# Cvp Analysis

Measuring, Monitoring, and Motivating Performance Cost Management Chapter 3 Cost-Volume-Profit Analysis Prepared by Gail Kaciuba Midwestern State University © John Wiley & Sons, 2005 Chapter 3: Cost-Volume-Profit Analysis Eldenburg & Wolcott’s Cost Management, 1e Slide # 1 Chapter 3: Cost-Volume-Profit Analysis Learning objectives •? - **Cvp Analysis** introduction?? •? •? •? •? •? Q1: What is cost-volume-profit (CVP) analysis, and how is it used for decision making? Q2: How are CVP calculations performed for a single product? Q3: How are CVP calculations performed for multiple products?

Q4: What is the breakeven point? Q5: What assumptions and limitations should managers consider when using CVP analysis? Q6: How are the margin of safety and operating leverage used to assess operational risk? Chapter 3: Cost-Volume-Profit Analysis Eldenburg & Wolcott’s Cost Management, 1e Slide # 2 © John Wiley & Sons, 2005 Q1, Q4: CVP Analysis and the Breakeven Point •? CVP analysis looks at the relationship between selling prices, sales volumes, costs, and profits. •? The breakeven point (BEP) is where total revenue equal total costs. $ BEP in sales $ Total Revenue (TR)

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Total Costs (TC) units BEP in units © John Wiley & Sons, 2005 Chapter 3: Cost-Volume-Profit Analysis Eldenburg & Wolcott’s Cost Management, 1e Slide # 3 Q1: How is CVP Analysis Used? •? CVP analysis can determine, both in units and in sales dollars: •? the volume required to break even •? the volume required to achieve target profit levels •? the effects of discretionary expenditures •? the selling price or costs required to achieve target volume levels •? CVP analysis helps analyze the sensitivity of profits to changes in selling prices, costs, volume and sales mix.

© John Wiley & Sons, 2005 Chapter 3: Cost-Volume-Profit Analysis Eldenburg & Wolcott’s Cost Management, 1e Slide # 4 Q2: CVP Calculations for a Single Product Units required to F + Profit achieve target = Q = P -V pretax profit where F = total fixed costs P = selling price per unit V = variable cost per unit P – V = contribution margin per unit To find the breakeven point in units, set Profit = 0. Chapter 3: Cost-Volume-Profit Analysis Eldenburg & Wolcott’s Cost Management, 1e © John Wiley & Sons, 2005 Slide # 5 Q2: CVP Calculations for a Single Product

Sales $ required to achieve target = F + Profit CMR pretax profit where F = total fixed costs CMR = contribution margin ratio = (P- V)/P Note that CMR can also be computed as Total Revenue ? Total Variable Costs CMR = Total Revenue To find the breakeven point in sales $, set Profit = 0. © John Wiley & Sons, 2005 Chapter 3: Cost-Volume-Profit Analysis Eldenburg & Wolcott’s Cost Management, 1e Slide # 6 Q2: Breakeven Point Calculations Bill’s Briefcases makes high quality cases for laptops that sell for $200. The variable costs per briefcase are $80, and the total fixed costs are $360,000.

Find the BEP in units and in sales $ for this company. F +0 $360,000 BEP in units = = P ? V $200 / unit ? $80 / unit $360,000 = = 3,000 units $120 / unit F $360,000 F +0 = = BEP in sales $ = (P ? V ) / P ($200 ? $80) / $200 CMR $360,000 = = $600,000 60% © John Wiley & Sons, 2005 Chapter 3: Cost-Volume-Profit Analysis Eldenburg & Wolcott’s Cost Management, 1e Slide # 7 Q2: CVP Graph Draw a CVP graph for Bill’s Briefcases. What is the pretax profit if Bill sells 4100 briefcases? If he sells 2200 briefcases? Recall that P = $200, V = $80, and F = $360,000. TR $1000s $600 $360 -$96,000 $132,000

Profit at 4100 units = $120 x 4100 – $360,000. TC Profit at 2200 units = $120 x 2200 – $360,000. More easily: 4100 units is 1100 units past BEP, so profit = $120 x 1100 units; 2200 units is 800 units before BEP, so loss = $120 x 800 units. 3000 4100 2200 © John Wiley & Sons, 2005 units Chapter 3: Cost-Volume-Profit Analysis Eldenburg & Wolcott’s Cost Management, 1e Slide # 8 Q2: CVP Calculations How many briefcases does Bill need to sell to reach a target pretax profit of $240,000? What level of sales revenue is this? Recall that P = $200, V = $80, and F = $360,000.

