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**Cost-Volume-Profit Analysis**

Chapter 10 Cost-Volume-Profit Analysis

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Learning Objectives Determine the number of units that must be sold to break even or to earn a targeted profit. Determine the amount of revenue required to break even or to earn a targeted profit.

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**Learning Objectives (continued)**

Apply cost-volume-profit analysis in a multiple-product setting. Prepare a profit-volume graph and a cost-volume-profit graph and explain the meaning of each.

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**Learning Objectives (continued)**

Explain the impact of risk, uncertainty, and changing variables on cost-volume- profit analysis. Discuss the impact of activity-based costing on cost-volume-profit analysis.

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**Sample Questions Raised and Answered by CVP Analysis**

1. How many units must be sold (or how much sales revenue must be generated) in order to break even? 2. How many units must be sold to earn a before-tax profit equal to $60,000? A before-tax profit equal to 15 percent of revenues? An after-tax profit of $48,750? 3. Will total profits increase if the unit price is increased by $2 and units sold decrease 15 percent? 4. What is the effect on total profit if advertising expenditures increase by $8,000 and sales increase from 1,600 to 1,750 units?

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**Sample Questions Raised and Answered by CVP Analysis (continued)**

5. What is the effect on total profit if the selling price is decreased from $400 to $375 per unit and sales increase from 1,600 units to 1,900 units? 6. What is the effect on total profit if the selling price is decreased from $400 to $375 per unit, advertising expenditures are increased by $8,000, and sales increased from 1,600 units to 2,300 units? 7. What is the effect on total profit if the sales mix is changed?

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**CVP: A Short-Term Planning and Analysis Tool**

Benefits of CVP: Assists in establishing prices of products. Assists in analyzing the impact that volume has on short-term profits. Assists in focusing on the impact that changes in costs (variable and fixed) have on profits. Assists in analyzing how the mix of products affects profits. 4

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**The Basics of Cost-Volume-Profit (CVP) Analysis**

Contribution Margin (CM) is the amount remaining from sales revenue after variable expenses have been deducted.

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**The Basics of Cost-Volume-Profit (CVP) Analysis**

CM goes to cover fixed expenses.

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**The Basics of Cost-Volume-Profit (CVP) Analysis**

After covering fixed costs, any remaining CM contributes to income.

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**The Contribution Approach**

For each additional unit Wind sells, $200 more in contribution margin will help to cover fixed expenses and profit.

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**The Contribution Approach**

Each month Wind must generate at least $80,000 in total CM to break even.

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**The Contribution Approach**

If Wind sells 400 units in a month, it will be operating at the break-even point.

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**The Contribution Approach**

If Wind sells one more bike (401 bikes), net operating income will increase by $200.

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**CVP Relationships in Graphic Form**

Viewing CVP relationships in a graph is often helpful. Consider the following information for Wind Co.:

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CVP Graph Total Sales Total Expenses Dollars Fixed expenses Units

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CVP Graph Profit Area Dollars Break-even point Loss Area Units

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**Cost-Volume-Profit Graph**

Total Revenue Revenue Profit Total Cost Y Loss X Units sold X = Break-even point in units Y = Break-even point in revenue

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**Contribution Margin Ratio**

The contribution margin ratio is: For Wind Bicycle Co. the ratio is: Total CM Total sales CM Ratio = $ 80,000 $200,000 = 40%

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**Contribution Margin Ratio**

Or, in terms of units, the contribution margin ratio is: For Wind Bicycle Co. the ratio is: Unit CM Unit selling price CM Ratio = $200 $500 = 40%

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**Contribution Margin Ratio**

At Wind, each $1.00 increase in sales revenue results in a total contribution margin increase of 40¢. If sales increase by $50,000, what will be the increase in total contribution margin?

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**Contribution Margin Ratio**

A $50,000 increase in sales revenue

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**Contribution Margin Ratio**

A $50,000 increase in sales revenue results in a $20,000 increase in CM. ($50,000 × 40% = $20,000)

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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

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**Unit contribution margin**

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

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**Changes in Fixed Costs and Sales Volume**

Wind is currently selling 500 bikes per month. The company’s sales manager believes that an increase of $10,000 in the monthly advertising budget would increase bike sales to 540 units. Should we authorize the requested increase in the advertising budget?

