1. Management AccountIng9
COST VOLUME PROFIT ANALYSIS
Breakeven Point

2. Cost-Volume-Profit (CVP) Analysis Definition
CVP, is a planning process that management uses to predict the future volume of activity, costs incurred, sales made, and profits received.

3. Cost-Volume-Profit (CVP) Analysis Definition
In other words, it’s a mathematical equation that computes how changes in costs and sales will affect profit in future periods.
Total Cost(TC) =ax+b
Total Income (TI)=fx
Profit P =(f−a)x − b

4. Cost-Volume-Profit (CVP) Analysis Profit Function
Profit=Total Income−Total Cost
Total Income=f ∗x
x=volume
f=unit selling price
Total Cost=ax+b
Profit=fx−ax −b
Profit= f−a x −b →x=units sold

5. Cost-Volume-Profit (CVP) Analysis Breakeven Point
At break-even point, a company will experience no income or loss. In other words breakeven point is the sales level at which operating income is zero.

6. Cost-Volume-Profit (CVP) Analysis Breakeven Point
Two methods: Income Statement and Contribution Margin Approach.
Income Statement Approach X Breakeven = Total Fixed Cost Contribution Margin x=units sold Unit Contribution Margin = Total Sales−Total Variable Cost Units Sold or Unit Contribution Margin = fx−ax x X Breakeven = Total Fixed Contribution Margin Ratio x= Sales TL. Contribution Margin Ratio= Total Sales−Total Variable Cost Total Sales Contribution Margin Ratio= fx−ax fx

7. Cost-Volume-Profit (CVP) Analysis Breakeven Point
Breakeven point is the sales level at which operating income is zero Two methods: Income Statement and Contribution Margin Approach Contribution Margin Approach X Breakeven = Total Fixed Cost Contribution Margin x=units sold Unit Contribution Margin = fx−ax x = f-a X Breakeven = Total Fixed Contribution Margin Ratio x= Sales TL. Unit Contribution Margin Ratio= fx−ax fx = f−a f

8. Cost-Volume-Profit (CVP) Analysis Breakeven Point
Two methods: Income Statement and Contribution Margin Approach.
Contribution Margin Approach X Breakeven = Total Fixed Cost Contribution Margin x=units sold Unit Contribution Margin = fx−ax x = f-a X Breakeven = Total Fixed Contribution Margin Ratio x= Sales TL. Unit Contribution Margin Ratio= fx−ax fx = f−a f

9. Cost-Volume-Profit (CVP) Analysis Breakeven Point
1.000
2.000
3.000
4.000
5.000
6.000
x=units sold
Example (KB A.10.8): The volume and profit graph has been demonstrated above.
Required:
Compute the breakeven point.
Ascertain the total fixed cost and unit contribution margin.
If company sells unit compute the profit or loss at stated volume.

10. Cost-Volume-Profit (CVP) Analysis Breakeven Point
1.000
2.000
3.000
4.000
5.000
6.000
x=units sold
Breakeven Point=XBEP
Fixed Costs=b
X Breakeven = Total Fixed Cost Unit Contribution Margin XBEP =4.000 units b=
4.000= Unit Contribution Margin
Unit Contribution Margin (f-a)=500 TL
𝑷𝒓𝒐𝒇𝒊𝒕/𝑳𝒐𝒔𝒔= 𝒇−𝒂 𝒙 −𝒃
𝑳𝒐𝒔𝒔=𝟓𝟎𝟎∗𝟐𝟕𝟎𝟎 −𝟐.𝟎𝟎𝟎.𝟎𝟎𝟎 𝑳𝒐𝒔𝒔=−𝟔𝟓𝟎.𝟎𝟎𝟎

