This document provides examples and explanations of break even analysis and cost-volume-profit analysis concepts. It defines key terms like contribution margin, break even point, margin of safety, and fixed and variable costs. It then works through multiple numerical examples calculating values like break even sales, units, and profits under various cost and sales assumptions. The examples illustrate how to use the analysis techniques to determine operating results at different production volumes and aid decision making.

1. Managerial Accounting
Roohullah (M.Com) Lecturer: 0333-8786389 The Standard College Page 1
CHAPTER # 24
Break Even and Cost-Volume-Profit Analysis
Break Even Analysis:
Break even analysis is used to determine the level of sales which are required to just recover
all costs incurred during the period.
Break Even Point
The point at which there is no profit no loss. In other words it is a point where total revenue
equal to total cost.
1. Contribution Margin
CM = Sale price – Variable Cost
2. CM ratio
3. Break Even Point in Units
( )
4. Break Even Point in Sales Revenue
( )
5. Sales Units to Achieve Target Profit
6. Sales Revenue To Achieve Target Profit
7. Margin of Safety
Margin of Safety = Expected or Actual Sale – Break Even Point
8. Margin of Safety (M/S) ratio
M/S ratio

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9. Break Even Point in Percentage of Capacity
Ex # 1
Solution
(i) CM ratio = CM / Sales
CM ratio = $2,700,000 / $4,500,000 = 0.6
CM = Sales – Variable Cost
CM = $4,500,000 - $1,800,000 = $2,700,000
(ii) ( )
R(BEP) = $1,200,000 / 0.6 = $2,000,000
(iii) Contribution Margin = $2,700,000
Ex # 2
(1) ( )
R(BEP) = $84,832 / 0.44 = $192,800
Profit = Sales – Variable cost – Fixed Cost
$31,768 = $265,000 – 148,400 – Fixed Cost
Fixed Cost = $116,600 – 31,768 = $84,832
CM ratio = $265,000 – 148,400 / 265,000 = 0.44
(2) Sales Revenue to Achieve Target Profit of $10,560
R = $216,800

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Ex # 3
Solution
(i) ( )
R(BEP) = $4290 / 0.33 = $13,000
CM ratio = CM / Sale Price = $0.825 / $2.5 = 0.33
CM = $2.5 - $1.675 = $0.825
( )
Q(BEP) = $4,290 / $0.825 = 5200 Units
(ii) Sales Revenue to Achieve Target Profit of $10,560
R = $38,000
Proof
Profit = Sales – Variable cost – Fixed cost
Profit = $13,000 – (5200 × $1.675) - $4,290
Profit = $13,000 - $8,710 - $4,290 = 0

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Ex # 4
R(BEP) = $252,396 / 0.38 = $ 664,200
CM ratio = $342,000 / $900,000 = 0.38
CM = $900,000 - $558,000 = $342,000
Ex # 5
R(BEP) = $4,000 / 0.5 = $8,000
CM ratio = $2.50 / $5 = 0.5
CM = $5 - $2.50 = $2.50
Ex # 6
1. CM ratio = $2,000,000 / $10,000,000 = 0.2
CM = $10,000,000 - $8,000,000 = $2,000,000
2. R(BEP) = $1,000,000 / 0.2 = $5,000,000
3. (a) R(BEP) = $1,100,000 / 0.2 = $5,500,000
(b) Profit = Sales – Variable cost – Fixed cost
Profit = $10,000,000 - $8,000,000 - $1,100,000
Profit = $900,000
4 (a) CM ratio = $2,500,000 / $10,000,000 = 0.25
CM = $10,000,000 - $7,500,000 = $2,500,000
(b) R(BEP) = $1,250,000 / 0.25 = $5,000,000
(c) Profit = Sales – Variable cost – Fixed cost
Profit = $10,000,000 - $7,500,000 - $1,250,000
Profit = $1,250,000

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Ex #7
1. R(BEP) = $46,200 / 0.7 = $66,000
CM = $80,000 - $24,000 = $56,000
CM ratio = $56,000 / $80,000 = 0.7
2. Q(BEP) = $46,200 / 1.4 = 33,000 units
CM per unit = Total CM / Units Sold
CM Per unit = $$56,000 / 40,000 units = $1.4
3. R(BEP) = $48,067 / 0.71 = $67,700
CM = $80,000 - $23,200 = $56,800
CM ratio = $56,800 / $80,000 = 0.71
4. Sales Revenue to Achieve Target profit of $9800
R = $84,300
CM ratio = $55,200 / $80,000 = 0.69
CM = $80,000 - $24,800 = $55,200
Increase in Sales
New Sales needed for $9800 profit $84,300
Budgeting Sales 80,000
Increase in sales $4,300
5. Budgeting Profit
Sales (34,000 Units × $2.1) $71,400
Less: Variable cost
Production (71,400 × 23.75%) $16,958
Marketing (71,400 × 6.25%) 4,463 21,421
Contribution Margin 49,979
Less: Fixed Cost
Production $20,000
Marketing 26,200 46,200
Profit $3,779

