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What is the breakeven point?

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Chapter 3 : Cost-Volume-Profit Analysis
Q1: What is the Cost-Volume-Profit Analysis?
CVP analysis looks at the relationship between cost, Volume and profits to
determine the breakeven point.
Q2: What is the breakeven point?
The breakeven point (BEP) is where: Total revenue = total costs.
Net Income = Zero
Total Contribution Margin = Fixed Cost
Q3: Explain the CVP analysis using graphic form?
Q4: How is CVP Analysis Used?
CVP analysis can determine:
1- Breakeven point both in sales volume and sales dollars.
2- Volume and sales dollars required to achieve target profit.
Break Even Points Formulas
1.
BEP (U) =
2.
BEP ($) =
C.M% =
C.M% =
𝑻𝒐𝒕𝒂𝒍 π‘­π’Šπ’™π’†π’… π‘ͺ𝒐𝒔𝒕𝒔
π‘ͺπ’π’π’•π’“π’Šπ’ƒπ’–π’•π’Šπ’π’ π‘΄π’‚π’“π’ˆπ’Šπ’ 𝑷𝒆𝒓 π‘Όπ’π’Šπ’•
𝑻𝒐𝒕𝒂𝒍 π‘­π’Šπ’™π’†π’… π‘ͺ𝒐𝒔𝒕𝒔
π‘ͺπ’π’π’•π’“π’Šπ’ƒπ’–π’•π’Šπ’π’ π‘΄π’‚π’“π’ˆπ’Šπ’ π‘Ήπ’‚π’•π’Šπ’
=
=
𝑭.π‘ͺ
π‘ͺ.𝑴/𝑼
𝑭.π‘ͺ
π‘ͺ.𝑴%
= ## units
{C.M/U = SP – V.C/U}
= $##
π‘Ίπ’†π’π’π’Šπ’π’ˆ π‘·π’“π’Šπ’„π’† 𝑷𝒆𝒓 π‘Όπ’π’Šπ’• (𝑺𝑷)−π‘½π’‚π’“π’Šπ’‚π’ƒπ’π’† π‘ͺ𝒐𝒔𝒕 𝑷𝒆𝒓 π‘Όπ’π’Šπ’• (𝑽.π‘ͺ/𝑼)
π‘Ίπ’†π’π’π’Šπ’π’ˆ π‘·π’“π’Šπ’„π’† 𝑷𝒆𝒓 π‘Όπ’π’Šπ’• (𝑺𝑷)
𝑺𝒂𝒍𝒆𝒔 𝑹𝒆𝒗𝒆𝒏𝒖𝒆 (𝑺𝑹)−π‘½π’‚π’“π’Šπ’‚π’ƒπ’π’† π‘ͺ𝒐𝒔𝒕 (𝑽.π‘ͺ)
𝑺𝒂𝒍𝒆𝒔 𝑹𝒆𝒗𝒆𝒏𝒖𝒆 (𝑺𝑹)
Ehab Abdou ( 00965 97672930 )
× 100 = #%
× 100 = #%
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Chapter 3 : Cost-Volume-Profit Analysis
𝑻𝒐𝒕𝒂𝒍 π‘­π’Šπ’™π’†π’… π‘ͺ𝒐𝒔𝒕𝒔 + π‘»π’‚π’“π’ˆπ’†π’• π‘·π’“π’π’‡π’Šπ’•
Units Required to Earn Profit =
4.
Sales Required to Earn Profit =
5.
Safety Margin
6.
Safety Margin Ratio =
7.
Safety Margin Ratio =
8.
Operating Leverage =
9.
Percentage Change in Net Income = Percentage Change in Sales × Operating Leverage
π‘ͺπ’π’π’•π’“π’Šπ’ƒπ’–π’•π’Šπ’π’ π‘΄π’‚π’“π’ˆπ’Šπ’ 𝑷𝒆𝒓 π‘Όπ’π’Šπ’•
𝑻𝒐𝒕𝒂𝒍 π‘­π’Šπ’™π’†π’… π‘ͺ𝒐𝒔𝒕𝒔 + π‘»π’‚π’“π’ˆπ’†π’• π‘·π’“π’π’‡π’Šπ’•
π‘ͺπ’π’π’•π’“π’Šπ’ƒπ’–π’•π’Šπ’π’ π‘΄π’‚π’“π’ˆπ’Šπ’ π‘Ήπ’‚π’•π’Šπ’
=
𝑭.π‘ͺ+π‘·π’“π’π’‡π’Šπ’•
3.
