2. CVP is the study of how Cost and Volume affect the profit
margin. It is a powerful tool in making managerial decisions
including marketing, production, investment, and financing
decisions.
Cost, Volume, Profit (CVP)Analysis
Prices of
products
Volume or
level of
activity
Per unit
variable
costs
Total
Fixed
Costs
Mixed of
products
sold
2
3. Cost Structure is the function of Fixed Cost and Variable Cost.
TC=VC+FC
Cost Structure
VC
(DM,DL, Factory
Overhead)
FC
(Factory rent,
Supervisors
Salary)
Which varies with the changes of
production “Proportionately”
Remain Fixed, doesn’t varies
with production
3
4. Contribution Margin is the amount remaining from sales
after variable expenses have been deducted.
Sales - Variable Expense = CM
150 – 50 = 100
CM Ratio:
CM/Sales = CMR
100/150 = 66.7%
Contribution Margin (CM)4
5. Formula:
BEP [Unit] = Fixed Cost / CM
BEP [Taka] = Fixed Cost / CM Ratio
Sales = Variable Cost + Fixed Cost+ Profit
Break Even Point (BEP)
BEP is the point where there is no profit no loss. (profit is Zero)
5
6. Selling Price=250/Unit, VC =150/Unit, FC=35,000
ABC Company is currently selling 400 speakers per month at 250 Taka per
speaker for total monthly sales of 1,00,000 Taka. Variable Expense is 150
taka/Unit. The sales manager feels that a 10,000 increase in the monthly
advertising budget would increase monthly sales by 30,000 Taka to a total of
520 Units. FC = 35,000 Taka. Should the advertising budget be increased ?
Change in Fixed Cost & Sales Volume
Particulars Current Sales New Sales Difference
Sales 100000 138000 38000
Variable Expenses 60000 90000 30000
Contribution
Margin
40000 48000 8000
Fixed Expense 35000 50000 10000
Net Operating
Income
5000 (2000) (2000)
6
7. The margin of safety is the positive difference between sales
and break even sales.
The Margin of Safety = Sales – Break even Sales
The Margin of Safety7
8. Operating leverage is a measure of how sensitive net operating
income is to a giver percentage change in dollar sales.
DOL= CM/Net operating income
Operating Leverage8
9. *Oslo Company prepared the following contribution format income statement based on a
sales volume of 1,000 units (the relevant range of production is 500 units to 1,500 units):
Required:
1. What is the contribution margin per unit?
2. What is the contribution margin ratio?
3. What is the variable expense ratio?
4. If sales increase to 1,001 units, what would be the increase in net operating income?
5. If sales decline to 900 units, what would be the net operating income?
6. If the selling price increases by $2 per unit and the sales volume decreases by 100
units, what would be the net operating income?
7. If the variable cost per unit increases by $1, spending on advertising increases by
$1,500, and unit sales increase by 250 units, what would be the net operating income?
9
Sales $20,000
Variable expenses 12,000
Contribution margin 8,000
Fixed expenses 6,000
Net operating income $ 2,000
Problem
10. 8. What is the break-even point in unit sales?
9. What is the break-even point in dollar sales?
10. How many units must be sold to achieve a target profit of $5,000?
11. What is the margin of safety in dollars? What is the margin of safety percentage?
12. What is the degree of operating leverage?
13. Using the degree of operating leverage, what is the estimated percent increase in net
operating income of a 5% increase in sales?
14. Assume that the amounts of the company’s total variable expenses and total fixed
expenses were reversed. In other words, assume that the total variable expenses are
$6,000 and the total fixed expenses are $12,000. Under this scenario and assuming that
total sales remain the same, what is the degree of operating leverage?
15. Using the degree of operating leverage that you computed in the previous question,
what is the estimated percent increase in net operating income of a 5% increase in sales?