Units needed to F + Profit $360,000 + $240,000 = reach target = $120 / unit P ? V pretax profit = 5,000 units Sales $ required F + $240,000 F = to reach target = (P ? V ) / P CMR pretax profit $600,000 = = $1,000,000 60% © John Wiley & Sons, 2005 Chapter 3: Cost-Volume-Profit Analysis Eldenburg & Wolcott’s Cost Management, 1e Of course, 5,000 units x $200/unit = $1,000,000, too. But sometimes you only know the CMR and not the selling price per unit, so this is still a valuable formula. Slide # 9 Q2: CVP Calculations How many briefcases does Bill need to sell to reach a target after-tax profit of $319,200 if the tax rate is 30%?

What level of sales revenue is this? Recall that P = $200, V = $80, and F = $360,000. First convert the target after-tax profit to its target pretax profit: After-tax profit $319,200 Pretax profit = = = $456,000 (1 ? Tax rate) (1 ? 0. 3) Units needed to $360,000 + $456,000 reach target = = 6,800 units $120 / unit pretax profit Sales $ needed to reach target pretax profit © John Wiley & Sons, 2005 $360,000 + $456,000 = = $1,360,000 60% Chapter 3: Cost-Volume-Profit Analysis Eldenburg & Wolcott’s Cost Management, 1e Slide # 10 Q1,2: Using CVP to Determine Target Cost Levels

Suppose that Bill’s marketing department says that he can sell 6,000 briefcases if the selling price is reduced to $170. Bill’s target pretax profit is $210,000. Determine the highest level that his variable costs can so that he can make his target. Recall that F = $360,000. Use the CVP formula for units, but solve for V: Q = 6,000 units = $360,000 + $210,000 $170/unit ? V $170/unit ? V = $360,000 + $210,000 = $95/unit 6,000 units V = $75/unit If Bill can reduce his variable costs to $75/unit, he can meet his goal. © John Wiley & Sons, 2005 Chapter 3: Cost-Volume-Profit Analysis Eldenburg & Wolcott’s Cost Management, 1e Slide # 11

Q5: Uncertainties in Bill’s Decision •? After this analysis, Bill needs to consider several issues before deciding to lower his price to $170/ unit. •? How reliable are his marketing department’s estimates? •? Is a $5/unit decrease in variable costs feasible? •? Will this decrease in variable costs affect product quality? •? If 6,000 briefcases is within his plant’s capacity but lower than his current sales level, will the increased production affect employee morale or productivity? © John Wiley & Sons, 2005 Chapter 3: Cost-Volume-Profit Analysis Eldenburg & Wolcott’s Cost Management, 1e Slide # 12

Q1: Using CVP to Compare Alternatives •? CVP analysis can compare alternative cost structures or selling prices. •? high salary/low commission vs. lower salary/higher commission for sales persons •? highly automated production process with low variable costs per unit vs. lower technology process with higher variable costs per unit and lower fixed costs. •? broad advertising campaign with higher selling prices vs. minimal advertising and lower selling prices •? The indifference point between alternatives is the level of sales (in units or sales $) where the profits of the alternatives are equal.

