Cost-Volume-Profit Relationships

Cost-Volume-Profit Relationships
6-1 Cost-Volume-Profit Relationships EMBA 5403 Fall 2010 This is one of the most important chapters in the text. It integrates much of what we have learned so far. We will learn the relationships among product costs, sales volumes and resulting profits.

Cost Estimation 1 Constant 250 Std Err of Y Est 299.304749934466
R squared No. of Observations 5 Degrees of Freedom 3 X Coefficient(s) Std Err of Coef Fall 2010 EMBA 5403

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

Estimation (continued)
Given: *T-value for sample size of 5 at 95% confidence level is (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 = £ (300) + (3.182 x £598.6) = £ £1911 Fall 2010 EMBA 5403

Cost Estimation Example 2
6-5 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. Fall 2010 EMBA 5403

Cost-Volume-Profit Analysis
6-6 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 revenues change in relation to production and sales costs can be divided in variable and fixed categories and fixed element constant over the relevant range revenues and costs behave in a linear fashion costs and prices are known if more than one product exists, the sales mix is constant inventories stay at the same level we can ignore the time value of money Fall 2010 EMBA 5403 Page 67

Contribution Margin Total for
6-7 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 Total for Per Unit 2 units % Revenue $200 $ % Variable costs % Contribution margin $80 $160 40% Fall 2010 EMBA 5403 Pages

Contribution Margin Income Statement
6-8 Contribution Margin Income Statement Income statement that groups line items by cost behaviour to highlight the contribution margin Packages Sold Revenue $0 $200 $400 $5,000 $8,000 Variable costs ,000 4,800 Contribution margin ,000 3,200 Fixed costs 2,000 2,000 2,000 2,000 2,000 Operating income $(2,000) $(1,920) $(1,840) $0 $1,200 Fall 2010 EMBA 5403 Page 69

Breakeven Point Breakeven point in units
6-9 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 Page 71

Cost-Volume-Profit Graph
6-10 Cost-Volume-Profit Graph Total revenues line Breakeven Point 25 units $10,000 $8,000 $6,000 $4,000 $2,000 $0 Total costs line Operating income Operating loss Units Sold Fall 2010 EMBA 5403 Page 72

Target Operating Income
6-11 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 Pages

6-12 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 Pages

Alternative Cost Structures
6-13 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 Rev Cost $ Units Breakeven = 20 units Option 1 $2,000 Fixed Fee Rev Cost $ Units Breakeven = 25 units Option 3 20% Commission Rev Cost $ Units Breakeven = 0 units Fall 2010 EMBA 5403 Pages

Basics of Cost-Volume-Profit Analysis
6-14 Basics of Cost-Volume-Profit Analysis Contribution margin is used first to cover fixed expenses. Any remaining contribution margin contributes to net operating income. CM is used first to cover fixed expenses. Any remaining CM contributes to net operating income. Fall 2010 EMBA 5403

The Contribution Approach
6-15 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. Sales, variable expenses, and contribution margin can also be expressed on a per unit basis. For each additional unit Racing Bicycle Company sells, $200 more in contribution margin will help to cover fixed expenses and provide a profit. Each month Racing Bicycle must generate at least $80,000 in total contribution margin to break-even (which is the level of sales at which profit is zero). If Racing sells 400 units a month, it will be operating at the break-even point. If Racing sells one more bike (401 bikes), net operating income will increase by $200. Fall 2010 EMBA 5403

6-16 The Contribution Approach Each month Racing must generate at least $80,000 in total CM to break even. Each month Racing Bicycle must generate at least $80,000 in total contribution margin to break-even (which is the level of sales at which profit is zero). Fall 2010 EMBA 5403

6-17 The Contribution Approach If Racing sells 400 units in a month, it will be operating at the break-even point. If Racing sells 400 units a month, it will be operating at the break-even point. If Racing sells one more bike (401 bikes), net operating income will increase by $200. Fall 2010 EMBA 5403

6-18 The Contribution Approach If Racing sells one more bike (401 bikes), net operating income will increase by $200. You can see that the sale of one unit above the break-even point yields net income of two hundred dollars for Racing Bicycle. Fall 2010 EMBA 5403