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Sale price = $80,000 / 40,000 units = $2
New Sale price $2 × 1.05 = $2.1
Variable percentage
Production = $19,000 / $80,000 × 100 = 23.75%
Marketing = $5,000 / $80,000 × 100 = 6.25%
R(BEP) = $46,200 / 0.7 = $66,000
CM ratio = $49,976 / $71,400 = 0.70
Ex # 8
Solution
(i) Direct Costing / Variable costing
Sales (100,000 × $100) $10,000,000
Less: Variable cost (100,000 × $25) 2,500,000
Contribution Margin $7,500,000
Less: Fixed Cost (100,000 × $50) 5,000,000
Profit $2,500,000
(ii)
( )
( )
R(BEP) = $6,666,667
= = 0.75
(iii)
Margin of safety ratio = 0.3333 or 33.33%

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Ex # 9
Sales $200,000
Less: Variable cost 100,000
Contribution Margin 100,000
Less: Fixed Cost 40,000
Profit $60,000
Ex # 10
(1) ( )
Fixed Cost = $57,600
(2) Sale for the year
= $240,000
(3) CM = Sales – Variable expense
$240,000 × 36% = $240,000 – Variable expense
Variable expense = $240,000 - $86,400 = $153,600
(4)
= 0.3333 or 33.33%
Margin of Safety = Sale – BEP = $240,000 - $160,000 = $80,000

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Ex # 11
Solution
(1) ( )
( ) = $40,500
(2) Actual Sales?
0.25 Sales = Sales - $40,000
$40,500 = Sales – 0.25 Sales
$40,500 = 0.75 Sales
Sales = $40,000 / 0.75
Sales = $54,000
(3) Profit = CM – Fixed cost
Profit = ($54,000 × 30%) - $12,150
Profit = $16,200 - $12,150
Profit = $4,050
Ex # 12
Solution
(1) Decrease in Sales
Last month sales $220,000
Current month sales 206,250
Decrease in Sales $13,750

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Old ratio New ratio
Sales $220,000 100% 100%
Variable cost 132,000 60 64
CM $88,000 40% 36%
× 100 = $206,250
(2) Break Even Point?
M/S ratio
0.24
– ( )
$49,500 = $206,250 – R(BEP)
R(BEP) = $206,250 - $49,500
R(BEP) = $156,750
(3) Profit = Sales – Variable cost – Fixed cost
Profit = $206,250 - $132,000 - $56,430
Profit = $17,820
R(BEP)
$156,750
Fixed cost = $56,430
Decrease in Fixed Cost
Last month Fixed Cost $61,600
Current Month Fixed Cost 56,430
Decrease in Fixed Cost $5,170
M/S ratio
0.3
( )
$66,000 = $220,000 – R(BEP)
R(BEP) = $220,000 - $66,000

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R(BEP) = $154,000
R(BEP)
$154,000
Fixed Cost = $61,600
Ex # 13
Solution
(1)
( )
( )
Q (BEP) = 50 Units
CM = Sale Price – Variable cost
CM = $10,000 - $5,000 = $5,000
(2) Operating Income
CM ( 5,000 units × 1.25) $6,250
Fixed cost 2,500
Operating Income $3,750
(3) ( )
( )
R(BEP) = $8,400

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Ex # 14
Solution (1)
Profit = Sale – Variable cost – Fixed cost – Advertising
(50,000 units × $6) × 10% = (50,000 × $6) – (50,000 × 3) - $100,000 –
Advertising
$30,000 = $300,000 – 150,000 – 100,000 – Advertising
Advertising = $300,000 – 150,000 – 100,000 – 30,000
Advertising = $20,000
(2) ( )
( )
R(BEP) = $240,000
CM = Sale price – Variable Cost
CM = $6 - $3 = $3
( )
( )
Q (BEP) = 40,000 Units

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Ex # 15
Solution
R( )
R( )
R (BEP) = $2,640,000
CM = Sale price – Variable Cost
CM = $20 - $14 = $6
( )
( )
Q (BEP) = 132,000 Units
(2) Units to be sold to achieve target profit of $60,000
Q
Q
Q = 142,000 Units
(3) Units to be sold to achieve target profit of $90,000 after tax
Q
Q
Q = 157,000 Units
Profit before tax $150,000
Income tax (40%) 60,000
Profit after tax (60%) $90,000
Income tax = 90,000 × 40/60 = $60,000