11. Cost-Volume-Profit (CVP) Analysis Contribution Margin Approach -Target Profit
The contribution margin approach can be used to determine the units sold for a target profit.
What is the units sold point to achieve the target profit?
𝑷𝒓𝒐𝒇𝒊𝒕= 𝒇−𝒂 𝒙 −𝒃
𝒙=𝒖𝒏𝒊𝒕𝒔 𝒔𝒐𝒍𝒅
𝑷𝒓𝒐𝒇𝒊𝒕+𝒃= 𝒇−𝒂 𝒙
𝒙= 𝑷𝒓𝒐𝒇𝒊𝒕+𝒃 (𝒇−𝒂) →𝒙=𝒖𝒏𝒊𝒕𝒔 𝒔𝒐𝒍𝒅
What is the sales level (TL) to achieve the target profit?
𝑷𝒓𝒐𝒇𝒊𝒕= 𝒇−𝒂 𝒇 𝒙 −𝒃
𝒙=𝒔𝒂𝒍𝒆𝒔 𝑻𝑳
𝑷𝒓𝒐𝒇𝒊𝒕+𝒃= (𝒇−𝒂) 𝒇 𝒙
𝒙= 𝑷𝒓𝒐𝒇𝒊𝒕+𝒃 𝒇−𝒂 𝒇 →𝒙=𝒔𝒂𝒍𝒆𝒔 𝑻𝑳

12. Cost-Volume-Profit (CVP) Analysis Contribution Margin Approach – Margin of Safety (Güvenlik Payı)
Margin of safety is the difference between budgeted (actual) sales and break-even sales. This informs management of the risk of loss to which a business is subjected by changes in sales. In other words, the margin of safety indicates the amount by which a company's sales could decrease before the company will become unprofitable.

13. Cost-Volume-Profit (CVP) Analysis Contribution Margin Approach – Margin of Safety (Güvenlik Payı)
The margin of safety answers the “what if “ question: If budgeted revenues are above breakeven and drop, how far can they fall below budget before the breakeven point is reached? In other words What is the amount by which sales can drop before losses begin to be incurred?

14. Cost-Volume-Profit (CVP) Analysis Contribution Margin Approach – Margin of Safety (Güvenlik Payı)
Margin of Safety in Units=Actual or estimated units− X BEP in units Margin of Safety in TL=Actual or estimated sales TL− X BEP sales TL Margin of Safety Percentage= Margin of Safety in Units Actual estimated units Margin of Safety Percentage= Margin of Safety in TL Actual estimated in TL

15. Cost-Volume-Profit (CVP) Analysis Operating Leverage
Operating leverage measures a company’s fixed costs as a percentage of its total costs. It is used to evaluate the break even point of a business, as well as the likely profit levels on individual sales.
Degree of Operating Leverage (DOL) = ∆% in Profit ∆% in Sales
Degree of Operating Leverage= Total Contribution Margin Operating Profit = Contribution Margin Ratio∗Total Sales Operating Profit

16. Cost-Volume-Profit (CVP) Analysis Operating Leverage
High Operating Leverage
Low Operating Leverage
A large proportion of the company’s costs are fixed costs. In this case, the firm earns a large profit on each incremental sale, but must attain sufficient sales volume to cover its substantial fixed costs. If it can do so, then the entity will earn a major profit on all sales after it has paid for its fixed costs.
A large proportion of the company’s costs are variable costs, so it only incurs these costs if there is a sale. In this case, the firm earns a smaller profit on each incremental sale, but does not have to generate much sales volume in order to cover its lower fixed costs. It is easier for this type of company to earn a profit at low sales levels, but it does not earn outsized profits if it can generate additional sales.

17. Cost-Volume-Profit (CVP) Analysis Contribution Margin Approach-Example
5-17
Cost-Volume-Profit (CVP) Analysis Contribution Margin Approach-Example
EX (KB. A.10.11): ABC Co. intends to make TL net sales and gain profit in current period. But actually, company achieved half of the sale objective and gained TL profit.
Required:
Expect the sales volume, the predicted assumptions about selling price and cost are realized. What is the actual breakeven point.
Compute the current period’s margin of safety percentage?
Compute the operating leverage at budgeted profit.