© John Wiley & Sons, 2005 Chapter 3: Cost-Volume-Profit Analysis Eldenburg & Wolcott’s Cost Management, 1e Slide # 13 Q1,2: Using CVP to Compare Alternatives Currently Bill’s salespersons have salaries totaling $80,000 (included in F of $360,000) and earn a 5% commission on each unit ($10 per briefcase). He is considering an alternative compensation arrangement where the salaries are decreased to $35,000 and the commission is increased to 20% ($40 per briefcase). Compute the BEP in units under the proposed alternative. Recall that P = $200 and V = $80 currently. First compute F and V under the proposed plan:

F = $360,000 – $45,000 decrease in salaries = $315,000 V = $80 + $30 increase in commission = $110 Then compute Q under the proposed plan: Units needed to breakeven © John Wiley & Sons, 2005 $315,000 F +0 = = 3,500 units =Q = P ? V $200 / unit – $110/unit Chapter 3: Cost-Volume-Profit Analysis Eldenburg & Wolcott’s Cost Management, 1e Slide # 14 Q1: Determining the Indifference Point Compute the volume of sales, in units, for which Bill is indifferent between the two alternatives. The indifference point in units is the Q for which the profit equations of the two alternatives are equal.

Current Plan Contribution margin per unit Total fixed costs $120 $360,000 Proposed Plan $90 $315,000 Profit (current plan) = $120Q – $360,000 Profit (proposed plan) = $90Q – $315,000 $120Q – $360,000 = $90Q – $315,000 $30Q = $45,000 © John Wiley & Sons, 2005 Q = 1,500 units Slide # 15 Chapter 3: Cost-Volume-Profit Analysis Eldenburg & Wolcott’s Cost Management, 1e Q1,2: CVP Graphs of the Indifference Point Draw a CVP graph for Bill’s that displays the costs under both alternatives. Notice that the total revenue line for both alternatives is the same, but the total cost lines are different.

BEP for the current plan TR TC-proposed plan TC-current plan $600 $360 $315 BEP for the proposed plan indifference point between the plans 1500 3000 3500 $1000s units © John Wiley & Sons, 2005 Chapter 3: Cost-Volume-Profit Analysis Eldenburg & Wolcott’s Cost Management, 1e Slide # 16 Q1,2: Comparing Alternatives The current plan breaks even before the proposed plan. At 1500 units, the plans have the same total cost. $1000s TR TC-proposed plan TC-current plan $600 $360 $315 Each unit sold provides a larger contribution to profits under the current plan. 1500 3000 3500 units © John Wiley & Sons, 2005

Chapter 3: Cost-Volume-Profit Analysis Eldenburg & Wolcott’s Cost Management, 1e Slide # 17 Q5: Uncertainties in Bill’s Decision •? Hopefully Bill is currently selling more than 1500 briefcases, because profits are negative under BOTH plans at this point. •? The total costs of the current plan are less than the those of the proposed plan at sales levels past 1500 briefcases. •? Therefore, it seems the current plan is preferable to the proposed plan. However, . . . © John Wiley & Sons, 2005 Chapter 3: Cost-Volume-Profit Analysis Eldenburg & Wolcott’s Cost Management, 1e Slide # 18

Q5: Uncertainties in Bill’s Decision . . . this may not be true because the level of future sales is always uncertain. •? What if the briefcases were a new product line? •? Estimates of sales levels may be highly uncertain. •? The lower fixed costs of the proposed plan may be safer. •? The plans may create different estimates of the likelihood of various sales levels. •? Salespersons may have an incentive to sell more units under the proposed plan. © John Wiley & Sons, 2005 Chapter 3: Cost-Volume-Profit Analysis Eldenburg & Wolcott’s Cost Management, 1e Slide # 19

Q3: CVP Analysis for Multiple Products When a company sells more than one product the CVP calculations must be adjusted for the sales mix. The sales mix should be stated as a proportion •? of total units sold when performing CVP calculations for in units. •? of total revenues when performing CVP calculations in sales $. © John Wiley & Sons, 2005 Chapter 3: Cost-Volume-Profit Analysis Eldenburg & Wolcott’s Cost Management, 1e Slide # 20 Q3: Sales Mix Computations •? The weighted average contribution margin is the weighted sum of the products’ contribution margins: = ? n ? CM where ? i is product i’s % of total WACM i=1 i i

sales in units, CMi is product i’s contribution margin, and n= the number of products. WACMR = ? n ? iCMR i i=1 •? The weighted average contribution margin ratio is the weighted sum of the products’ contribution margin ratios: where ? i is product i’s % of total sales revenues, CMRi is product i’s contribution margin ratio, and n= the number of products. © John Wiley & Sons, 2005 Chapter 3: Cost-Volume-Profit Analysis Eldenburg & Wolcott’s Cost Management, 1e Slide # 21 Q3: Multiple Product Breakeven Point Peggy’s Kitchen Wares sells three sizes of frying pans. Next year she hopes to sell a total of 10,000 pans.

