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## EMBA 5403 Fall 2010

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**EMBA 5403 Fall 2010**Cost-Volume-Profit Relationships**Cost Estimation 1**Constant 250 Std Err of Y Est 299.304749934466 R squared 0.944300518134715 No. of Observations 5 Degrees of Freedom 3 X Coefficient(s) 6.75 Std Err of Coef. 0.9464847243**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.**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**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.**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 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 Total for Per Unit 2 units % Revenue $200 $400 100% Variable costs 12024060% Contribution margin $80 $160 40% Pages 68 - 69**Contribution Margin Income Statement**• Income statement that groups line items by cost behaviour to highlight the contribution margin Packages Sold 0 1 2 25 40 Revenue $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 Fixed costs 2,000 2,000 2,000 2,000 2,000 Operating income $(2,000) $(1,920) $(1,840) $0 $1,200 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 Page 71**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 0 10 20 30 40 50 Units Sold 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 % 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 Pages 76 - 77**Option 2**$1,400 Fixed Fee + 5% Commission Option 1 $2,000 Fixed Fee Option 3 20% Commission Rev Rev Rev $ $ $ Cost Cost Cost Units Units Units Breakeven = 25 units Breakeven = 20 units Breakeven = 0 units Alternative Cost Structures • CVP helps managers assess the risks and potential benefits of adopting alternative cost structures Example: Alternative rental arrangements Pages 77 - 78**Basics of Cost-Volume-Profit Analysis**CM is used first to cover fixed expenses. Any remaining CM contributes to net operating income.**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.**The Contribution Approach**Each month Racing must generate at least $80,000 in total CM to break even.**The Contribution Approach**If Racing sells 400 unitsin a month, it will be operating at the break-even point.**The Contribution Approach**If Racing sells one more bike (401 bikes), net operating income will increase by $200.**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.**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.**CVP Graph**Dollars In a CVP graph, unit volume is usually represented on the horizontal (X) axis and dollars on the vertical (Y) axis. Units**Fixed Expenses**CVP Graph Dollars Units**Total Expenses**Fixed Expenses CVP Graph Dollars Units**Total Sales**Total Expenses Fixed Expenses CVP Graph Dollars Units**Break-even point(400 units or $200,000 in sales)**CVP Graph Profit Area Dollars Loss Area Units**Total CM**Total sales CM Ratio = $80,000 $200,000 = 40% Contribution Margin Ratio The contribution margin ratio is:For Racing Bicycle Company the ratio is: Each $1.00 increase in sales results in a total contribution margin increase of 40¢.**Unit CM**Unit selling price CM Ratio = $200 $500 = 40% Contribution Margin Ratio Or, in terms of units, the contribution margin ratiois:For Racing Bicycle Company the ratio is:**A $50,000 increase in sales revenue results in a $20,000**increase in CM. ($50,000 × 40% = $20,000) Contribution Margin Ratio**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?**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**Unit contribution margin**Unit selling price CM Ratio = ($1.49-$0.36) $1.49 = $1.13 $1.49 = = 0.758 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**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?**$80,000 + $10,000 advertising = $90,000**Changes in Fixed Costs and Sales Volume Sales increased by $20,000, but net operating income decreased by $2,000.**Changes in Fixed Costs and Sales Volume**The Shortcut Solution**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?**580 units × $310 variable cost/unit = $179,800**Change in Variable Costs and Sales Volume Sales increase by $40,000, and net operating income increases by $10,200.**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?**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.**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?**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.**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?**Break-Even Analysis**Break-even analysis can be approached in two ways: • Equation method • Contribution margin method**At the break-even point**profits equal zero Equation Method Profits = (Sales – Variable expenses) – Fixed expenses OR Sales = Variable expenses + Fixed expenses + Profits**Break-Even Analysis**Here is the information from Racing Bicycle Company:**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**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**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**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**Break-even point**in units sold Fixed expenses Unit contribution margin = Break-even point in total sales dollars Fixed expenses CM ratio = Contribution Margin Method The contribution margin method has two key equations.