=
π‘ͺ.𝑴/𝑼
𝑭.π‘ͺ+π‘·π’“π’π’‡π’Šπ’•
π‘ͺ.𝑴%
= Sales (U) – BEP (U)
= Sales ($) – BEP ($)
𝑺𝒂𝒍𝒆𝒔 (𝑼) – 𝑩𝑬𝑷 (𝑼)
𝑺𝒂𝒍𝒆𝒔 (𝑼)
𝑺𝒂𝒍𝒆𝒔 ($) – 𝑩𝑬𝑷 ($)
𝑺𝒂𝒍𝒆𝒔 ($)
𝑻𝒐𝒕𝒂𝒍 π‘ͺπ’π’π’•π’“π’Šπ’ƒπ’–π’•π’Šπ’π’ π‘΄π’‚π’“π’ˆπ’Šπ’
𝑡𝒆𝒕 π‘°π’π’„π’π’Žπ’†
10. Change in Net Income (Contribution Margin) = Change in Sales × CM%
Contribution Format Income Statement:
Sales Revenue (10,000 units)
(-) Variable Costs
(=) Total Contribution Margin
(-) Fixed Costs
(=) Net Income
Ehab Abdou ( 00965 97672930 )
Total
100,000
40,000
60,000
20,000
40,000
Per Unit
SP/U
$10
V.C/U
$4
C.M/U
$6
Percentage
100%
V.C %
40%
C.M%
60%
www.hca4u.com
Chapter 3 : Cost-Volume-Profit Analysis
Breakeven Point For Multi Products
1. BEP (U) =
2. BEP ($) =
𝑻𝒐𝒕𝒂𝒍 π‘­π’Šπ’™π’†π’… π‘ͺ𝒐𝒔𝒕𝒔
𝑢𝒗𝒆𝒓𝒂𝒍𝒍 π‘ͺπ’π’π’•π’“π’Šπ’ƒπ’–π’•π’Šπ’π’ π‘΄π’‚π’“π’ˆπ’Šπ’ 𝑷𝒆𝒓 π‘Όπ’π’Šπ’•π’”
𝑻𝒐𝒕𝒂𝒍 π‘­π’Šπ’™π’†π’… π‘ͺ𝒐𝒔𝒕𝒔
𝑢𝒗𝒆𝒓𝒂𝒍𝒍 π‘ͺπ’π’π’•π’“π’Šπ’ƒπ’–π’•π’Šπ’π’ π‘΄π’‚π’“π’ˆπ’Šπ’ π‘Ήπ’‚π’•π’Šπ’
3. Units Required To Earn Profit =
4. Sales Required To Earn Profit =
=
=
𝑭.π‘ͺ
𝑢𝒗𝒆𝒓𝒂𝒍𝒍 π‘ͺ.𝑴/𝑼
𝑭.π‘ͺ
𝑢𝒗𝒆𝒓𝒂𝒍𝒍 π‘ͺ.𝑴%
= ## units
= $ ##
𝑻𝒐𝒕𝒂𝒍 π‘­π’Šπ’™π’†π’… π‘ͺ𝒐𝒔𝒕𝒔+π‘·π’“π’π’‡π’Šπ’•
𝑢𝒗𝒆𝒓𝒂𝒍𝒍 π‘Όπ’π’Šπ’•π’” π‘ͺπ’π’π’•π’“π’Šπ’ƒπ’–π’•π’Šπ’π’ π‘΄π’‚π’“π’ˆπ’Šπ’
𝑻𝒐𝒕𝒂𝒍 π‘­π’Šπ’™π’†π’… π‘ͺ𝒐𝒔𝒕𝒔+π‘·π’“π’π’‡π’Šπ’•
𝑢𝒗𝒆𝒓𝒂𝒍𝒍 π‘ͺπ’π’π’•π’“π’Šπ’ƒπ’–π’•π’Šπ’π’ π‘΄π’‚π’“π’ˆπ’Šπ’ π‘Ήπ’‚π’•π’Šπ’
= ## units
= $ ##
5. Change in Net Income (Contribution Margin) = Change in Sales × Overall CM
Overall Units Contribution Margin
Products
A
B
S.P/U
V.C/U
C.M/U
$10
$4
$6
$20
$12
$8
Overall Contribution Margin
Sales Mix
40%
60%
Overall
$2.4
$4.8
$7.2
Overall Contribution Margin Ratio
Products
A
B
S.P/U
$10
$20
V.C/U
C.M/U
C.M %
$4
$6
60%
$12
$8
40%
Overall Contribution Margin Ration
Sales
(-) Variable Costs
(=) Contribution Margin
(-) Fixed Costs
(=) Net Income
Ehab Abdou ( 00965 97672930 )
A
$400,000
160,000
240,000
B
$600,000
360,000
240,000
Sales Mix
40%
60%
Overall
24%
24%
48%
Total
