Engineering Economics Ppt Break Even Analysis Uses of BEA Examples of BEA

1. Break Even Analysis

2. • Breakeven Analysis- A decision-making aid that enables a manager to
determine whether a particular volume of sales will result in losses or
profits.

3. • The theory behind the breakeven analysis
• Made up of four basic concepts
• Fixed costs- costs that do not change
• Variable costs- costs that rise in propitiation to sales
• Revenue- the total income received
• Profit- the money you have after subtracting fixed and variable cost
from revenue

4. • Break-even analysis is of vital importance in determining the practical
application of cost functions. It is a function of three factors, i.e. sales
volume, cost and profit. It aims at classifying the dynamic
relationship existing between total cost and sale volume of a
company.
• It is also used to determine when your business will be able to cover
all its expenses and begin to make a profit.
• It is also known as “cost-volume-profit analysis”.

5. • It helps to know the operating condition that exists when a company
‘breaks-even’, that is when sales reach a point equal to all expenses
incurred in attaining that level of sales.
• This concept has been proved highly useful to the company
executives in profit forecasting and planning and also in examining
the effect of alternative business management decisions.
• Contents :
• Break-Even Point
• Determination of Break-even Point
• Managerial Uses of Break-Even Analysis

6. • Break-even point represents that volume of production where total
costs equal to total sales revenue resulting into a no-profit no-loss
situation.
• If output of any product falls below that point there is loss; and if
output exceeds that point there is profit.
• Thus, it is the minimum point of production where total costs are
recovered. Therefore, at break-even point.

7. • The break-even point (B.E.P.) of a firm can be found out in two ways.
It may be determined in terms of physical units, i.e., volume of
output or it may be determined in terms of money value, i.e., value
of sales.

8. Output
in
units
Total
Revenue
Total
Fixed
Cost
Total
Variable
Cost
0 0 150 0
50 200 150
100 400 300
150 600 450
200 800 600
250 1000 750

9. Output
in
units
Total
Revenue
Total
Fixed
Cost
Total
Variable
Cost
Total
Cost
0 0 150 0 150
50 200 150 150 300
100 400 150 300 450
150 600 150 450 600 BEP
200 800 150 600 750
250 1000 150 750 900
300 1200 150 900 1050

10. Assumptions
• Some assumptions are made in illustrating the ВЕР. The price of the
commodity is kept constant at Rs. 4 per unit, i.e., perfect competition
is assumed. Therefore, the total revenue is increasing proportionately
to the output. All the units of the output are sold out. The total fixed
cost is kept constant at Rs. 150 at all levels of output.

11. • The total variable cost is assumed to be increasing by a given amount
throughout. From the Table we can see that when the output is zero,
the firm incurs only fixed cost. When the output is 50, the total cost
is Rs. 300. The total revenue is Rs. 200. The firm incurs a loss of Rs.
100.

12. • Similarly when the output is 100 the firm incurs a loss of Rs. 50. At
the level of output 150 units, the total revenue is equal to the total
cost. At this level, the firm is working at a point where there is no
profit or loss. From the level of output of 200, the firm is making
profit

13. Break Even Charts
• Break-Even charts are being used in recent years by the managerial
economists, company executives and government agencies in order
to find out the break-even point. In the break-even charts, the
concepts like total fixed cost, total variable cost, and the total cost
and total revenue are shown separately. The break even chart shows
the extent of profit or loss to the firm at different levels of activity.
The following Fig. illustrates the typical break-even chart.

14. Co n t .

15. General Assumptions
• All costs can be separated into fixed and variable components,
• Fixed costs will remain constant at all volumes of output,
• Variable costs will fluctuate in direct proportion to volume of output,
• Selling price will remain constant,
• Product-mix will remain unchanged,

16. • The number of units of sales will coincide with
the units produced so that there is no opening or closing
stock,
• Productivity per worker will remain unchanged,
• There will be no change in the general price level.

17. Uses of BEA
It helps in the determination of selling price which will give the desired
profits.
It helps in the fixation of sales volume to cover a given return on capital
employed.
It helps in forecasting costs and profit as a result of change in volume.
It gives suggestions for shift in sales mix.
It helps in making inter-firm comparison of profitability.

18. • It helps in determination of costs and revenue at various levels of
output.
• It is an aid in management decision-making (e.g., make or buy,
introducing a product etc.), forecasting, long-term planning and
maintaining profitability.
• It reveals business strength and profit earning capacity of a concern
without much difficulty and effort.

