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Cost-Volume-Profit Relationships

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Cost-Volume-Profit Relationships

Chapter 03

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?

What is the implication of Contribution margin per unit?

Sales

Total costs

Fixed costs

$

units

What is the implication of Contribution margin ratio?

CM per unit

SP per unit

CM Ratio =

$200

$500

= 40%

The contribution margin ratio at Racing Bicycle is:

=

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. 1.319

b. 0.758

c. 0.242

d. 4.139

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?

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

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

The Shortcut Solution

Break-even analysis can be approached in three ways:

- Graphical analysis.
- Equation method.
- Contribution margin 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 Racing Bicycle Co.:

- 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:

Sales = Variable expenses + Fixed expenses + Profits

$500Q = $300Q + $80,000 + $0

$200Q = $80,000

Q = $80,000 ÷ $200 per bike

Q = 400 bikes

- 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 + $80,000 + $0

Where:

X = Total sales dollars

0.60 = Variable expenses as a % of sales

$80,000 = Total fixed expenses

- 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 + $80,000 + $0

0.40X = $80,000

X = $80,000 ÷ 0.40

X = $200,000

Break-even point

in units sold

Fixed expenses

Unit contribution margin

=

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

Break-even point in

total sales dollars

Fixed expenses

CM ratio

=

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. 872 cups

b. 3,611 cups

c. 1,200 cups

d. 1,150 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. 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

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.

Sales = Variable expenses + Fixed expenses + Profits

$500Q = $300Q + $80,000 +$100,000

$200Q = $180,000

Q =900 bikes

Unit sales to attain

the target profit

Fixed expenses + Target profit

Unit contribution margin

=

$80,000 + $100,000

$200 per bike

= 900 bikes

We can determine the number of bikes that must be sold to earn a profit of $100,000 using the contribution margin approach.

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

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

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.

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

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. 950 cups

c. 1,150 cups

d. 2,100 cups

- School of Accounting & Auditing launches monthly tax accounting courses (10 sessions, 2 hours each). There are three alternatives for tuition fees:
tuition feeNo. of learners

VND 600,00025

500,00032

400,00042

- 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?

Cost structure

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

What is an increase in net operating income if each company’s sales increaseby20%?

Ford

Increase in Operating income:

Vinaxuki

Increase in Operating income:

Cost structure

Cost structure

What is an increase in net operating income if each company’s sales decreaseby20%?

Vinaxuki

Decrease in Operating income:

Ford

Decrease in Operating income:

Cost structure

Degree of

operating leverage

Contribution margin

Net operating income

=

Degree of operating leverage (DOL)

∆%Net operating income

=

∆% Sales

- 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.

Operating leverage

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

Operating levegare

∆%Net operating income = DOL x ∆% Sales

- 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

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

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%

- 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

30% 7up

UCM: VND600 per litre

70% Pepsi

UCM: VND500 per litre

Average contribution margin per unit

500 x 70% + 600 x 30% = 530

6000x 30% = 1800 litres

6000 x 70% = 4200 litres

Breakeven point

3.180.000/530 = 6000 litres

Breakeven analysis with sales mix

Fixed costs

VND318,000,000

Tỷ lệ lợi nhuận góp bình quân

30% x 70% + 40% x 30% = 33%

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

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

Breakeven point

3.300/33% = VND 10,000 mil.

30% Internet services

CM rate 40%

70% Telephone services

CM rate 30%

Fixed costs

VND3,300 mil.

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.

- 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).