$1,000,000
520,000
480,000
300,000
180,000
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Chapter 3 : Cost-Volume-Profit Analysis
Exercises:
1.
NTQ Corporation produces and sells a single product with a price of $12 per unit and
variable costs of $8 per unit. Total fixed costs per month are $8,000.
a. Calculate NTQ’s contribution margin per unit.
b. How many units must NTQ sell monthly to break even?
c. If fixed costs increase by $500 per month, how many extra units must NTQ sell each
month to continue breaking even?
Solution:
a. Contribution margin per unit
b. Breakeven point in units =
c. Breakeven point in units =
= Selling Price – Variable cost per unit
=
$12
$8
= $4
𝐹𝑖π‘₯𝑒𝑑 πΆπ‘œπ‘ π‘‘
πΆπ‘œπ‘›π‘‘π‘Ÿπ‘–π‘π‘’π‘‘π‘–π‘œπ‘› π‘šπ‘Žπ‘Ÿπ‘”π‘–π‘› π‘π‘’π‘Ÿ 𝑒𝑛𝑖𝑑
𝑁𝑒𝑀 𝐹𝑖π‘₯𝑒𝑑 πΆπ‘œπ‘ π‘‘
πΆπ‘œπ‘›π‘‘π‘Ÿπ‘–π‘π‘’π‘‘π‘–π‘œπ‘› π‘šπ‘Žπ‘Ÿπ‘”π‘–π‘› π‘π‘’π‘Ÿ 𝑒𝑛𝑖𝑑
=
=
$ 8,000
$4
$ 8,500
$4
= 2,000 units
= 2,125 units
Extra Units = 2,125 – 2,000 = 125 units
Another Solution:
Extra Units =
πΌπ‘›π‘π‘Ÿπ‘’π‘Žπ‘ π‘’ 𝑖𝑛 𝐹𝑖π‘₯𝑒𝑑 πΆπ‘œπ‘ π‘‘
πΆπ‘œπ‘›π‘‘π‘Ÿπ‘–π‘π‘’π‘‘π‘–π‘œπ‘› π‘šπ‘Žπ‘Ÿπ‘”π‘–π‘› π‘π‘’π‘Ÿ 𝑒𝑛𝑖𝑑
Ehab Abdou ( 00965 97672930 )
=
$ 500
$4
= $125 units
www.hca4u.com
Chapter 3 : Cost-Volume-Profit Analysis
2.
Julie’s Jewels sells cubic zirconium (fake diamond) rings for $80 each. The projected
income statement for 2006 follows:
Sales
$4,000,000
Variable costs
(2,200,000)
Contribution Margin
1,800,000
Fixed costs
(1,600,000)
Pretax profit
$ 200,000
a. Compute the contribution margin per ring and the number of rings that must be sold to
break even.
b. Compute the contribution margin ratio and the breakeven point in total revenue.
c. Suppose the total revenues were $200,000 greater than expected. What is the total
pretax profit?
d. What is the margin of safety in number of rings?
e. Assume a tax rate of 25%. How many rings must be sold to earn an after-tax profit of
$300,000?