19. Determination of BEP
• The formula for calculating the break-even point is
• ВЕР = Total Fixed Cost/Contribution Margin Per Unit
• Contribution margin per unit can be found out by deducting the
average variable cost from the selling price. So the formula will be
• BEP = Total Fixed Cost/Selling Price – AVC

20. 20
Breakeven formula
P(X) = F + V(X)
F = fixed costs
V = variable costs per unit
X = volume of output (in units)
P = price per unit

21. • If we rearrange the equation the breakeven is X then the formula look
like this
• X = F /( P – V)
• This formula says that the breakeven point is where the number of
sales needed to make the cost equal to the revenue.

22. Example:
• Suppose the fixed cost of a factory in Rs. 10,000, the selling price is
Rs. 4 and the average variable cost is Rs. 2, so the break-even point
would be
• 5000 units?

23. • ВЕР = 10,000/(4-2) = 5,000 units
• Prove that 5000 units is the BEP

24. Proof
• It means if the company makes the sales of 5,000 units, it would make neither loss nor
profit. This can be seen in the analysis.
• Sales = Rs.20, 000 ( 5000x4)
• Cost of goods sold:
• Variable cost at Rs.2 x 5000 = Rs. 10,000
• Fixed costs = Rs. 10,000
• Total Cost = Rs. 20,000
• Net Profit = Nil

25. Contribution margin
• AR/SP = rs. 50
• AVC = rs.40
• AFC= rs.15
• Should the firm continue its business?
• AC = rs.55 >50- loss
• 50-40
• SP – AVC = contribution margin = Rs 10

26. Break Even in terms of sales value
• Multi-product firms are not in a position to measure the break- even
point in terms of any common unit of product. They find it
convenient to determine the break-even point in terms of total rupee
sales. Here again the break-even point would be where the
contribution margin (sales value - variable costs) would be equal to
fixed costs. The contribution margin however, is expressed as a ratio
to sales.

27. BEP in terms of sales value
• The formula for calculating the break-even point is
• BEP = Fixed Cost/Contribution Ratio
• Contribution Ratio (CR) =
• Total Revenue (TR)-Total Variable Cost (TVC)/Total Revenue (TR)

28. Example
• if TR is Rs. 600 and TVC is Rs. 450 & TFC is 150
• Find BEP in terms of sales value

29. • contribution ratio is
• CR = 600 – 450/600 =150/ 600 = 0.25
• The Contribution Ratio is 0.25
• BEP = Total Fixed Cost /Contribution Ratio = 150/0.25 = 600

30. proof
• The firm achieves its ВЕР when its sales are Rs. 600
• Total Revenue = Rs.600
• Total Cost = Rs.600
• Net Profit/loss = Nil

31. Example
• Lets say you own a business selling burgers
• It costs $1.00 to make one burger
• You sell each burger for $2.80
• Your cost for rent, utilities, overhead, etc... is $100,000 per month
• How many burgers you have to sell to reach the BEP??

32. Solution
• X = F /( P – V)
• X = 100,000 / ( 2.80 - 1 ) X = 100,000 / ( 1.80 )
• X = 55,555
• To breakeven you would need to sell 55,555 burgers

33. Example
You own a lemonade stand
It costs you $0.05 to make cup of lemonade
You sell your lemonade for $0.25
It cost you $50.00 to make the stand
How many cups of lemonade do you have to sell to breakeven?

34. Solution
• X = F /( P – V)
• X = 50 / ( .25 - .05 ) X = 50/ ( .20 )
• X =250
• You would need to sell 250 cups of lemonade to breakeven

35. Managerial Applications of BEA
To the management, the utility of break-even analysis lies in the fact
that it presents a microscopic picture of the profit structure of a
business enterprise. The break-even analysis not only highlights the
area of economic strength and weakness in the firm but also
sharpens the focus on certain leverages which can be operated upon
to enhance its profitability.
It guides the management to take effective decision in the context of
changes in government policies of taxation and subsidies.

36. 1. Safety Margin
• The break-even chart helps the management to know at a glance the
profits generated at the various levels of sales. The safety margin
refers to the extent to which the firm can afford a decline in sales
before it starts incurring losses.
• The formula to determine the sales safety margin is:
• Safety Margin= (Sales – BEP)/ Sales x 100

37. Example
The FC of a factory are Rs. 10000 per year and the VC is Rs. 2 per unit
and SP is Rs. 4 per unit. Find out the BEP. If the sales are 8000 units,
find out the safety margin?

38. • BEP = 10000/ 4-2 = 5000 units
• Safety Margin = 8000-5000 / 8000 * 100 = 37.5%
• Interpretation:
The company can afford to lose sales upto 37.5 % of the present level
before incurring a loss.

39. Safety margin---- Interpret
37.5%
Sales
25 %

40. Question
• Can the Safety margin be negative ??

41. • In the previous example……
• If the sales are 4000 units then what is the safety margin?

