cost-volume-profit relationships

Cost-Volume-Profit Relationships

Chapter 03

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2

Quick Check

Racing Bicycle Company

•Selling price per unit: $500

•Variable costs per unit: $300

•Fixed costs per month: $80,000

What is the company’s net operating income if the

production and selling is 500 units in January

2014?

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Contribution Margin Approach

Total Per UnitSales (500 bicycles) 250,000$ 500$ Less: Variable expenses 150,000 300 Contribution margin 100,000 200$

Less: Fixed expenses 80,000 Net operating income 20,000$

Racing Bicycle CompanyContribution Income Statement

For January, 2014

What is the implication of Contribution margin per unit?

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CVP Graph

300 units 400 units 500 unitsSales 150,000$ 200,000$ 250,000$ Variable expenses 90,000 120,000 150,000 Contribution margin 60,000$ 80,000$ 100,000$ Fixed expenses 80,000 80,000 80,000 Net operating income (20,000)$ -$ 20,000$

300 units 400 units 500 unitsSales 150,000$ 200,000$ 250,000$ Variable expenses 90,000 120,000 150,000 Contribution margin 60,000$ 80,000$ 100,000$ Fixed expenses 80,000 80,000 80,000 Net operating income (20,000)$ -$ 20,000$

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-

50,000

100,000

150,000

200,000

250,000

300,000

350,000

400,000

450,000

- 100 200 300 400 500 600 700 800

CVP Graph

Fixed costs

units

$

Total costs

Sales

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Contribution Margin Ratio (CM Ratio)

Total Per Unit %Sales (500 bicycles) 250,000$ 500$ 100%Less: Variable expenses 150,000 300 60%Contribution margin 100,000 200$ 40%

Less: Fixed expenses 80,000 Net operating income 20,000$

Racing Bicycle CompanyContribution Income Statement

For the Month of June

What is the implication of Contribution margin ratio?

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Contribution Margin Ratio (CM Ratio)

The contribution margin ratio at Racing Bicycle is:

CM per unitSP per unit

CM Ratio = = 40%$200$500

=

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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. 1.319b. 0.758c. 0.242d. 4.139

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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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Current Sales (500 bikes)

Projected Sales (540

bikes)

Sales 250,000$ 270,000$ Less: variable expenses 150,000 162,000 Contribution margin 100,000 108,000 Less: fixed expenses 80,000 90,000 Net operating income 20,000$ 18,000$

Current Sales (500 bikes)

Projected Sales (540

bikes)

Sales 250,000$ 270,000$ Less: variable expenses 150,000 162,000 Contribution margin 100,000 108,000 Less: fixed expenses 80,000 90,000 Net operating income 20,000$ 18,000$


Sales increased by $20,000, but net operating income decreased by $2,000..

Sales increased by $20,000, but net operating income decreased by $2,000..

$80,000 + $10,000 advertising = $90,000$80,000 + $10,000 advertising = $90,000

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The Shortcut SolutionThe Shortcut Solution

Increase in CM (40 units X $200) 8,000$ Increase in advertising expenses 10,000 Decrease in net operating income (2,000)$

Increase in CM (40 units X $200) 8,000$ Increase in advertising expenses 10,000 Decrease in net operating income (2,000)$

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Break-Even Analysis

Break-even analysis can be approached in three ways:

1. Graphical analysis.2. Equation method.3. Contribution margin method.

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Equation Method

Profits = Sales – (Variable expenses + Fixed expenses)

Sales = Variable expenses + Fixed expenses + Profits

OR

At the break-even point profits equal zero.

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Break-Even AnalysisHere is the information from Racing Bicycle Co.:

Total Per Unit PercentSales (500 bikes) 250,000$ 500$ 100%Less: variable expenses 150,000 300 60%Contribution margin 100,000$ 200$ 40%

Less: fixed expenses 80,000 Net operating income 20,000$

Total Per Unit PercentSales (500 bikes) 250,000$ 500$ 100%Less: variable expenses 150,000 300 60%Contribution margin 100,000$ 200$ 40%

Less: fixed expenses 80,000 Net operating income 20,000$

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Equation Method We calculate the break-even point as follows:


$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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Equation Method We calculate the break-even point as follows:


$500Q = $300Q + $80,000 + $0$200Q = $80,000 Q = $80,000 ÷ $200 per bike Q = 400 bikes

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Equation Method We can also use the following equation to compute the break-even point in sales dollars.


X = 0.60X + $80,000 + $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 X = $80,000 ÷ 0.40 X = $200,000

We can also use the following equation to compute the break-even point in sales dollars.


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Contribution Margin Method

The contribution margin method is a variation of the equation method.

Fixed expensesUnit contribution margin

=Break-even point

in units sold

Fixed expenses CM ratio

=Break-even point intotal sales dollars

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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. 872 cupsb. 3,611 cupsc. 1,200 cupsd. 1,150 cups

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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. $1,300b. $1,715c. $1,788d. $3,129

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Target Profit Analysis

Suppose Racing Bicycle 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


$500Q = $300Q + $80,000 + $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

$80,000 + $100,000 $200 per bike

= 900 bikes

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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 cupsb. 2,212 cupsc. 1,150 cupsd. 4,200 cups

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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

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Racing Bicycle has a break-even point of $200,000. If actual sales are $250,000, the margin of safety is $50,000 or 100

bikes.Break-even

sales 400 units

Actual sales 500 units

Sales 200,000$ 250,000$ Less: variable expenses 120,000 150,000 Contribution margin 80,000 100,000 Less: fixed expenses 80,000 80,000 Net operating income -$ 20,000$

Break-even sales

400 unitsActual sales

500 unitsSales 200,000$ 250,000$ Less: variable expenses 120,000 150,000 Contribution margin 80,000 100,000 Less: fixed expenses 80,000 80,000 Net operating income -$ 20,000$

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The margin of safety can be expressed as 20% of sales.