Solution:
.
a. Contribution margin per ring = $1,800,000 ÷ 50,000 units = $36
Breakeven point = $1,600,000/$36 per ring = 44,445 rings
b. Contribution margin ratio = ($1,800,000÷$4,000,000) × 100 = 45%
Revenue at breakeven = $1,600,000÷0.45 = $3,555,556
c. Increase in Pretax profit = $200,000 x 0.45 = $90,000.
Add this to current profit of $200,000 to calculate new profit of $290,000.
d. Margin of safety in number of rings
= Current number of rings sold – breakeven number of rings
= 50,000 – 44,445 = 5,555 rings
e. Pretax profit = $300,000 ÷ (1- 0.25) = $400,000
Units to meet target profit =
=
Ehab Abdou ( 00965 97672930 )
𝐹𝑖π‘₯𝑒𝑑 πΆπ‘œπ‘ π‘‘+π‘ƒπ‘Ÿπ‘œπ‘“π‘–π‘‘
πΆπ‘œπ‘›π‘‘π‘Ÿπ‘–π‘π‘’π‘‘π‘–π‘œπ‘› π‘šπ‘Žπ‘Ÿπ‘”π‘–π‘›π‘” π‘π‘’π‘Ÿ 𝑒𝑛𝑖𝑑
$1,600,000+$400,000
$36
= 55,556 rings
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Chapter 3 : Cost-Volume-Profit Analysis
3.
FTH Corporation produces and sells two products: regular scooters and electric scooters.
Last month, the company produced and sold 500 regular and 300 electric scooters. Last
month’s per-unit financial data for both models is presented below:
Regular
Electric
Selling price
$100
$150
Variable cost
30
40
Product line fixed cost
25
45
Corporate fixed cost
10
10
Product line fixed costs can be avoided if the product is dropped, but corporate fixed costs
can only be avoided if FTH goes out of business entirely. Calculate the following amounts:
a. Total fixed product line costs for each product
b. Total corporate fixed costs
c. Overall corporate breakeven point in sales dollars assuming a constant sales mix
d. Breakeven point in sales dollars for regular scooters, ignoring corporate fixed costs
e. Breakeven point in sales dollars for electric scooters, ignoring corporate fixed costs
Solution
a. Fixed Product line Costs = ($25 x 500) + ($45 x 300) = $26,000
b. Fixed Corporate Costs
c. BEP ($) =
= ($10 x 500) + ($10 x 300) = $8,000
𝐹𝑖π‘₯𝑒𝑑 πΆπ‘œπ‘ π‘‘π‘ 
π‘‚π‘£π‘’π‘Ÿπ‘Žπ‘™π‘™ πΆπ‘œπ‘›π‘‘π‘Ÿπ‘–π‘π‘’π‘‘π‘–π‘œπ‘› π‘šπ‘Žπ‘Ÿπ‘”π‘–π‘›π‘” π‘…π‘Žπ‘‘π‘–π‘œπ‘›
Weighted average CMR
Regular
$50,000
Sales Revenue
500×$100
(-) Variable Costs
Electric
$45,000
300×$150
$15,000
500×$30
$12,000
BEP ($) =
$πŸπŸ”,𝟎𝟎𝟎+$πŸ–,𝟎𝟎𝟎
πŸ•πŸ%
$ 27,000
300×$40
(=) Contribution Margin
Then : Weighted Average CMR =
Total
$ 95,000
$ 68,000
$ 68,000
$ 95,000
× 100 = 72%
= $47,222
d. Product line fixed cost = $25 x 500 = $12,500
CM Ratio = ($100 - $30) / $100 = 70%
$12,500 / 70% = $17,858 breakeven sales for regular scooters
e. Product line fixed cost = $45 x 300 = $13,500
CM Ratio = ($150 - $40) / $150 = 73% (rounded)
$13,500 / 73% = $18,410 breakeven sales for electric scooters
Ehab Abdou ( 00965 97672930 )
www.hca4u.com
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