Peggy’s total fixed costs are $40,800. Each product’s selling price and variable costs is given below. Find the BEP in units for this company. Expected sales in units Selling price per unit Variable costs per unit Contribution margin per unit Small Medium 2,000 5,000 $10. 00 $4. 00 $6. 00 Large Total 3,000 10,000 $15. 00 $18. 00 $8. 00 $11. 00 $7. 00 $7. 00 First note the sales mix in units is 20%:50%:30%, respectively; then compute the weighted average contribution margin: WACM = 20%x$6 + 50%x$7 + 30%x$7 = $6. 80 © John Wiley & Sons, 2005 Chapter 3: Cost-Volume-Profit Analysis Eldenburg & Wolcott’s Cost Management, 1e Slide # 22

Q3: Multiple Product Breakeven Point Next, compute the BEP in terms of total units: Total units F +0 $40,800 needed to = Q = = = 6,000 units P ? V $6. 80/unit breakeven But 6,000 units is not really the BEP in units; the BEP is only 6,000 units if the sales mix remains the same. The BEP should be stated in terms of how many of each unit must be sold: Units required to break even: Small pans 20% 1,200 Medium pans 50% 3,000 Large pans 30% 1,800 6,000 © John Wiley & Sons, 2005 Chapter 3: Cost-Volume-Profit Analysis Eldenburg & Wolcott’s Cost Management, 1e Slide # 23 Q3: Multiple Product Breakeven Point

Find the BEP in sales $ for Peggy’s Kitchen Wares. The total revenue and total variable cost information below is based on the expected sales mix. Expected sales in units Total revenue Total variable costs Total contribution margin Contribution margin ratio Small Medium 2,000 5,000 Large 3,000 Total 10,000 $20,000 $75,000 $54,000 $149,000 $8,000 $40,000 $33,000 $81,000 $12,000 $35,000 $21,000 $68,000 60. 0% 46. 7% 38. 9% 45. 6% First compute the weighted average contribution margin ratio: WACMR = (20/149)x60% + (75/149)x46. 7% + (54/149)x38. 9% = Chapter 3: Cost-Volume-Profit Analysis Eldenburg & Wolcott’s Cost Management, 1e

© John Wiley & Sons, 2005 Slide # 24 Q3: Multiple Product Breakeven Point . . . = 45. 6%, of course! Depending on how the given information is structured, it may be easier to compute the CMR as Total contribution margin/Total revenue. Next compute the BEP in sales $: BEP in sales $ = F + 0 $40,800 = = $89,474* CMR 0. 456 * If you sum the number of units of each size pan required at breakeven times its selling price you get $89,400. The extra $74 in the answer above comes from rounding the contribution margin ratio to three decimals. © John Wiley & Sons, 2005

Chapter 3: Cost-Volume-Profit Analysis Eldenburg & Wolcott’s Cost Management, 1e Slide # 25 Q6: Margin of Safety The margin of safety is a measure of how far past the breakeven point a company is operating, or plans to operate. It can be measured 3 ways. margin of safety in units margin of safety in $ margin of safety percentage = actual or estimated units of activity – BEP in units actual or estimated sales $ – BEP in sales $ Margin of safety in units Actual or estimated units = = Margin of safety in $ = Actual or estimated sales $ Chapter 3: Cost-Volume-Profit Analysis Eldenburg & Wolcott’s Cost Management, 1e Slide # 26

© John Wiley & Sons, 2005 Q6: Margin of Safety Suppose that Bill’s Briefcases has budgeted next year’s sales at 5,000 units. Compute all three measures of the margin of safety for Bill. Recall that P = $200, V = $80, F = $360,000, the BEP in units = 3,000, and the BEP in sales $ = $600,000. margin of safety in units = 5,000 units – 3,000 units = 2,000 units margin of safety in $ = $200 x 5,000 – $600,000 = $400,000 margin of safety percentage = 2,000 units $400,000 = = 40% 5,000 units $200 x 5,000 The margin of safety tells Bill how far sales can decrease before profits go to zero.