6-19 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. If we develop equations to calculate break-even and net income, we will not have to prepare an income statement to determine what net income will be at any level of sales. For example, we know that if Racing Bicycle sells four hundred thirty bikes, net income will be six thousand dollars. The company will sell thirty bikes above the break-even unit sales and the contribution margin is two hundred dollars per bike. So, we multiply thirty bikes times two hundred dollars per bike and get net income of six thousand dollars.. Fall 2010 EMBA 5403

CVP Relationships in Graphic Form
6-20 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. The relationship among revenue, cost, profit and volume can be expressed graphically by preparing a cost-volume-profit (CVP) graph. To illustrate, we will use contribution income statements for Racing Bicycle Company at three hundred, four hundred, and five hundred units sold. Fall 2010 EMBA 5403

6-21 CVP Graph Dollars In a CVP graph, unit volume is usually represented on the horizontal (X) axis and dollars on the vertical (Y) axis. In a CVP graph, unit volume is usually represented on the horizontal (X) axis and dollars on the vertical (Y) axis. Once we have settled on this convention we will plot the fixed cost. Units Fall 2010 EMBA 5403

CVP Graph Fixed Expenses Dollars Units
6-22 CVP Graph Dollars Fixed Expenses The first step begins by drawing a line parallel to the volume axis to represent total fixed expenses of eighty thousand dollars. Units Fall 2010 EMBA 5403

CVP Graph Total Expenses Fixed Expenses Dollars Units
6-23 CVP Graph Total Expenses Dollars Fixed Expenses Next, choose some sales volume (for example, five hundred units) and plot the point representing total expenses (e.g., fixed and variable) at that sales volume. Draw a line through the data point back to where the fixed expenses line intersects the dollar axis. Units Fall 2010 EMBA 5403

CVP Graph Total Sales Total Expenses Fixed Expenses Dollars Units
6-24 CVP Graph Total Sales Total Expenses Dollars Fixed Expenses Finally, choose some sales volume (for example, five hundred units) and plot the point representing total sales dollars at the chosen activity level. Draw a line through the data point back to the origin. Units Fall 2010 EMBA 5403

Break-even point (400 units or $200,000 in sales)
6-25 CVP Graph Break-even point (400 units or $200,000 in sales) Profit Area Dollars The break-even point is where the total revenue and total expenses lines intersect. In the case of Racing Bicycle, break-even is four hundred bikes sold, or sales revenue of two hundred thousand dollars. Loss Area Units Fall 2010 EMBA 5403

Contribution Margin Ratio
6-26 Contribution Margin Ratio The contribution margin ratio is: For Racing Bicycle Company the ratio is: Total CM Total sales CM Ratio = = 40% $80,000 $200,000 We can calculate the contribution margin ratio of Racing Bicycle by dividing total contribution by total sales. In the case of Racing Bicycle, the contribution margin ratio is forty percent. This means that for each dollar increase in sales the company will produce forty cents in contribution margin. Each $1.00 increase in sales results in a total contribution margin increase of 40¢. Fall 2010 EMBA 5403

6-27 Contribution Margin Ratio Or, in terms of units, the contribution margin ratio is: For Racing Bicycle Company the ratio is: Unit CM Unit selling price CM Ratio = $200 $500 = 40% We may also calculate the contribution margin ratio using per unit amounts. Fall 2010 EMBA 5403

6-28 Contribution Margin Ratio A $50,000 increase in sales revenue results in a $20,000 increase in CM. ($50,000 × 40% = $20,000) Let’s see how we can use the contribution margin ratio to look at the contribution margin income statement of Racing Bicycle in a little different way. If Racing is able to increase its sales by fifty thousand dollars, it will increase contribution margin by twenty thousand dollars, that is, fifty thousand dollars times forty percent. Fall 2010 EMBA 5403

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

6-30 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 b c d Can you calculate the contribution margin ratio for Coffee Klatch? The calculation may take a minute or so to complete. Fall 2010 EMBA 5403

Unit contribution margin
6-31 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 b c d Unit contribution margin Unit selling price CM Ratio = = ($1.49-$0.36) $1.49 $1.13 = 0.758 How did you do? The CM ratio is seventy-five point eight percent. Fall 2010 EMBA 5403

