COSTVOLUMEPROFIT ANALYSIS CHAPTER 7 Professor Garvin JD CPA

COST-VOLUMEPROFIT ANALYSIS CHAPTER 7 Professor Garvin, JD; CPA – ACG 2071

Cost-Volume-Profit (CVP) 2 Analysis Is a powerful tool that helps managers make important business decisions Is a relationship among costs, volume, and profit or loss Determines how much the company must sell each month just to cover costs or to break even Helps managers decide how sales volume would need to change to achieve the same profit level

Components of CVP Analysis 3 CVP analysis relies on the interdependency of five components or pieces of information Sales price per unit Volume sold Variable costs per unit Fixed costs Operating income If you know or can estimate four of these five components, you can compute the remaining unknown amount

CVP Assumptions 4 Change in volume is only factor that affects total costs; No Volume discounts Managers can classify each cost as either variable or fixed These costs are linear throughout relevant range Revenues are linear throughout relevant range Inventory levels will not change The sales mix of products will not change

5 CVP Example Facts: Kay’s Posters Kay has an Internet poster business. She currently sells each poster for $35, while each poster has a variable cost of $21. Kay has fixed costs of $7, 000. Kay is currently selling 550 posters per month.

6 Contribution Margin Income Statement Kay’s Internet poster bsn. example from prior slide Sales revenue (550 posters). . . . . $ 19, 250 Less: Variable expenses. . . (11, 550) Contribution margin. . . . 7, 700 Less: Fixed expenses. . . . (7, 000)

Contribution Margin per Unit 7 Sales price per unit $35 - Variable costs per unit (21) = Contribution margin per unit $14 What will profit be if can sell 650 units next month (increase of 100) Contribution margin (650 units x $14) $9, 100 - Fixed Costs (7, 000) Operating Income $2, 100 $1, 400 increase in op. inc. when sell extra 100 posters

Contribution Margin Ratio 8 Contribution margin ratio = percentage of each sales dollar that is available for covering fixed expenses and generating a profit. Contribution = Contribution margin/unit = $14 = 40% CMR margin ratio Sales price per unit $35 We can also compute CMR from Contribution Margin Income St. Contribution = Contribution margin = $ 7, 700 = 40% margin ratio Sales revenue $19, 250 (Numbers above are from the Kay’s Internet poster example on previous

9 Bay Cruiseline offers nightly dinner cruises off the coast of Miami, San Francisco, and Seattle. Dinner cruise tickets sell for $50 per passenger. Bay Cruiseline’s variable cost of providing the dinner is $20 per passenger, and the fixed cost of operating the vessels (depreciation, salaries, docking fees, and other expenses) is $210, 000 per month. The company’s relevant range extends to 15, 000 monthly passengers. a. What is the contribution margin per passenger? Sales revenue (1 passenger) Less: Variable expenses Contribution margin/unit $50 (20) 30

b. What is the contribution margin ratio? 10 Contribution margin/unit = $ = 60% margin ratio 30 c. Use=the contribution to project=operating Sales margin/unit price per unit $ income if monthly sales total 50 10, 000 passengers. 10, 000 x $30 = $300, 000 CM (210, 000) TFC = $90, 000 Op Inc. d. Use the contribution margin ratio to project operating income if monthly sales revenue totals $400, 000. Contribution margin ( $400, 000 sales X 60%) 240, 000 Fixed cost Operating Income $ (210, 000) $ 30, 000

11 Bay Cruiseline offers nightly dinner cruises off the coast of Miami. Dinner cruise tickets sell for $50 per passenger. Bay Cruiseline’s variable cost of providing the dinner is $20 per passenger, and the fixed cost of operating the vessels (depreciation, salaries, docking fees, and other expenses) is $210, 000 per month. The company’s relevant range extends to 15, 000 monthly passengers. If Bay Cruiseline sells an additional 500 tickets, by what amount will its operating income increase (or operating loss decrease)? Contribution Margin per unit x additional tickets 500 extra tickets X $30 CM/unit = $15, 000 incremental

Breakeven Point 12 Breakeven point: Sales level at which operating income is zero If sales above breakeven point, then profit If sales below breakeven point, then loss At Breakeven point: Fixed expenses = total contribution margin Total sales = total expenses at B/E point

Calculating Breakeven Point 13 Three approaches to calculating breakeven: Income statement approach Shortcut approach using contribution margin/unit Shortcut approach using contribution margin ratio

14 CM Income Statement Approach Sales - Variable Expenses Contribution Margin - Fixed Expenses Operating Income ($35) x units sold) – ($21 x units sold) - $7, 000 = 500 posters