10
11. Solution
11
Given volume=1000 units
CM per unit = CM/Volume = 8000/1000 = $8 per unit
CM ratio = (CM/sales)*100 = (8000/20000)*100 = 40%
Variable expenses ratio = (Variable cost/sales)*100 = (12000/20000)*100 =60%
1
2
3
12. 12
CM per unit = $8 per unit
Increase in unit sales (1001-1000)=1 unit
Increase in Net operating income (8*1) = $8
For 900 units
Particulars Amount
Sales (900*20) 18000
Variable expense (900*12) 10800
CM 7200
Fixed expense 6000
Net operating income 1200
4
5
13. Sales increase $2 per unit, volume decrease 100 units so, for (1000-100)=900 units
13
Particulars Amount
Sales (900*22) 19800
Variable expense (900*12) 10800
CM 9000
Fixed expense 6000
Net operating income 3000
6
14. Variable cost increase $1 unit increase 250 spending on advertising
increases so fixed cost increases $ 1500 For (1000+250) = 1250 units.
14
Particulars Amount
Sales (1250*20) 25000
Variable expense (1250*13) 16250
CM 8750
Fixed expense 7500
Net operating income 1250
7
15. 15
BEP in unit = (fixed cost /CM per unit ) = (6000/8) = 750 units
BEP unit sales = ( fixed cost /CM ratio ) = (6000/40%) = 150001
Given, target profit =5000
Unit sales = (fixed cost+ target profit /CM per unit)
= (6000+5000/8) =1375 units
8
10
9
16. 16 MOS in dollars =sales-BEP sales = 20000-15000=5000
MOS in % =( MOS/ sales)*100= (5000/20000)*100 = 25%
DOL= (CM/ Net operating income) = (8000/2000) = 4
Present increase=DOL * increase =4*5=20%
11
13
12
19. Morton Company’s contribution format income statement for last month is given below:
Sales (15,000 units 3 $30 per unit) . . . . . . . . . $450,000
Variable expenses . . . . . . . . . . . . . . . . . . . . . . 315,000
Contribution margin . . . . . . . . . . . . . . . . . . . . . 135,000
Fixed expenses . . . . . . . . . . . . . . . . . . . . . . . . 90,000
Net operating income . . . . . . . . . . . . . . . . . . . . $ 45,000
The industry in which Morton Company operates is quite sensitive to cyclical movements in
the economy. Thus, profits vary considerably from year to year according to general economic
conditions.The company has a large amount of unused capacity and is studying ways of
improving profits.
19
Problem
20. Required:
1.New equipment has come onto the market that would allow Morton
Company to automate a portion of its operations. Variable expenses would be
reduced by $9 per unit. However, fixed expenses would increase to a total of
$225,000 each month. Prepare two contribution format income statements, one
showing present operations and one showing how operations would appear if
the new equipment is purchased. Show an Amount column, a Per Unit column,
and a Percent column on each statement. Do not show percentages for the fixed
expenses.
2. Refer to the income statements in (1) above. For both present operations and
the proposed new operations, compute (a) the degree of operating leverage, (b)
the break-even point in dollar sales, and (c) the margin of safety in both dollar
and percentage terms.
20
21. 3. Refer again to the data in (1) above. As a manager, what factor would be
paramount in your mind in deciding whether to purchase the new equipment?
(Assume that enough funds are available to make the purchase.)
4. Refer to the original data. Rather than purchase new equipment, the
marketing manager argues that the company’s marketing strategy should be
changed. Rather than pay sales commissions, which are currently included in
variable expenses, the company would pay salespersons fixed salaries and
would invest heavily in advertising. The marketing manager claims this new
approach would increase unit sales by 30% without any change in selling
price; the company’s new monthly fixed expenses would be $180,000; and its
net operating income would increase by 20%. Compute the break-even point
in dollar sales for the company under the new marketing strategy. Do you
agree with the marketing manager’s proposal?