Changes in Fixed Costs and Sales Volume
6-32 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? Let’s assume that the management of Racing Bicycle believes it can increase unit sales from five hundred to five hundred forty if it spends ten thousand dollars on advertising. Would you recommend that the advertising campaign be undertaken? See if you can solve this problem before going to the next screen. Fall 2010 EMBA 5403

6-33 Changes in Fixed Costs and Sales Volume $80,000 + $10,000 advertising = $90,000 As you can see, even if sales revenue increases to two hundred seventy thousand dollars, Racing will experience a twelve thousand dollar increase in variable costs and a ten thousand dollar increase in fixed costs (the new advertising campaign). As a result net income will actually drop by two thousand dollars. The advertising campaign would certainly not be a good idea. We can help management see the problem before any additional monies are spent. Sales increased by $20,000, but net operating income decreased by $2,000. Fall 2010 EMBA 5403

6-34 Changes in Fixed Costs and Sales Volume The Shortcut Solution Here is a shortcut approach to looking at the problem. You can see that an increase in contribution margin is more than offset by the increased advertising costs. Fall 2010 EMBA 5403

Change in Variable Costs and Sales Volume
6-35 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? Management at Racing Bicycle believes that using higher quality raw materials will result in an increase in sales from five hundred to five hundred eighty. The higher quality raw materials will lead to a ten dollar increase in variable costs per unit. Would you recommend the use of the higher quality raw materials? Fall 2010 EMBA 5403

Change in Variable Costs and Sales Volume
6-36 Change in Variable Costs and Sales Volume 580 units × $310 variable cost/unit = $179,800 As you can see, revenues will increase by forty thousand dollars (eighty bikes times five hundred dollars per bike), and variable costs will increase by twenty-nine thousand eight hundred dollars. Contribution margin will increase by ten thousand two hundred dollars. With no change in fixed costs, net income will also increase by ten thousand two hundred dollars. The use of higher quality raw materials appears to be a profitable idea. Sales increase by $40,000, and net operating income increases by $10,200. Fall 2010 EMBA 5403

Change in Fixed Cost, Sales Price and Volume
6-37 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? Here is a more complex situation because we will experience a change in selling price, advertising expense, and unit sales. Would you support this plan? Fall 2010 EMBA 5403

Change in Fixed Cost, Sales Price and Volume
6-38 Change in Fixed Cost, Sales Price and Volume This appears to be a good plan because net income will increase by two thousand dollars. Take a few minutes and analyze the change in sales revenue, variable expenses and fixed expenses. Sales increase by $62,000, fixed costs increase by $15,000, and net operating income increases by $2,000. Fall 2010 EMBA 5403

Change in Variable Cost, Fixed Cost and Sales Volume
6-39 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? Here is another complex question involving cost-volume-profit relationships. In this question we eliminate a fixed cost and substitute a variable cost while increasing the units sold. Be careful with your calculation of the profit impact of these changes. Fall 2010 EMBA 5403

Change in Variable Cost, Fixed Cost and Sales Volume
6-40 Net income increases by twelve thousand three hundred seventy-five dollars. Notice that sales revenue and variable expenses increased as well. Fixed expenses were decreased as a result of making sales commissions variable in nature. How did you do? We hope you are beginning to see the potential power of CVP analysis. Sales increase by $37,500, variable costs increase by $31,125, but fixed expenses decrease by $6,000. Fall 2010 EMBA 5403

Change in Regular Sales Price
6-41 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? Suppose Racing Bicycle has a one-time opportunity to sell one hundred fifty bikes to a wholesaler. There would be no change in the cost structure as a result of this sale. Racing wants the one-time sale to produce a profit of three thousand dollars. What selling price should Racing quote to the wholesaler? Fall 2010 EMBA 5403

Change in Regular Sales Price
6-42 Change in Regular Sales Price If we desire a profit of three thousand dollars on the sale of one hundred fifty bikes, we must have a profit of twenty dollars per bike. The variable expenses associated with each bike are three hundred dollars, so we would quote a selling price of three hundred twenty dollars. You can see the proof of the quote in the blue schedule. Fall 2010 EMBA 5403