Cost-Volume-Profit Analysis 15 The Profit Equation Profit = SP(x) – VC(x) – TFC Equation Abbreviations x = Quantity of units produced and sold SP = Selling price per unit VC = Variable cost per unit; TFC = Total fixed cost $0 = $35(x) - $21(x) - $7, 000 $0 = $14(x) - $7, 000 X = 500 units

16 Short-Cut Approach to Calculating Breakeven Using CM/Units sold = Fixed expenses + Operating income Contribution margin per unit Units sold = $7, 000 + $0 $14 = 500 posters

17 Short-Cut Using Contribution Margin Ratio Sales in $ = Fixed expenses + Operating income Contribution margin ratio Sales in $ = $7, 000 + $0 0. 40 = $17, 500 Dividing fixed costs by CM/unit gives breakeven in units Dividing fixed costs by CM Ratio gives breakeven in sales revenue dollars

Finding the Volume Needed for a Target Profit Using CM/Unit 18 CVP analysis helps managers determine what they need to sell to earn a target amount of profit. Units sold = Fixed expenses + Operating income Contribution margin per unit $7, 000 + $4, 900 $11, 900 = $14 = 850 posters Check our calculations: Sales (850 units) x $35 = $29, 750 Less: Variable Costs (850 x $21) ( 17, 850) Fixed Costs (7, 000) Profit $4, 900

Finding the Sales Volume Needed for a Target Profit Using CM Ratio 19 CVP analysis helps managers determine what amount of sales revenue needed to earn a target amount of profit. Sales $ = Fixed exp + Target profit (operating inc) Contribution margin ratio $7, 000 + $4, 900 = $11, 900 Sales $ = 0. 40 Sales = $29, 750 to generate profit of $4, 900 Check: $29, 750 ÷ $35 = 850 posters

Use information from Bay Cruise Line Data to compute # of dinner cruise tickets it must sell to break even. 20 a. Use the income statement equation approach. ($50 x units) – ($20 x units) $30 x units = $210, 000/$30 units = 7, 000 - $210, 000 b. Profit Equation: (Profit) = SP(x) – VC(x) – TFC $0 x = $50(x) - $210, 000 = 7, 000 units Facts: SP/unit = $50; VC/unit = $20; TFC = $210, 000 Relevant range up to 15, 000 passengers = $0

21 B. Use the shortcut contribution margin/unit approach, then perform a numerical proof to ensure that your answer is correct. Units sold = Fixed expenses + Operating income Contribution margin per unit Units sold =$210, 000 + $0 = 7, 000 tickets $30 Proof: 7000 tix x $50 sp/unit <VC/unit x 7000> <TFC> $350, 000 <$140, 000> <210, 000> = 0 C. Use your answers from a and b to determine the sales revenue needed to break even. 7, 000 units to break even X $50 sales price/unit =

D. Use the contribution margin ratio approach to verify the sales revenue needed to break even. 22 Sales in $ = Fixed expenses + Operating income Contribution margin ratio Sales in $ = $210, 000 + 0 0. 60 (CM/unit ÷ SP/unit) Sales in $ = $210, 000 0. 60 = $350, 000 Sales Revenue to Break even

23 Graphing the CVP Relationships Step 1: Choose a sales volume (Units x $Price) Plot point for total sales revenue Draw sales revenue line from origin through the plotted point

Preparing a CVP Chart Co. sells units for $10 per unit. $20, 000 Sales Dollars $15, 000 $10, 000 Revenues $5, 000 $0 0 500 Volume of Units 1000 1500

Preparing a CVP Chart 25 Step 2: Draw the fixed cost line. Fixed Costs are $4, 000

Preparing a CVP Chart Dollars Step 3: Draw the total cost line (fixed plus variable) Variable cost/unit is $4 $15, 000 $10, 000 Revenues Fixed costs Total cost $5, 000 $0 0 500 1000 1500 Volume of Units

Preparing a CVP Chart Step 4: Identify the breakeven point $20, 000 Breakeven point Dollars $15, 000 $10, 000 $5, 000 $0 0 500 667 1000 Volume of Units 1500

Preparing a CVP Chart Step 5: Mark operating income and operating loss areas on the graph. $20, 000 Breakeven point Dollars $15, 000 tin era Op $10, 000 $5, 000 s os L g tin a r pe O g $0 0 500 667 1000 Volume of Units 1500 om Inc e

Sensitivity Analysis 29 Managers need to be prepared for increasing costs, pricing pressure from competitors, and other changing business conditions. Sensitivity Analysis: Conducts “What if” analysis What if the sales price changes? What if costs change? What if the sales mix changes?