21
22. Particulars Present
Amount Per unit %
Sales(15000 units)
Variable expense
450000
315000
30
21
100
70
CM 135000 9 30
Fixed expense 90000
Net operating
income
45000
22
Solution
1
23. In proposed variable expense reduced$9 so, it is (21-9) = $12
and fixed expense is $225000
Particulars Present
Amount Per unit %
Sales(15000 units)
Variable expense
450000
180000
30
12
100
40
CM 270000 18 60
Fixed expense 225000
Net operating
income
45000
23
24. 24
a) Degree of operating leverage :
Present, DOL = (CM/NOI) = (135000/45000) = 3
Proposed, DOL= (CM/NOI) = (270000/45000) = 6
b) BEP in dollar sales
Present, BEP in dollar sales = (fixed expense /CM ratio)
= (90000/.3)
= $300000
Proposed, BEP in dollar sales = (fixed expense /CM ratio)
= (225000/0.6)
= $375000
2
25. 25
C) Margin of safety in dollars and %
Present, MOS in dollars = actual sales –BEP sales
=450000-300000 = $150000
Present,
MOS %= (MOS/ actual sales)*100 = (150000/450000)*100 = 33.33%
Proposed, MOS in dollars=actual sales –BEP sales
=450000-375000 = $75000
Proposed,
MOS %= (MOS/ actual sales)*100 = (75000/450000)*100 =16.67%
27. 27
30% sales increase so, 450000+30% of 450000 = $585000
Fixed expense will be = $180000
NOI increase 20% = 45000+20%of 45000 = 54000
We know,
Profit = (sales- Variable expense) - Fixed expense
Or, 54000= (585000- Variable expense)- 180000
Variable expense=$351000
4
28. Alternative way
28
We know, sales- Variable expense= CM
CM - Fixed expense = NOI
Let,
CM=x Variable expense=y
x- 180000= 54000
x= CM= 234000
then,
sales –y =234000
585000-y=234000
Y= Variable expense = 351000
29. Tax related Math
Taves Donuts sells donuts, coffee, and other related food
items. The following information is available:
Service varies from a single coffee to multiple dozen
donuts. The average revenue earned for each customer is
$8.00.
The average cost of food and other variable costs for each
customer is $3.00.
Total fixed costs for the year is $450,000.
The income tax rate is 30%.
Target (i.e., desired) net income is $105,000.
29
30. Data: SP = $8.00; VC = $3.00; FC = $450,000;
Target income = $105,000; Tax Rate = .30
How many customers are needed to reach the desired
profit?
Solution:
BE(units)= Total Fixed Cost/ CM(units)
= $450,000/($8 – 3)
= 90,000 customers
30
31. Desired customers,Q= (FC + Desired Profit)/ CM(units)
As we know,
Revenue – Cost of goods sold = Gross Margin
Gross Margin – Other Expense = Net Income Before Tax
Net Income Before Tax – Income Tax = Net Income
So,
NIBT – (NIBT* tax rate) = NI
NIBT (1 – tax rate) = NI
NIBT = NI/ (1 – tax rate)
= $105,000/ (1 – .30)
= $150,000
31
34. Particulars Velcro Metal Nylon
Normal annual
sales volume
100,000 200,000 400,000
Unit selling price
$1.65 $1.50 $0.85
Variable expense
per unit
$1.25 $0.70 $0.25
Total fixed expenses are $400,000 per year.
All three products are sold in highly competitive markets, so the Walmart
company is unable to raise its prices without losing unacceptable numbers of
customers.
The company has an extremely effective lean production system, so there are
no beginning or ending work in process or finished goods inventories
CVP for Multi-Product
Company
35. Required:
1. What is the company’s over-all break-even point in dollar sales?
2. Of the total fixed expenses of $400,000, $20,000 could be avoided if the
Velcro product is dropped, $80,000 if the Metal product is dropped, and
$60,000 if the Nylon product is dropped. The remaining fixed expenses of
$240,000 consist of common fixed expenses such as administrative salaries
and rent on the factory building that could be avoided only by going out of
business entirely.
a. What is the break-even point in unit sales for each product?
b . If the company sells exactly the break-even quantity of each
product, what will be the overall profit of the company? Explain this result.
36. Particular Velcro Metal Nylon Total
Sales $165,000 $300,000 $340,000 $805,000
Variable expenses 125,000 140,000 100,000 365,000
Contribution
margin
$40,000 $160,000 $240,000 440,000
Fixed expenses 400,000
Net operating
income
40,000
Solution
1.
37. Continued..
2. The issue is what to do with the common fixed cost when computing
the break-evens for the individual products. The correct approach is to
ignore the common fixed costs. If the common fixed costs are included in
the computations, the break-even points will be overstated for individual
products and managers may drop products that in fact are profitable.
a. The break-even points for each product can be computed using the
contribution margin approach as follows:
38. b. If the company were to sell exactly the break-even quantities computed
above, the company would lose $240,000—the amount of the common
fixed cost. This can be verified as follows:
Continued..