Break-even analysis can be approached in two ways:
6-43 Break-Even Analysis Break-even analysis can be approached in two ways: Equation method Contribution margin method We can accomplish break-even analysis in one of two ways. We can use the equation method or the contribution margin method. We get the same results regardless of the method selected. You may prefer one method over the other. It’s a personal choice, but be aware there are some problems associated with either method. Some are easier to solve using the equation method, while others can be quickly solved using the contribution margin method. Fall 2010 EMBA 5403

At the break-even point
6-44 Equation Method Profits = (Sales – Variable expenses) – Fixed expenses OR Sales = Variable expenses + Fixed expenses + Profits At the break-even point profits equal zero The equation method is based on the contribution approach income statement. The equation can be stated in one of two ways: Profits equal Sales less Variable expenses, less Fixed Expenses, or Sales equal Variable expenses plus Fixed expenses plus Profits Remember that at the break-even point profits are equal to zero. Fall 2010 EMBA 5403

Here is the information from Racing Bicycle Company:
6-45 Break-Even Analysis Here is the information from Racing Bicycle Company: Here is some information provided by Racing Bicycle that we will use to solve some problems. We have the contribution margin income statement, the selling price and variable expenses per unit, and the contribution margin ratio. Fall 2010 EMBA 5403

We calculate the break-even point as follows:
6-46 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 The break-even point in units is determined by creating the equation as shown, where Q is the number of bikes sold, five hundred dollars is the unit selling price, three hundred dollars is the unit variable expense, and eighty thousand dollars is the total fixed expense. We need to solve for Q. Fall 2010 EMBA 5403

We calculate the break-even point as follows:
6-47 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 Solving this equation shows that the break-even point in units is 400 bikes. We want to be careful with the algebra when we group terms. Fall 2010 EMBA 5403

Equation Method X = 0.60X + $80,000 + $0
6-48 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, $0 Where: X = Total sales dollars 0.60 = Variable expenses as a % of sales $80,000 = Total fixed expenses The equation can be modified as shown to calculate the break-even point in sales dollars. In this equation, X is total sales dollars, point six zero (or sixty percent) is the variable expense as a percentage of sales, and eighty thousand dollars is the total fixed expense. We need to solve for X. Fall 2010 EMBA 5403

Equation Method 0.40X = $80,000 X = $80,000 ÷ 0.40 X = $200,000
6-49 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, $0 0.40X = $80,000 X = $80,000 ÷ 0.40 X = $200,000 Solving this equation shows that the break-even point is sales dollars is two hundred thousand dollars. Once again, be careful when you combine the X values in the equation. Fall 2010 EMBA 5403

Contribution Margin Method
6-50 Contribution Margin Method The contribution margin method has two key equations. Fixed expenses Unit contribution margin = Break-even point in units sold The contribution margin method has two key equations: Break-even point in units sold equals Fixed expenses divided by CM per unit, and Break-even point in sales dollars equals Fixed expenses divided by CM ratio. Fixed expenses CM ratio = Break-even point in total sales dollars Fall 2010 EMBA 5403

Contribution Margin Method
6-51 Contribution Margin Method Let’s use the contribution margin method to calculate the break-even point in total sales dollars at Racing. Fixed expenses CM ratio = Break-even point in total sales dollars $80,000 40% = $200,000 break-even sales Part I Let’s use the contribution margin method to calculate break-even in total sales dollars. Part II The break-even sales revenue is two hundred thousand dollars. Fall 2010 EMBA 5403

6-52 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? 872 cups b. 3,611 cups c. 1,200 cups d. 1,150 cups Now use the contribution margin approach to calculate the break-even point in cups of coffee sold. Fall 2010 EMBA 5403

6-53 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 cups b. 3,611 cups c. 1,200 cups d. 1,150 cups Fixed expenses Unit CM Break-even = $1,300 $1.49/cup - $0.36/cup = $1.13/cup = 1,150 cups The contribution margin per cup of coffee is one dollar and thirteen cents. The number of cups to sell to reach break-even is one thousand one hundred fifty. Fall 2010 EMBA 5403

6-54 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 Let’s calculate the break-even in sales dollars for Coffee Klatch. Fall 2010 EMBA 5403

6-55 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 Fixed expenses CM Ratio Break-even sales $1,300 0.758 = $1,715 = With a contribution margin ratio of seventy-five point eight percent rounded, break-even sales revenue is one thousand seven hundred fifteen dollars. Fall 2010 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