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(4) Break Even Point in Units if Wages and Salaries increase by 10%
Labor = Variable cost × 50% × 10%
= $14 × 50% × 10% = $0.7
Labor = Fixed × 20% × 10%
= $792,000 × 20% × 10% = $15,840
( )
( )
( )
Q (BEP) = 152,423 Units
CM per unit = Sale price – Variable cost
CM per unit = $20 - $14.7 = $5.3
Ex # 16
Solution
(1)
CM = Sale price – Variable Cost
CM = $1,227,375 – $954,625 = $272,750
(2) R( )
R( )
R (BEP) = $1,260,126
( )
( ) 28,000 days

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CM per unit
CM per unit
(3) M/S ratio =
M/S ratio =
M/S ratio =
(4) R( )
R( )
R (BEP) = $1,575,158
( )
( )
Q (BEP) = 35,000 days
Ex # 17
R( )
R( )
R (BEP) = $300,000
( )
( ) 133,333 units
CM ratio
CM ratio = 0.4
CM per unit = Sale price – Variable cost
= $2.25 - $1.35 = $0.9

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Break Even Point in Percentage of Capacity
= 66.7%
(2) Margin of Safety = Sale – BEP
= $450,000 - $300,000
= $150,000
M/S ratio
M/S ratio
M/S ratio = 33.33%
(3) R( )
R( )
R (BEP) = $369,231
CM ratio
CM ratio = 0.325
CM per unit = Sale price – Variable cost
= $2 - $1.35 = $0.65
(4) (i) Sales to achieve target profit of $30,000
R = $375,000
R = $461,538

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(5) ( )
( )
R (BEP) = $250,000
( )
( ) 111,111 units
Break Even Point in Percentage of Capacity
= 55.6%
(6) Budget Profit
(a) (b)
Sales
Less: Variable Cost
Contribution Margin
Less: Fixed Cost
Expected Profit
$450,000
270,000
180,000
120,000
$60,000
$450,000
303,750
146,250
120,000
$26,250
Variable Cost
Units Sold × Variable cost per unit
(a) 200,000 units × $1.35 = $270,000
(b) 225,000 units × $1.35 = $303,750
( )
( )

17. Managerial Accounting
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Ex # 18
(1)
(a) ( )
( ) = 750 Units
(b) Sales (900 × 100) $90,000
Less: Variable Cost (900 × 60) 54,000
CM 36,000
Less: Fixed Cost 30,000
Profit $6,000
(2)
(a) ( ) = 888 Units
Reduction in variable cost = $60 × 0.25 = $15
Variable Cost = $60 - $15 = $45
CM Per Unit = $90 - $45 = $45
(b) Sales (900 × 90) $81,000
Less: Variable Cost (900 × 45) 40,500
CM 40,500
Less: Fixed Cost 40,000
Profit $ 500
(c) Sales (1000 × 90) $90,000
Less: Variable Cost (1000 × 45) 45,000
CM 45,000
Less: Fixed Cost 40,000
Profit $ 500
(3) Sales (950 × 90) $85,500
Less: Variable Cost (950 × 60) 57,000
CM 28,500
Less: Fixed Cost 30,000
Loss ($1,500)

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Ex # 19
Requirement (1)
Compusite Break Even Point in Dollars
=
Composite CM ratio
Composite CM = Composite Sales price – Composite Variable cost
Composite CM = $112 - $40 = $72
Composite Sales Price
Method of payment Average Daily Rate Patient Mix Weighted Daily
Rate
Self-payment $120 20% $24
Private Insurance 120 25 30
Madicare 110 30 33
Madcaid 100 25 25
Composite Sale Price $112
Composite Variable cost
Method of payment Average Daily Rate Patient Mix Weighted Daily
Rate
Self-payment $40 20% $8
Private Insurance 40 25 10
Madicare 40 30 12
Madcaid 40 25 10
Composite Variable cost $40
Coposite Break Even Point in patient days
=
Requirement (2)
Compusite Break Even Point in Dollars
=
Composite CM ratio
Composite CM = Composite Sales price – Composite Variable cost