30 What if the Sales Price Changes? Calculate a new contribution margin/unit using the new sales price Use the new contribution margin/unit to compute breakeven sales in units Use the new contribution margin/unit to compute breakeven sales to maintain target profit Using the new breakeven numbers, decide if a change should be made to sales price

Kay want to know what sales price/unit needs to be to earn a profit of $10, 000 next month? 31 Base Info: SP/unit - $35; VC/unit - $21; TFC - $7, 000 Breakeven units – 500 Profit Equation: Profit=SP/unit(x) – VC/unit(x) - TFC $10, 000 = SP(500 units) - $21(500 units) - $7, 000 SP(500 units) = $27, 500 ÷ 500 units SP = $55/unit What if she can sell 700 posters? $10, 000 = SP(700) - $21(700) - $7000; SP = $45. 29

What if Fixed Costs Change? 32 Mgt. considering change in production process that will increase fixed costs/month by $2, 000, but will decrease variable costs/unit to $16. Current Info VC/unit = TFC = Proposed 21 $7, 000 $16 $9, 000 Currently selling 850 posters so Current profit = $35(850) - $21(850) - $7, 000 = $4, 900 Proposed profit = $35(850) - $16(850) - $9, 000 = $7, 150 What if Variable Costs Change? Supplier raises price for Kay’s raw materials. Everything else stays same. What is breakeven point? Higher variable cost/unit has same effect as lower sales price/unit – both reduce product’s

33 What if Fixed Costs & Volume Changes? Sales Mgr thinks a $5, 000 increase in advertising budget would increase sales by $12, 250 to a total of 1200 units. Should advertising budget be increased? Current: SP = $35/unit; Volume = 850 units Incremental CM: $12, 250 x 40% CM Ratio = $4, 900 Increased CM Less: incremental advertising expense (5, 000) Decreased profit $ (100) Proof: Current Proposed Difference Sales $29, 750 $42, 000 $12, 250 (VC) (17, 850) (25, 200) (7, 350) CM 11, 900 16, 800 4, 900 TFC (7, 000) (12, 000) (5, 000) Incr. Profit(Loss) $ 4, 900 4, 800 (100)

34 Information Technology and Sensitivity Analysis Allows managers to perform a wide array of sensitivity analyses before committing to decisions. Uses Excel spreadsheets to perform sensitivity analyses Allows managers to estimate how one change (or several simultaneous changes) affects business operations

35 Breakeven in Sales Revenue: Multiproduct Firm Kay has decided to start selling large posters in addition to regular posters. None of her original costs will change. Large poster sales price = $70; V. C. /unit = $40 so CM/unit = $30. For every 5 regular posters sold, Kay expects to sell 3 large posters. (5/8 of sales will be reg. posters & 3/8 will be large posters, that is a 5: 3 sales mix of posters). Kay estimates total sales of 800 posters. What is weighted-average CMR?

36 Breakeven in Sales Revenue: Multiproduct Firm Total expected contribution margin: Regular posters (500 x $14) $ 7, 000 Large posters (300 x $30) $ 9, 000 Total expected contribution margin $16, 000 Divided by total expected sales revenue: Regular posters (500 x $35) $17, 500 Large posters (300 x $70) 21, 000 Total expected sales ÷ $38, 500 Wtd. Avg. Contribution margin ratio = 41. 558%

37 Breakeven in Sales Revenue: Kay’s Posters Fixed expenses + Operating income Wtd. Avg. Contribution margin ratio B/E - Sales $ = $7, 000 + 0 = $7, 000 0. 41558 = $16, 844 (rounded) Sales Revenue B/E-Sales $ = For every 5 reg. posters, Kay expects to sell 3 lrg posters; 5: 3 sales mix. $16, 844 ÷ 8 posters = $2, 106 x 5 reg. posters= $10, 530 rev from sale of reg. posters, & $2, 106 x 3 large posters = $ 6, 318 rev from sale of lrg posters Now Kay wants to know what sales revenue needs to be to reach target monthly income of $10, 000. (Just replace 0 above with $10, 000)

38 Bay Cruise Line decides to offer 2 types of dinner cruises: regular & executive cruises. Exec. cruise includes free cocktails & a 5 -course dinner on upper deck. Fixed expenses stay at $210, 000/mo & ticket prices & variable expenses are as listed: Regular Cruise Executive Cruise Sales price per ticket $50 $130 Variable expense per passenger $20 $40 Assuming that Bay Cruise Line expects to sell four regular cruises for every executive cruise, compute the weighted-average contribution margin per unit. Sales Mix Calculation Sales price per unit. . . Less: Variable cost per unit. . . Contribution margin per unit. . . . Sales mix. . . . . Contribution margin. . . . . Weighted-average contribution margin per unit ($210/5). . . Regular $ 50 (20) $ 30 x 4 $120 Executive $130 (40) $ 90 x 1 = $ 90 = Total 5 $210 $ 42

39 Same info as previous slide Sales Mix Calculation Regular Executive Total Sales price per unit $ 50 $130 Less: Variable cost per unit (20) (40) Contribution margin per unit $ 30 $ 90 Sales mix x 4 x 1 5 Contribution margin $120 $ 90 $210 Wtd-avg CM peravg. unit C/M/unit ($210/5) higher or lower than the old C/M/unit when $ 42 Is this weighted they just sold regular cruises? (higher) Why? Will this new sales mix cause Bay Cruiseline’s breakeven point to increase or decrease its breakeven point?