($50,000 ÷ $250,000)

Break-even sales



Break-even sales



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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 cupsb. 950 cupsc. 1,150 cupsd. 2,100 cups

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Example – SAA• School of Accounting & Auditing launches monthly tax accounting

courses (10 sessions, 2 hours each). There are three alternatives for tuition fees:

tuition fee No. of learnersVND 600,000 25 500,000 32 400,000 42

• Each course incurs: ▫Instructor expense: VND500,000/session; ▫Classroom rent expense: VND100,000/session;▫Advertising & administrative expense: VND3,000,000đ/course▫Learning materials & certification preparation: VND100,000/learner

• How many leaners should each course have to breakeven?• What alternative the School should choose?

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Example - SAA

Alt. #1 Alt. #2 Alt. #31 Tuition fee 2 Variable costs per learner3 Contribution margin per learner4 Contribution margin ratio5 Total fixed costs6 Breakeven - No. of learners7 Breakeven - Sales dollars8 Expected No. of learners9 Expected operating profit

10 Expected Sales dollars11 Safety margin ($)12 Safety margin (No. of learners)

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Cost structure refers to the types and relative proportions of variable and fixed

costs that a business incurs.

Which cost structure is better? More fixed or more variable?

Cost structure refers to the types and relative proportions of variable and fixed

costs that a business incurs.

Which cost structure is better? More fixed or more variable?

Cost structure

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Ford Vinaxuki

Sales 1.000 1.000

Variable costs 500 600

Contribution margin 500 400

Fixed costs 300 200

Net operating margin 200 200

Cost structure

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What is an increase in net operating income if each

company’s sales increase by 20%?


company’s sales increase by 20%?

Cost structure

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FordIncrease in Operating

income:

VinaxukiIncrease in Operating

income:

Cost structure

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company’s sales decrease by 20%?


company’s sales decrease by 20%?

Cost structure

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VinaxukiDecrease in Operating

income:

FordDecrease in Operating

income:

Cost structure

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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 ofoperating leverage =

∆% Sales

Degree of operating

leverage (DOL)=

∆%Net operating income

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Operating leverage

Ford: DOL = 500/200 = 2,5Vinaxuki: DOL = 400/200 =2,0

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Ford•Increase in Net operating income (%) = 2,5 x 20% = 50%•Increase in Net operating income ($) = 50% x 200 = 100

Vinaxuki•Increase in Net operating income (%)= 2,0 x 20% = 40%• Increase in Net operating income ($) = 40% x 200 = 80

∆%Net operating income = DOL x ∆% Sales

Operating levegare

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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. 2.21b. 0.45c. 0.34d. 2.92

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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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The Concept of Sales Mix

•Sales mix is the relative proportions in which a company’s products are sold.▫In units▫In dollars

•Average contribution margin per unit = ∑ UCMi X unit sales mixi

•Average contribution margin rate = ∑ CM ratei X $ sales mixi

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Average contribution margin per unit500 x 70% + 600 x 30% = 530

70% PepsiUCM: VND500 per litre

30% 7upUCM: VND600 per litre

Breakeven point3.180.000/530 = 6000 litres

6000 x 70% = 4200 litres 6000x 30% = 1800 litres

Breakeven analysis with sales mix

Fixed costs

VND318,000,000

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Tỷ lệ lợi nhuận góp bình quân 30% x 70% + 40% x 30% = 33%

Breakeven point3.300/33% = VND 10,000 mil.

70% Telephone servicesCM rate 30%

30% Internet services CM rate 40%

Fixed costsVND3,300 mil.

Breakeven analysis with sales mix

10,000 x 70% = VND 7,000mil.10,000x 30% = VND 3,000

mil.

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Example 2

In VND 000’ Sticky rice Mooncake

Baked Mooncake

Total

Unit selling price 20 25

Unit variable costs 8 12,5

Total fixed costs 60,000

Sales for Jan. 2014 40% 60% 300,000

Sales for Feb. 2014 60% 40% 300,000

Nhu Ngoc is a Mooncake producer. The information for the performance in Jan. and Feb. 2014 as below. Calculate net operating income for each month and explain for the difference.

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Total1 piece 1 piece

SalesVariable costsContribution marginFixed costsNet operating income

Nhu Ngoc Inc.Income StatementFor January, 2014

Sticky rice mooncake

Baked mooncake

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Total1 piece 1 piece

SalesVariable costsContribution marginFixed costsNet contribution margin

Nhu Ngoc Inc.Income statement

For Feb. 2014Sticky rice mooncake

Baked mooncake

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Key Assumptions of CVP Analysis

Selling price is constant. Costs are linear and can be accurately

divided into variable (constant per unit) and fixed (constant in total) elements.

In multiproduct companies, the sales mix is constant.

In manufacturing companies, inventories do not change (units produced = units sold).

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End of Chapter 03

cost-volume-profit relationships

Documents

fixed costs

contribution margin

fixed expenses80

sales variable expenses

variable costs

contribution margin100

average fixed expense

companys net operating