Chapter 3: Cost-Volume-Profit Analysis Eldenburg & Wolcott’s Cost Management, 1e © John Wiley & Sons, 2005 Slide # 27 Q6: Degree of Operating Leverage •? The degree of operating leverage measures the extent to which the cost function is comprised of fixed costs. •? A high degree of operating leverage indicates a high proportion of fixed costs. •? Businesses operating at a high degree of operating leverage •? face higher risk of loss when sales decrease, •? but enjoy profits that rise more quickly when sales increase. Chapter 3: Cost-Volume-Profit Analysis Eldenburg & Wolcott’s Cost Management, 1e

© John Wiley & Sons, 2005 Slide # 28 Q6: Degree of Operating Leverage The degree of operating leverage can be computed 3 ways. Contribution margin Profit degree of operating leverage 1 Margin of safety percentage = Fixed costs +1 Profit © John Wiley & Sons, 2005 Chapter 3: Cost-Volume-Profit Analysis Eldenburg & Wolcott’s Cost Management, 1e Slide # 29 Q6: Degree of Operating Leverage Suppose that Bill’s Briefcases has budgeted next year’s sales at 5,000 units. Compute Bill’s degree of operating leverage. Recall that P = $200, V = $80, F = $360,000, and the margin of safety percentage at 5,000 units is 40%.

First, compute contribution margin and profit at 5,000 units: Contribution margin = ($200 – $80) x 5,000 = $600,000 Profit = $600,000 – $360,000 = $240,000 Degree of operating leverage = $600,000 = 2. 5 $240,000 or, degree of operating leverage = $360,000 + 1 = 2. 5 $240,000 or, degree of operating leverage = Chapter 3: Cost-Volume-Profit Analysis Eldenburg & Wolcott’s Cost Management, 1e 1 = 2. 5 40% Slide # 30 © John Wiley & Sons, 2005 Q6: Using the Degree of Operating Leverage •? The degree of operating leverage shows the sensitivity of profits to changes in sales. •? On the prior slide Bill’s degree of operating leverage was 2.

5 and profits were $240,000. •? If expected sales were to increase to 6,000 units, a 20% increase, then profits would increase by 2. 5 x 20%, or 50%, to $360,000. * •? If expected sales were to decrease to 4,500 units, a 10% decrease, then profits would decrease by 2. 5 x 10%, or 25%, to $180,000. ** * $240,000 x 1. 5 = $360,000 ** $240,000 x 0. 75 = $180,000 © John Wiley & Sons, 2005 Chapter 3: Cost-Volume-Profit Analysis Eldenburg & Wolcott’s Cost Management, 1e Slide # 31 Q5: Assumptions in CVP Analysis CVP analysis assumes that costs and revenues are linear within a relevant range of activity.

•? Linear total revenues means that selling prices per unit are constant and the sales mix does not change. •? Offering volume discounts to customers violates this assumption. •? Linear total costs means total fixed costs are constant and variable costs per unit are constant. •? If volume discounts are received from suppliers, then variable costs per unit are not constant. •? If worker productivity changes as activity levels change, then variable costs per unit are not constant. © John Wiley & Sons, 2005 Chapter 3: Cost-Volume-Profit Analysis Eldenburg & Wolcott’s Cost Management, 1e Slide # 32

Q5: Assumptions in CVP Analysis •? These assumptions may induce a small relevant range. •? Results of CVP calculations must be checked to see if they fall within the relevant range. •? Linear CVP analysis may be inappropriate if the linearity assumptions hold only over small ranges of activity. •? Nonlinear analysis techniques are available. •? For example, regression analysis, along with nonlinear transformations of the data, can be used to estimate nonlinear cost and revenue functions. © John Wiley & Sons, 2005 Chapter 3: Cost-Volume-Profit Analysis Eldenburg & Wolcott’s Cost Management, 1e Slide # 33