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**Changes in Fixed Costs and Sales Volume**

$80,000 + $10,000 advertising = $90,000 Sales increased by $20,000, but net operating income decreased by $2,000.

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**Changes in Fixed Costs and Sales Volume**

The Shortcut Solution

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Break-Even Analysis Break-even analysis can be approached in three ways: Graphical analysis. Equation method. Contribution margin method.

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**At the break-even point**

Equation Method Profits = Sales – (Variable expenses + Fixed expenses) OR Sales = Variable expenses + Fixed expenses + Profits At the break-even point profits equal zero.

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**Here is the information from Wind Bicycle Co.:**

Break-Even Analysis Here is the information from Wind Bicycle Co.:

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**We calculate the break-even point as follows:**

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

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**We calculate the break-even point as follows:**

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

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**Equation Method X = 0.60X + $80,000 + $0**

We can also use the following equation to compute 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

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**Equation Method X = 0.60X + $80,000 + $0 0.40X = $80,000**

We can also use the following equation to compute 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

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**Contribution Margin Method**

The contribution margin method is a variation of the equation method. Fixed expenses Unit contribution margin = Break-even point in units sold Break-even point in total sales dollars Fixed expenses CM ratio =

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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

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**Unit contribution margin**

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 contribution margin Break-even = $1,300 $1.49 per cup - $0.36 per cup = $1.13 per cup = 1,150 cups

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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

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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 =

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**Target Profit Analysis**

Suppose Wind Co. wants to know how many bikes must be sold to earn a profit of $100,000. We can use our CVP formula to determine the sales volume needed to achieve a target net profit figure.

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**The CVP Equation Sales = Variable expenses + Fixed expenses + Profits**

$500Q = $300Q + $80, $100,000 $200Q = $180,000 Q = 900 bikes

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**The Contribution Margin Approach**

We can determine the number of bikes that must be sold to earn a profit of $100,000 using the contribution margin approach. Fixed expenses + Target profit Unit contribution margin = Unit sales to attain the target profit $80, $100,000 $200 per bike = 900 bikes

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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

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Quick Check Fixed expenses + Target profit Unit contribution margin Unit sales to attain target profit $1,300 + $2,500 $ $0.36 = $3,800 $1.13 = 3,363 cups = 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

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**Variable-Costing Income Statement**

Sales (10,000 x $10) $100,000 Less: Variable costs (10,000 x $6) ,000 Contribution margin $ 40,000 Less: Fixed costs ,000 Profit before taxes $0 Less: Income taxes Profit after taxes $ =====

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**CVP Analysis: Targeted After-Tax Income**

What sales in units and dollars are needed to obtain a targeted profit after taxes of $24,000? Let X = break-even point in units Sales $ = $10X Less: Variable costs$ = X Contribution margin$ = $ 4X Less: Fixed costs ,000 Profit before taxes $ Less income taxes Profit after taxes $24,000 ======

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**CVP Analysis: Targeted After-Tax Income (continued)**

The Approach: AFTER = Profit after taxes BEFORE = Profit before taxes AFTER = (1 - tax rate) x BEFORE $24,000 = (1 - .4) x BEFORE $24,000/.6 = BEFORE $40,000 = BEFORE

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**Sales 10X CV (6X) CM 4 X FC (40,000) EBT ? Income Tax (?) EAT 24,000**

EAT = (1-Tax) EBT 24,000 = (1-0.4) EBT EBT = 40,000 EBT - Income Tax = EAT 40,000 – IT = 24,000 IT = 16,000 4X - 40,000 = 40,000 X = 20,000

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**CVP Analysis: Targeted After-Tax Income (continued)**

The income statement below illustrates that $200,000 in sales will give you an after-tax profit of $24,000. Sales $200,000 Less: Variable costs 120,000 Contribution margin $ 80,000 Less: Fixed costs ,000 Profit before taxes $ 40,000 Less: Income taxes ,000 Profit after taxes $ 24,000 ======

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The Margin of Safety Excess of budgeted (or actual) sales over the break-even volume of sales. The amount by which sales can drop before losses begin to be incurred. Margin of safety = Total sales - Break-even sales Let’s calculate the margin of safety for Wind.