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

Target Profit Analysis
6-58 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. We can use either method to determine the revenue or units needed to achieve a target level of profits. Suppose Racing Bicycle wants to earn net income of one hundred thousand dollars. How many bikes must the company sell to achieve this profit level? Fall 2010 EMBA 5403

The CVP Equation Method
6-59 The CVP Equation Method Sales = Variable expenses + Fixed expenses + Profits $500Q = $300Q + $80, $100,000 $200Q = $180,000 Q = 900 bikes Instead of setting profit to zero like we do in a break-even analysis, we set the profit level to one hundred thousand dollars. Solving for Q, we see that the company will have to sell nine hundred bikes to achieve the desired profit level. Fall 2010 EMBA 5403

The Contribution Margin Approach
6-60 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. Fixed expenses + Target profit Unit contribution margin = Unit sales to attain the target profit A quicker way to solve this problem is to add the desired profits to the fixed cost and divide the total by the contribution margin per unit. Notice we get the same result of nine hundred bikes. $80, $100,000 $200/bike = 900 bikes Fall 2010 EMBA 5403

6-61 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 The Coffee Klatch wants to earn a monthly profit of two thousand five hundred dollars. How many cups of coffee must the company sell to reach this profit goal? Fall 2010 EMBA 5403

6-62 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 We add the desired profit to the fixed cost and divide by the unit contribution of one dollar thirteen cents. The company must sell three thousand three hundred and sixty-three cups of coffee to reach its profit goal. Fall 2010 EMBA 5403

Fixed expenses + Target profit Unit sales to attain target profit
Unit breakeven Fixed expenses + Target profit Unit CM Unit sales to attain target profit = 3,363 cups = $3,800 $1.13 $1,300 + $2,500 $ $0.36 Fall 2010 EMBA 5403

6-64 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. The margin of safety helps management assess how far above or below the break-even point the company is currently operating. To calculate the margin of safety we take total current sales and subtract break-even sales. Let’s calculate the margin of safety for Racing Bicycle. Fall 2010 EMBA 5403

6-65 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 Racing Bicycle is currently selling five hundred bikes and producing total sales revenue of two hundred fifty thousand dollars. Sales at the break-even point are two hundred thousand dollars, so the company’s margin of safety is fifty thousand dollars. Fall 2010 EMBA 5403

6-66 The Margin of Safety The margin of safety can be expressed as 20% of sales. ($50,000 ÷ $250,000) We can express the margin of safety as a percent of sales. In the case of Racing Bicycle, the margin of safety is twenty percent (fifty thousand dollars divided by two hundred fifty thousand dollars). Fall 2010 EMBA 5403

Margin of Safety in units
6-67 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 Safety in units = = 100 bikes $50,000 $500 We can express the margin of safety as a percent of sales. In the case of Racing Bicycle, the margin of safety is twenty percent (fifty thousand dollars divided by two hundred fifty thousand dollars). Fall 2010 EMBA 5403

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 x% = CMR SALES $ = x% *SALES +FC (1-x)* SALES $ = FC THAT IS CMR*SALES = FC SALES $ AT BREAKEVEN = FC/ CMR Fall 2010 EMBA 5403

6-69 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 cups c. 1,150 cups d. 2,100 cups Let’s see if you can calculate the margin of safety in cups of coffee for the Coffee Klatch. Fall 2010 EMBA 5403

6-70 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 cups c. 1,150 cups d. 2,100 cups The margin of safety is nine hundred fifty cups, or we can calculate the margin of safety as forty five percent. Fall 2010 EMBA 5403

Margin of safety percentage
Margin of safety = Total sales – Break-even sales = 950 cups = 2,100 cups – 1,150 cups or 950 cups 2,100 cups Margin of safety percentage = = 45% Fall 2010 EMBA 5403

Cost Structure and Profit Stability
6-72 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. A company’s cost structure refers to the relative proportion of fixed and variable expenses. Some companies have high fixed expenses relative to variable expenses. Do you remember our discussion of utility companies? Because of the heavy investment in property, plant and equipment, many utility companies have a high proportion of fixed costs. Fall 2010 EMBA 5403