40 Sales Mix Calculation Regular Executive Total Sales price per unit $ 50 $130 Less: Variable cost per unit (20) (40) Contribution margin per unit $ 30 $ 90 Sales mix x 4 x 1 5 Contribution margin $120 $ 90 $210 Wtd-avg CM per unit ($210/5) $42 Will this new sales mix cause Bay Cruise Line’s breakeven point to increase or decrease from what it was when it sold only regular cruises? Fixed expenses + Operating income B/E Sales in $ = Weighted Average Contribution margin per unit Sales in $ =$210, 000 + 0 – B/E $42 wtd avg CM/unit = 5, 000 tickets Decrease, down from 7, 000 tickets before

What if the Sales Mix Changes? Must recalculate based on new Sales Mix 41 Sales Mix Calculation Reg Product Large Product Sales price per unit $ 35 $ 70 Less: Variable cost per unit (21) (40) Contribution margin per unit $ 14 $ 30 Sales mix x 5 x 3 Contribution margin $ 70 $ 90 Weighted-average contribution margin per unit ($160/8) $ Calculation 20 Sales Mix Regular Product Large Product Sales price per unit $ 35 Less: Variable cost per unit (21) Contribution margin per unit $ 14 Sales mix x 6 x 2 Contribution margin $ 84 $ 60 Weighted-average contribution margin per unit ($144/8) Total 8 $160 Total $ 70 (40) $ 30 8 $144 $

Common Indicators of Risk 42 Margin of Safety The excess of expected sales over breakeven sales Operating Leverage The relative amount of fixed and variable costs that make up a company’s total costs

Margin of Safety 43 Excess of expected sales over breakeven sales Drop in sales that the company can absorb before incurring a loss Used to evaluate the risk of current operations as well as the risk of new plans 43

44 Margin of Safety for Kay’s Poster Bsn Margin of safety in units Expected sales in units = 950 units = = Margin of safety in dollars − − Breakeven sales in units 500 units 450 units = Expected sales − Breakeven sales = $33, 250 – $17, 500 = $15, 750

45 Margin of Safety as a Percentage Margin of safety as a percentage = Margin of safety in units Expected sales in units = 450 Units 950 Units = 47. 4% (rounded) = = = Margin of safety in dollars Expected sales in dollars $15, 750 $33, 250 47. 4% (rounded)

High Operating Leverage 46 High operating leverage companies have: Higher levels of fixed costs and lower levels of variable costs Higher contribution margin ratios For high operating leverage companies, changes in volume significantly affect operating income, so they face: Higher risk Higher potential for reward Examples include golf courses, hotels, rental car agencies, theme parks, airlines, cruise lines

Low Operating Leverage 47 Low operating leverage companies have: Higher levels of variable costs and lower levels of fixed costs Lower contribution margin ratios For low operating leverage companies, changes in volume do NOT have as significant an effect on operating income, so they face: Lower risk Lower potential for reward Examples include merchandising companies.

Operating Leverage Factor 48 How responsive a Co. ’s operating income is to changes in volume Lowest value for Operating Leverage factor is 1, if Co. has Contribution margin no fixedleverage costs factor = Operating income Operating leverage factor = $13, 300 $6, 300 = 2. 11 (rounded) If sales revenue increases by 10%, then operating income will increase by 10% x 2. 11 (OL factor) = 21% increase in op. income

Using OLF to Measure Expected Change in Profit Taco King & Mexi Land are competitors & reported same sales revenue & before-tax profit during May: 49 If sales drop by 20% for both, which company suffers more? Taco King Mexi Land Sales $40, 000 Variable costs (22, 000) (8, 000) Contribution margin 18, 000 32, 000. Fixed costs (8, 000) (22, 000) $10, 000. Operating Income Taco King Degree of operating leverage Decrease in profit $18, 000 CM = 1. 8 OLF $10, 000 Op. Inc. 1. 8 × 20% = 36% Decline in Profit $40, 000. Mexi Land $32, 000 CM = 3. 2 OLF $10, 000 Op. Inc. 3. 2 × 20% = 64% Decline in Profit Mexi Land’s higher operating leverage results in a larger profit

END OF SEGMENT Professor Garvin, JD; CPA – ACG 2071