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The Margin of Safety Wind has a break-even point of $200,000. If actual sales are $250,000, the margin of safety is $50,000 or 100 bikes.

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The Margin of Safety The margin of safety can be expressed as 20% of sales. ($50,000 ÷ $250,000)

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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

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**Margin of safety percentage**

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 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%

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Operating Leverage A measure of how sensitive net operating income is to percentage changes in sales. With high leverage, a small percentage increase in sales can produce a much larger percentage increase in net operating income. Contribution margin Net operating income Degree of operating leverage =

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Operating Leverage $100,000 $20,000 = 5

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**Here’s the verification!**

Operating Leverage With a operating leverage of 5, if Wind increases its sales by 10%, net operating income would increase by 50%. Here’s the verification!

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**10% increase in sales from . . . results in a 50% increase in**

Operating Leverage 10% increase in sales from $250,000 to $275, . . . results in a 50% increase in income from $20,000 to $30,000.

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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

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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 Contribution margin Net operating income Operating leverage = $2,373 $1,073 = 2.21

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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%

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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%

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**Verify increase in profit**

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**The Concept of Sales Mix**

Sales mix is the relative proportions in which a company’s products are sold. Different products have different selling prices, cost structures, and contribution margins. Let’s assume Wind sells bikes and carts and see how we deal with break-even analysis.

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**Multiple-Product Example**

Product P - V = CM x Mix = Total CM A $10 - $6 = $4 x 3 = $12 B = x 2 = Total CM per package $18 === Total fixed expenses = $180,000

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**Multiple-Product Example (continued)**

Break-even point: X = Fixed cost / Unit contribution margin = $180,000 / $18 = 10,000 packages to break even Each package contains 3 units of A and 2 units of B. Therefore, to break even, we need to sell the following units of A and B: A: 3 x 10,000 = 30,000 units B: 2 x 10,000 = 20,000 units

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**Multi-product break-even analysis**

Wind Bicycle Co. provides the following information: $265,000 $550,000 = 48.2% (rounded)

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**Multi-product break-even analysis**

Fixed expenses CM Ratio Break-even sales = $170,000 0.482 = $352,697 = Rounding error

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**Another 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 of $50,000? 13

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**Another Multiple-Product Example: BEP**

BEP = Fixed cost / CM ratio for sales mix = $130,000 / 0.486 = $267,490 for the firm BEP for Regular Model: (400/600) x $267,490 = $178,327 BEP for Deluxe Model: (200/600) x $267,490 = $89,163 14

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**Another Multiple-Product Example: Targeted Revenue**

BEP = (Fixed Costs + Targeted income) / CM ratio per sales mix = ($130,000 + $50,000) / 0.486 = $370,370 for the firm BEP for Regular Model: (400/600) x $370,370 = $246,913 BEP for Deluxe Model: (200/600) x 370,370 = $123,457 15

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**CVP and ABC Assume the following: Sales price per unit $15**

Variable cost Fixed costs (conventional) $180,000 Fixed costs (ABC) ,000 with $80,000 subject to ABC analysis Other Data: Unit Level of Variable Activity Activity Driver Costs Driver Setups $ Inspections 1. What is the BEP under conventional analysis? 2. What is the BEP under ABC analysis? 3. What is the BEP if setup cost could be reduced to $450 and inspection cost reduced to $40? 18

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**CVP and ABC (continued)**

1. Break-even units (conventional analysis) BEP = $180,000/$10 = 18,000 units 2. Break-even units (ABC analysis) BEP = [$100, (100 x $500) + (600 x $50)]/$10 3. BEP = [$100,000 + (100 x $450) + (600 x $40)]/$10 = 16,900 units What implications does ABC have for improving performance? 19

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**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).

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