Cost Structure and Profit Stability
6-73 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 with lower proportion of fixed costs. Generally, companies with a high fixed cost structure will show higher net income in good years than companies with lower fixed cost structures. Just the opposite is true in bad years. A disadvantage of a high fixed cost structure is that income will be lower in bad years compared to companies with lower proportion of fixed costs. Fall 2010 EMBA 5403

Operating Leverage Contribution margin Net operating income Degree of
6-74 Operating Leverage A measure of how sensitive net operating income is to percentage changes in sales. Contribution margin Net operating income Degree of operating leverage = The degree of operating leverage is a measure, at any given level of sales, of how a percentage change in sales volume will affect profits. It is computed by dividing contribution margin by net operating income. Let’s look at Racing Bicycle. Fall 2010 EMBA 5403

Operating Leverage $100,000 = 5 $20,000
6-75 Operating Leverage At Racing, the degree of operating leverage is 5. Recall that Racing is currently selling five hundred bikes and producing net income of twenty thousand dollars. Contribution margin is one hundred thousand dollars. Operating leverage is five. We determine this by dividing the one hundred thousand contribution by net income of twenty thousand dollars. Now that we calculated the degree of operating leverage for Racing, let’s see exactly what this means to management. $100,000 $20,000 = 5 Fall 2010 EMBA 5403

Here’s the verification!
6-76 Operating Leverage With an operating leverage of 5, if Racing increases its sales by 10%, net operating income would increase by 50%. If Racing is able to increase sales by ten percent, net income will increase by fifty percent. We multiply the percentage increase in sales by the degree of operating leverage. Let’s verify the fifty percent increase in profit. Here’s the verification! Fall 2010 EMBA 5403

10% increase in sales from . . . results in a 50% increase in
6-77 Operating Leverage A ten percent increase in sales would increase bike sales from the current level of five hundred to five hundred fifty. Look at the contribution margin income statement and notice that income increased from twenty thousand to thirty thousand dollars. That ten thousand dollar increase in net income is a fifty percent increase. So it is true that a ten percent increase in sales results in a fifty percent increase in net income. This is powerful information for a manager to have. 10% increase in sales from $250,000 to $275, . . . results in a 50% increase in income from $20,000 to $30,000. Fall 2010 EMBA 5403

6-78 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 See if you can calculate the degree of operating leverage for the Coffee Klatch. Fall 2010 EMBA 5403

6-79 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 The computations took a while to complete, didn’t they. You can see that operating leverage is two point two one. Contribution margin Net operating income Operating leverage = $2,373 $1,073 = 2.21 Fall 2010 EMBA 5403

Con’t Fall 2010 EMBA 5403

6-81 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% If the Coffee Klatch is able to increase sales by twenty percent, what will be the increase in net income? Fall 2010 EMBA 5403

6-82 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% You are right. The increase in net income is forty-four point two percent. Fall 2010 EMBA 5403

Cost Structure and Operating Leverage
6-83 Cost Structure and Operating Leverage Operating leverage is greatest in companies that have a high proportion of fixed costs in relation to variable costs. Fall 2010 EMBA 5403

Operating Leverage Factor
6-84 Operating Leverage Factor A measure of how a percentage change in sales will affect profits. The greater the operating leverage, the greater the sensitivity of its profit to changes in volume. Contribution margin Net income Operating leverage factor = Fall 2010 EMBA 5403

Operating Leverage Factor
6-85 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

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

Verify Increase in Profit
6-87 Verify Increase in Profit Here is our verification of the increase in net income. Take a few minutes and make sure you understand how we calculated all the numbers. Fall 2010 EMBA 5403

Structuring Sales Commissions
6-88 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. You have probably heard that salespersons can be compensated on a commission basis. The commission is usually based on sales revenue generated. Some salespersons work on a salary plus commission. When salespersons are paid a commission based on sales dollars generated, the income statement impact may not be fully understood. Let’s look at an example. Fall 2010 EMBA 5403

6-89 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. This company produces two surfboards. The XR7 model sells for one hundred dollars and has a contribution margin per unit of twenty-five dollars. The second surfboard, the Turbo model, sells for one hundred fifty dollars and has a contribution margin of eighteen dollars per unit sold. The sales force at Pipeline is paid on sales commissions. Fall 2010 EMBA 5403

