1. Cost-Volume-Profit Relationships
Chapter 03
Chapter 5: Cost-volume-profit relationships
Cost-volume-profit (CVP) analysis helps managers understand the interrelationships among cost, volume, and profit by focusing their attention on the interactions among the prices of products, volume of activity, per unit variable costs, total fixed costs, and mix of products sold. It is a vital tool used in many business decisions such as deciding what products to manufacture or sell, what pricing policy to follow, what marketing strategy to employ, and what type of productive facilities to acquire.

2. Racing Bicycle Company
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?

3. Contribution Margin Approach
The contribution margin ratio is calculated by dividing the total contribution margin by total sales. In the case of Racing Bicycle, the ratio is 40%. Thus, each $1.00 increase in sales results in a total contribution margin increase of 40¢.
What is the implication of Contribution margin per unit?

4. CVP Graph

5. CVP Graph $
Sales
Total costs
Fixed costs
units

6. Contribution Margin Ratio (CM Ratio)
The contribution margin ratio is calculated by dividing the total contribution margin by total sales. In the case of Racing Bicycle, the ratio is 40%. Thus, each $1.00 increase in sales results in a total contribution margin increase of 40¢.
What is the implication of Contribution margin ratio?

7. Contribution Margin Ratio (CM Ratio)
The contribution margin ratio at Racing Bicycle is:
CM per unit
SP per unit
CM Ratio =
= 40%
$200
$500 =
The CM ratio can also be calculated by dividing the contribution margin per unit by the selling price per unit. Racing Bicycle has a CM ratio of 40%. This means that for each dollar increase in sales the company will produce 40¢ in contribution margin.

8. 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

9. 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?

10. 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.

11. Changes in Fixed Costs and Sales Volume
The Shortcut Solution

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

13. 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.

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

15. 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

16. 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

17. 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

18. 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

19. 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 =

20. 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

21. 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

22. 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.

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

24. 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

25. 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

26. 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

27. The Margin of Safety
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.

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

29. 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

30. 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 learners
VND 600,
500,
400,
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?

31. Example - SAA

32. 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?

33. Cost structure Ford Vinaxuki Sales 1.000 Variable costs 500 600
Contribution margin
400
Fixed costs
300
200
Net operating margin

34. Cost structure
What is an increase in net operating income if each company’s sales increase by 20%?

35. Cost structure Ford Increase in Operating income: Vinaxuki

36. Cost structure
What is an increase in net operating income if each company’s sales decrease by 20%?

37. Cost structure Vinaxuki Decrease in Operating income: Ford
Generally, companies with a high fixed cost structure will show higher net income in good years than companies with lower fixed cost structures. Just the opposite is true in bad years. Companies with low fixed cost structures enjoy greater stability in income across good and bad years.
Ford
Decrease in Operating income:

38. 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.
∆% Sales
Degree of operating leverage (DOL) =
∆%Net operating income
Contribution margin
Net operating income
Degree of
operating leverage =

39. Operating leverage Ford: DOL = 500/200 = 2,5
Vinaxuki: DOL = 400/200 =2,0

40. ∆%Net operating income = DOL x ∆% Sales
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

41. 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

42. 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%

43. 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
Different products have different selling prices, cost structures, and contribution margins.

44. Average contribution margin per unit
Breakeven analysis with sales mix
70% Pepsi
UCM: VND500 per litre
30% 7up
UCM: VND600 per litre
Average contribution margin per unit
500 x 70% x 30% = 530
Fixed costs
VND318,000,000
6000 x 70% = 4200 litres
6000x 30% = 1800 litres
Breakeven point
/530 = 6000 litres

45. Breakeven analysis with sales mix
30% Internet services
CM rate 40%
70% Telephone services
CM rate 30%
Tỷ lệ lợi nhuận góp bình quân
30% x 70% + 40% x 30% = 33%
Fixed costs
VND3,300 mil.
10,000 x 70% = VND 7,000mil.
10,000x 30% = VND 3,000 mil.
Breakeven point
3.300/33% = VND 10,000 mil.

46. Example 2
Nhu Ngoc is a Mooncake producer. The information for the performance in Jan. and Feb as below. Calculate net operating income for each month and explain for the difference.
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

49. 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).
Here are the four key assumptions of cost-volume-profit analysis. You are probably familiar with the first three by now. The forth assumption tells us that there can be no change in inventory levels. That is, all units produced are sold in the current period.

50. End of Chapter 03
End of Chapter 5.