42. Solution
• - 25%
• Interpretation:
• The co. must strive to increase the sales by at least 25% to avoid
losses.

43. 2. Volume needed to attain target profit
• Target Sales Volume: Fixed Costs + Target Profit/ CM per unit
• In the previous example
• If the desired profit is Rs. 6000, then how much is the target sales?

44. Solution
• TSV = 10000+6000/2 = 8000 units
• Prove that at 8000 units the profit is Rs. 6000

45. 3. Change in the Selling Price
• If the selling price changes, what needs to be changed to maintain the
earlier level of profit ??

46. Contd….
• New Volume of Sales=
Qn = FC + TP / SPn - VC

47. Example
• If there is a reduction of 10% in the price, then what would be the
new volume of sales?

48. solution
• 10000 + 6000 / 3.6 – 2 = 10000 units
• Prove that with the new price the co. maintains the desired level of
profit

49. Contd….
• It implies that there needs to be an increase in the production by
2000 units ( from 8000 to 10000 units)
• The firm has to decide the feasibility of the same.

50. Contd…
• If there is an increase in price by 12.5 % ?
• Prove

51. solution
• 10000 + 6000 / 4.5 – 2 = 6400 units
• If the decline in sales due to an increase in the price is less than 1600
units, it would be profitable to increase the price. If the decline is
more than 1600 units, the proposed price increase would reduce the
profit.
• Prove

52. 4. Change in production costs
• If the variable cost changes
• New quantity Qn = FC + P/ SP- VCn
• New selling price SPn = SP + ( VCn- VC)

53. example
• If the variable costs increases from Rs. 2 to Rs. 2.5 per unit
• Find out the new quantity and new selling price to ensure same
amount of profits..

54. Solution…
• Qn= 10000 + 6000/ 4 – 2.5
• = 10667 units
• SPn = 4 + (2.5 – 2)
• Rs. 4.5

55. Cont…..change in cost of production
• If fixed costs change
• New quantity Qn= Q+ FCn- FC/ SP –VC
• New selling price SPn = SP + FCn- FC / Q

56. Example
• If FC increases from 10000 to 15000
• Find out the new quantity and new selling price to ensure same level
of profits..

57. 5. To make or buy decision
• BEP = FC/ Purchase price - VC
• A manufacturer buys a certain component at Rs. 8 each. In case he
makes it himself the FC is Rs. 10000 and the variable cost is Rs. 3 per
component. Should the manufacturer make or buy the component?

58. • BEP = FC/ purchase price- Vc
• = 2000 units
• If the producer needs more than 2000 components per year then it is
profitable to make. However if requirement is less than 2000 units
then it is profitable to buy the unit.

59. Example
• A producer sells his product at Rs. 5 each. VC are Rs. 2 per unit and FC
amount to Rs. 60000.
• Calculate the BEP
• What would be the profit if the firm sells 30000 units
• What would be the BEP if the firm spends Rs. 3000 on
advertisement?
• How much the producer should sell to make a profit of Rs. 30000
after spending Rs. 3000 for advertisement.

60. 6. Equipment selection
• A producer has to choose between three machines:
1. an automatic machine which will add Rs. 20000 a year to his FC but
the VC will be 40 paisa per unit.
2. A semi automatic machine which will add Rs. 8000 per year to FC but
VC will be Rs. 2 per unit.
3. A hand operated machine which will add only Rs. 2000 per year to FC
but will cause VC of Rs. 4 per unit.

61. Contd…
• Calculate the range of output over which automatic, semi automatic
and hand operated machines would be economical.
• How to choose between hand operated and automatic machines,
supposing semi automatic machines does not exist?

62. solution
• The cost formulas for the 3 machines are as follows:
Machine Cost formula
Automatic Rs. 20000 + 0.40 S
Semi automatic Rs. 8000 + 2S
Hand operated Rs. 2000 + 4S

63. Solving the value
1. Auto and Semi Automatic
Rs. 20000 + 0.40 S = Rs. 8000 + 2S
S = 7500 units
2. Semi Automatic and Hand
Rs. 8000 + 2 S = Rs. 2000 + 4S
S= 3000 units

64. Up to 3000 units hand operated is to be used . Semi automatic
between 3000 – 7500 units. Beyond 7500 units automatic is to be
used.
If choice has to be made between automatic and hand operated then
2000 + 4S = 20000 + 0.4
S= 5000 units
Up to 5000 units, hand operated and beyond 5000 automatic is more
economical.

