# Cost-Volume-Profit Analysis

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Cost-Volume-Profit Analysis
Chapter 10 Cost-Volume-Profit Analysis

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.

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.

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.

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?

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?

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

The Basics of Cost-Volume-Profit (CVP) Analysis
Contribution Margin (CM) is the amount remaining from sales revenue after variable expenses have been deducted.

The Basics of Cost-Volume-Profit (CVP) Analysis
CM goes to cover fixed expenses.

The Basics of Cost-Volume-Profit (CVP) Analysis
After covering fixed costs, any remaining CM contributes to income.

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

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

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

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

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

CVP Graph Total Sales Total Expenses Dollars Fixed expenses Units

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

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

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%

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%

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?

Contribution Margin Ratio
A \$50,000 increase in sales revenue

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

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
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

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?

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.

Changes in Fixed Costs and Sales Volume
The Shortcut Solution

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

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.

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

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

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

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

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

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 =

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

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

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

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 =

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.

The CVP Equation Sales = Variable expenses + Fixed expenses + Profits
\$500Q = \$300Q + \$80, \$100,000 \$200Q = \$180,000 Q = 900 bikes

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

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

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

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 \$ =====

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 ======

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

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

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 ======

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.

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.

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

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 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%

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 =

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

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!

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.

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

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

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%

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%

Verify increase in profit

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.

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

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

Multi-product break-even analysis
Wind Bicycle Co. provides the following information: \$265,000 \$550,000 = 48.2% (rounded)

Multi-product break-even analysis
Fixed expenses CM Ratio Break-even sales = \$170,000 0.482 = \$352,697 = Rounding error

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

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

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

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

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

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).