6-90 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. If you were on the sales force, you would try to sell all the Turbo models you could because it has a higher selling price per unit. The problem is that the XR7 model produces a higher contribution margin to the company. It might be a good idea for Pipeline to base its sales commissions on contribution margin rather than selling price alone. Fall 2010 EMBA 5403

The Concept of Sales Mix
6-91 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. When a company sells more than one product, break-even analyses become more complex because of the relative mix of the products sold. Different products will have different selling prices, cost structures and contribution margins. Let’s expand the product line at Racing Bicycle and see what impact this has on break-even. We are going to assume that the sales mix between the products remains the same in our example. Fall 2010 EMBA 5403

6-92 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 Pages

Multi-product break-even analysis
6-93 Multi-product break-even analysis Racing Bicycle Co. provides the following information: Racing Bicycle sells both bikes and carts. Look at the contribution margin for each product. Notice that we subtract fixed expenses from the total contribution margin. We do not allocate the fixed costs to each product. The sales mix shows that forty-five percent of the company’s sales revenue comes from the sale of bikes and fifty-five percent comes from the sale of carts. The combined contribution margin ratio is forty-eight point two percent (rounded). Let’s look at break-even. $265,000 $550,000 = 48.2% (rounded) Fall 2010 EMBA 5403

Multi-product break-even analysis
6-94 Multi-product break-even analysis Fixed expenses CM Ratio Break-even sales $170,000 48.2% = $352,697 = Part I Break-even in sales dollars is three hundred fifty-two thousand six hundred ninety-seven dollars. We calculate this amount in the normal way. We divide total fixed expenses of one hundred seventy thousand dollars by the combined contribution margin ratio. Part II We begin by allocating total break-even sales revenue to the two products. Forty-five percent of the total is assigned to the bikes and fifty-five percent to the carts. The variable costs-by-product are determined by multiplying the variable expense percent times the assigned revenue. The contribution margin is the difference between the assigned revenue and the variable expenses. Once again we subtract fixed expenses from the combined total contribution margin for the two products. Because we used a rounded contribution margin percent, we have a rounding error of one hundred seventy-six dollars. Obviously, the more products a company has, the more complex the break-even analysis becomes. Fall 2010 EMBA 5403

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

Key Assumptions of CVP Analysis
6-96 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). Here are the four key assumptions of cost-volume-profit analysis. You are probably familiar with the first three by now. The forth assumption tells us that there can be no change in inventory levels. That is, all units produced are sold in the current period. Fall 2010 EMBA 5403

Multiple Cost Drivers In many cases there may be multiple cost drivers
6-97 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

Examples Please do the exercises before the next session. Fall 2010
EMBA 5403

Contribution Margin & Gross Margin
6-99 Contribution Margin & Gross Margin Merchandising Sector Contribution Margin Format Revenues $200 Variable costs: Cost of goods sold $120 Other variable Contribution margin 37 Fixed costs: Cost of goods sold 5 Other fixed 19 24 Operating income $13 Gross Margin Format Revenues $200 Cost of goods sold (120+5) 125 Gross margin 75 Operating costs (43+19) 62 Operating income $13 Fall 2010 EMBA 5403 Pages

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

Fall 2010 EMBA 5403

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

Example 1 con’t Fall 2010 EMBA 5403

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

Example 2 Cont’d –answer part 1
Fall 2010 EMBA 5403

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

Fall 2010 EMBA 5403

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

Fall 2010 EMBA 5403

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 $ The average cost of food and other variable costs for each customer is $ The income tax rate is 30%. Target net income is $105,000. Fall 2010 EMBA 5403

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

Example 3 - answers Fall 2010 EMBA 5403

Multiple-Product Example
Assume the following: Regular Deluxe Total Percent Units sold Sales price per unit $ $ Sales $200,000 $150,000 $350, % Less: Variable expenses , , , Contribution margin $ 80,000 $ 90,000 $170, % Less: Fixed expenses ,000 Net income $ 40,000 ======= 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

Multi product example -answer
Fall 2010 EMBA 5403

Multiple product - verify
Fall 2010 EMBA 5403

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 ; in contrast, the manual method has variable costs of TL 4.20 per unit and committed costs of TL 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

Example 4 Answer Fall 2010 EMBA 5403

Example 4 answer Fall 2010 EMBA 5403

Cost-Volume-Profit Relationships

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