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Composite CM = $120 - $40 = $80
Composite Sales Price
Method of payment Average Daily Rate Patient Mix Weighted Daily
Rate
Self-payment $120 50% $60
Private Insurance 120 50 60
Composite Sale Price $120
Composite Variable cost
Method of payment Average Daily Rate Patient Mix Weighted Daily
Rate
Self-payment $40 50% $20
Private Insurance 40 50 20
Composite Variable cost $40
Coposite Break Even Point in patient days
=
Ex # 20
Sales
Variable cost:
Manufacturing
Nonmanufacturing
Total Var. Cost
Contribution Margin
Increase in annual
program fixed cost
Manufacturing
Nonmanufacturing
Contribution to other
fixed costs & Income
before income tax
Current Operation
(50,000 Units
(a)
Low Elasticity
(52,000 Units
(b)
High Elasticity
(80,000 Units)
Per Unit
$10.00
$5.00
1.00
$6.00
$4.00
Total
$500,000
$250,000
50,000
$300,000
$200,000
$200,000
Per Unit
$9
$5.00
.90
$5.90
$3.10
Total
$468,000
$260,000
46,800
$306,000
$161,200
$161,200
Per Unit
$9
$5.00
.90
$5.90
$3.10
Total
$720,000
$400,000
72,000
$472,000
$248,000
$5,000
1,000
$6,000
$242,000
The low elasticity sales level can be anticipated to result in a contribution margin reduction of
$38,800 ($200,000 - $161,200)

20. Managerial Accounting
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The high elasticity sales level can be anticipated to result in a contribution marging increase
of $42,000 ($242,000 -$200,000)
Ex # 21 (1)
Abite Belite
(a) Profit per dollar of sales (profit ÷ Sales) $ 0.20 $ 0.15
(b) Contribution margin per unit (Sale price – Variable cost) $7.00 $3.75
(c) C/M ratio (CM ÷ Sale price) 0.47 0.56
(d) Contribution Margin per hour (CM per unit × Units per hour) $70.00 $93.75
(e) Profit per hour (Profit per unit × Units per hour) $30.00 $25.00
(2) Belite is more profitable because of its greater contribution margin per hour.
PROBLEMS
P # 1
(1) ( )
( )
Q(BEP) = 275,000 boxes
(2) Current
Current
( )
0.4 Sale price = Sale price - $2.7
$2.7 = Sale price – 0.4 Sale price
$2.7 = 0.6 Sale price
Sales price = $4.5

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Roohullah (M.Com) Lecturer: 0333-8786389 The Standard College Page 21
(3) Sale to achieve target profit $184,000 ($110,400 × 100/60)
R = $1,920,000
P # 2
Solution
(1) Projected income after tax for 19A
Income Statement – Direct Costing
Sales
Less: Variable cost
Contribution Margin
Less: Fixed Cost
Operating income
Less: Tax ($90,000 × 40%)
Profit after tax
$500,000
275,000
225,000
135,000
90,000
36,000
$54,000
(2) ( )
( )
Q (BEP) = 12,000 units
CM per unit = Sale price – variable cost
CM per unit = $25 - $13.75 = $11.25

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(3) Net Income 19B
Sales
Less: Variable cost
Contribution Margin
Less: Fixed Cost
Operating income
Less: Tax ($90,000 × 40%)
Profit after tax
$550,000
302,500
247,500
146,250
101,250
40,500
$60,500
(4)
( )
( ) = $325,000
= 0.45
(5) Sale to achieve profit of $90,000 after advertising of $11,250
= $525,000
(6) Advertising expense
Sales – Variable cost – Fixed cost – Advertising = profit
$550,000 – 302,500 – 135,000 – Advertising = $100,000
$112,500 – Advertising = $100,000
$112,500 - $100,000 = Advertising
Advertising = $12,500

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P # 3
Solution
(1) ( )
( )
R (BEP) = $723,065
Composite CM ratio
Composite CM ratio = 0.2766
Composite CM = Composite Sale price – Composite variable cost
Composite CM = $141 - $102 = $39
Composite Sale Price
A ($10 × 4) $40
B ($8 × 3) 24
C ($11 × 7) 77
$141
Composite Variable Cost
A ($6 × 4) $24
B ($5 × 3) 15
C ($9 × 7) 63
$102
Break Even Point by Dollars
( )
(2) ( )
Product Units Sale Price BEP in Dollars
A (5128 × 4) 20,512 $10 $205,120
B (5128 × 3) 15,384 8 123,072
C (5128 × 7) 35,896 11 394,856

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( ) = $646,512
= 0.3094
Composite CM = Composite Sale price – Composite Variable cost
Composite CM = $139 - $96 = $43
Composite Sale Price
A ($10 × 6) $60
B ($8 × 3) 24
C ($11 × 5) 55
$139
Composite Variable Cost
A ($6 × 6) $36
B ($5 × 3) 15
C ($9 × 5) 45
$96
( ) = 4,651 packages
Break Even Point by Dollars
Product Units Sale Price BEP in Dollars
A (4651 × 6) 27,906 $10 $279,060
B (4651 × 3) 13,953 8 111,624
C (4651 × 5) 23,255 11 255,805