $4.80 150000 $720,000 $450,000 $270,000 81000 $189,000 113/109 Multiple-Product Example Assume the following: Units sold Sales price per unit Sales Less: Variable expenses Contribution margin Less: Fixed expenses Net income Regular Deluxe Total Percent 400 $ 500 $200,000 120,000 $ 80,000 200 $750 $150,000 60,000 $ 90,000 600 ---$350,000 180,000 $170,000 130,000 $ 40,000 ======= ------100.0% 51.4 48.6% 1. What is the break even point? 2. How much sales revenue of each product must be generated to earn a before tax profit $50,000? Fall 2010 EMBA 5403 114/109 Multi product example -answer 1. What is the break even point? fixed costs weighted cont. margin ratio BE sales dollars $130,000 48.60% $267,490 2. How much sales revenue of each product must be generated to earn a before tax profit $50,000? target income fixed costs weighted cont. margin ratio fixed cost + target income sales revenue targeted- total sales mix (percent) regular (200.000/350.000) deluxe (150.000 / 350.000) Sales of regular Sales of deluxe (sales mix % x sales target) Fall 2010 EMBA 5403 $50,000 $130,000 48.60% $180,000 $370,370.37 57.14% 42.86% $211,640.21 $158,730.16 115/109 Multiple product - verify cmr - regular cmr - deluxe contribution margin -regular contribution margin - deluxe total contribution Fixed costs before tax income Fall 2010 EMBA 5403 40.00% 60.00% $84,656.08 $95,238.10 $179,894.18 $130,000 $49,894.18 116/109 Example 4 A financial analyst is studying the feasibility of two alternative assembly methods, manual and automated. The automated method has variable costs of TL 2.10 per unit and annual committed costs of TL 130.000; in contrast, the manual method has variable costs of TL 4.20 per unit and committed costs of TL 60.000. The company sells its products for TL 23 per unit. What is break-even of each method? Above what volume level will management prefer the automated method to the manual method? Fall 2010 EMBA 5403 117/109 Selling price Automated variable fixed Example 4 Answer Manual variable fixed TL23.00 TL2.10 per unit TL130,000 per year TL4.20 per unit TL60,000 per year Automated BE units: fixed cost TL130,000 cont.per unit TL20.90 BE units 6,220.10 6221 units Manual BE units: fixed cost TL60,000 cont.per unit TL18.80 BE units Fall 2010 EMBA 5403 3,191.49 3.192 units 118/109 Example 4 answer Find the indifference point: 2.1q+130000=4.2q+60000 change in cost TL70,000 change in q 2.1 33333.333 33.334 units after 33.334 units automated is better at 35.000 units at 30.000 units manual cont. margin per unit number of units Contribution Margin Fixed Costs Operating Income Fall 2010 EMBA 5403 automated TL18.80 TL20.90 35000 35000 TL658,000.00 TL731,500.00 manual cont. margin per unit number of units Contribution Margin TL60,000 TL130,000 Fixed Costs TL598,000 TL601,500 Operating Income automated TL18.80 TL20.90 30000 30000 TL564,000.00 TL627,000.00 TL60,000 TL130,000 TL504,000 TL497,000 119/109