65. Policy Guidelines
1. A high BEP indicates a vulnerable profit position of the firm.
2. To reduce the BEP, SP may be increased or costs cut down.
3. If VC per unit are large relative to SP, an increase in SP or reduction
in VC would be more effective.
4. Whether it is desirable to increase the price or cut cost depends
Competitive market conditions
Elasticity of demand
Efficiency of its operations

66. Contd….
5. The higher the contribution margin, the higher is the endurance of
the business, i.e withstand losses when prices are cut down.
6. In a period of expansion a firm with higher % of FC to sales earns
higher profits as compared to the business with higher % of variable
expenses.
7. In a period of recession, a firm with higher % of FC to sales suffers
greater losses than the business with higher % of variable expenses.

67. Example
• The HK company manufactures a single product – product X. A unit of
product X is sold to customers for $80. The per unit variable expense
and the total expected fixed expenses for the first quarter of the year
2012 are as follows:
• Variable expenses to manufacture and sell a unit of product X: $50
• Total fixed expenses for the first quarter of the year 2012: $40,000
• The company wants to earn a profit of $80,000 for the first quarter of
the year 2012.

68. Calculate sales in units and in dollars to earn a target profit of $80,000
during the first quarter of 2012 using:
Contribution margin method.

69. Contd….
• (Target profit + fixed expenses)/contribution margin per unit
= ($40,000 + $80,000) / $30*
= 4,000 units
• Or
• = 4,000 units × $80
= $320,000
• *Unit contribution margin is equal to sales price per unit less variable
expenses per unit i.e., $80 – $50.

70. Example
• The John & David Corporation provides you the following data:
• Selling price per unit: $140
• Variable cost per unit: $90
• Expected annual fixed expenses: $400,000

71. Find out
• Determine the break even point of John & David Corporation using
above data.
• Based on the above data, how many units the corporation needs to
sell for making a profit of $200,000 for the next year?
• What would be the margin of safety in dollars and in units if the
corporation achieves the sales volume required to make the target
profit of $200,000 next year?

72. solution
• 1. Break even point
• Break even point in terms of units:
• Fixed cost/(Selling price per unit – Variable cost per unit)
= $400,000/($140 – $90)
= $400,000/$50
= 8,000 units
• Break even point in terms of dollars:
• Break even point in units × Selling price per unit
= 8,000 units × $140
= $1,120,000

73. • 2. Required sales volume to earn $200,000
• Sales volume required in terms of units:
• (Fixed cost + Target profit)/(Selling price per unit – Variable cost per unit)
= ($400,000 + $200,000)/($140 – $90)
= $600,000/$50
= 12,000 units
• Sales volume required in terms of dollars:
• Sales volume in units × Selling price per unit
= 12,000 units × $140
= $1,680,000

74. • Margin of safety
• The margin of safety in this problem is equal to target sales volume less break even sales volume.
• Margin of safety in dollars:
• Target sales in dollars – Break even sales in dollars
= $1,680,000 – $1,120,000
= $560,000
• Margin of safety in units:
• Target sales in units – Break even sales in units
= 12,000 units – 8,000 units
= 4,000 units
• OR
• Margin of safety in dollars/Selling price per unit
= $560,000/$140
= 4,000 units

75. Example
Price per kayak $500
variable costs per kayak $225
Contribution margin per kayak $275
Fixed costs/month $7,700
With this information, how many kayaks do we need to sell to show a
$30,000 profit at the end of the month?
How much in sales do we need?

76. solution
Unit Sales to attain the target profit
Target Profit+Fixed expenses / Unit CM
Unit sales needed=$30,000+$7,700 / $275=$37,700 / $275
• So we need 137 kayaks sold to make a $30,000 profit
• 137 kayaks × $500 selling price per kayak = $68,500 in sales

77. Contd…
• Let’s assume their current sales of kayaks is 50 kayaks per month at
$500 each. what is their margin of safety?

78. Solution…
Minnesota Kayak Company needs to sell 28 kayaks at $500 each to
break even. So in this example, $14,000 in sales is their break even
point.
$25,000−$14,000=$11,000 is their margin of safety.
What is their margin of safety percentage?
$11,000 / $25,000=44% is their margin of safety percentage.

79. Mike’s Bikes wants to show a $10,000 profit this month. He sells his
bikes for $150 each. If he has $40 in contribution margin per bike, and
$4,000 in fixed costs per month. How many bikes does he need to sell
and how much in dollar sales to meet his target profit?

80. solution
• 350 bikes

81. Example
Farmer Jane is selling 5000 pounds of tomatoes each month at $3 per
pound. Her variable cost per pound is $1 and she has fixed costs per
month of $2,500. What is Jane’s break-even point and margin of
safety?

82. Solution:
• BEP = $ 3750
• Margin of safety = 11250
• Margin of safety percentage = 75%