18. Cost-Volume-Profit (CVP) Analysis Contribution Margin Approach -Target Profit
Solution (KB. A.10.11):
Budgeted
Actual
Net Sales
4.000TL
2.000 TL
Profit
1.000 TL
200 TL
Profit= f−a f x −b x=sales TL
1.000= f−a f −b
200= f−a f −b
𝑋 𝐵𝐸𝑃 = 600 0,4 =1.500 𝑇𝐿 𝑥=𝑠𝑎𝑙𝑒𝑠 𝑖𝑛 𝑇𝐿
𝑆𝑎𝑓𝑒𝑡𝑦 𝑀𝑎𝑟𝑔𝑖𝑛=𝐴𝑐𝑡𝑢𝑎𝑙 𝑆𝑎𝑙𝑒𝑠 𝑖𝑛 𝑇𝐿− 𝑋 𝐵𝐸𝑃 𝑆𝑎𝑓𝑒𝑡𝑦 𝑀𝑎𝑟𝑔𝑖𝑛
𝑆𝑎𝑓𝑒𝑡𝑦 𝑀𝑎𝑟𝑔𝑖𝑛=2.000−1.500=500
𝑆𝑎𝑓𝑒𝑡𝑦 𝑀𝑎𝑟𝑔𝑖𝑛 𝑅𝑎𝑡𝑖𝑜= =0,25
𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝐿𝑒𝑣𝑒𝑟𝑎𝑔𝑒= 𝑇𝑜𝑡𝑎𝑙 𝐶𝑜𝑛𝑡𝑟. 𝑀𝑎𝑟𝑔𝑖𝑛 𝑃𝑟𝑜𝑓𝑖𝑡 = 0,4∗ =1,6
1.000=4.000𝐶𝑅−𝑏
∓200= ∓2.000𝐶𝑅±𝑏
800=2.000𝐶𝑅
𝐶𝑅= =0,4
1.000=4.000(0,4)−𝑏
𝑏=600 𝑇𝐿

19. Cost-Volume-Profit (CVP) Analysis Contribution Margin Approach-Example
5-19
Cost-Volume-Profit (CVP) Analysis Contribution Margin Approach-Example
EX (KB. A.10.1): The production unit and the costs occurred in the first half of the year are as follows:
Mounts
Production Unit
Total Cost
January
1.800
2.400
February
3.800
2.700
March
1.000
2.200
April
1.500
2.300
May
2.500
June
4.000
2.800
Required:
Compute the total cost function according to High and Low Method.
The unit selling price is 1,2 TL.
Compute the monthly breakeven point both in units and TL.
In the case of units sold in a month, compute the profit.
To gain TL profit at actual selling price for a month, ascertain the sales in TL occurred in a month.
In the case of units sold in a year, compute the profit and margin of safety.

20. Cost-Volume-Profit (CVP) Analysis Parameter Changes in Profit Function
Profit= f−a x −b →x=units sold Profit= f−a f x −b →x=sales TL
Parameters in Profit Function
f=unit selling price
a=unit variable cost
b=Total fixed cost

21. Cost-Volume-Profit (CVP) Analysis Parameter changes in Profit Function
Changes in Contribution Margin Parameters
Changes in Unit Selling Price
Changes in Unit Variable Cost
Changes in unit selling price causes change in breakeven point.
As the unit selling price increases, the breakeven point decreases to low volumes.
As the unit selling price decreases, the breakeven point increases to high volumes.
Changes in unit variable cost causes change in breakeven point.
As the unit variable cost decreases, the breakeven point increases to high volumes.
As the unit variable cost decreases, the breakeven point increases high volumes.

22. Cost-Volume-Profit (CVP) Analysis Parameter changes in Profit Function
Changes in Contribution Margin Parameters
Changes in Unit Selling Price
Example: ABC Co. has sold unit in 20X1 while the selling price is 10 TL. The annual total fixed cost is TL. Unit contribution margin is 6 TL. Company plans a 20% increase in selling price. Required: Except selling price, assume that the remaining parameters will be constant, compute the monthly breakeven point and the profit accordingly.

23. Cost-Volume-Profit (CVP) Analysis Parameter changes in Profit Function
Current Situation: Annual selling volume unit , monthly selling volume unit. Annual fixed cost TL, Monthly fixed cost TL and Unit Contribution Margin is 6 TL. 6=10−𝑎→𝑎=4 𝑃𝑟𝑜𝑓𝑖𝑡 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 = 𝑓−𝑎 𝑥 −𝑏 𝑃𝑟𝑜𝑓𝑖𝑡 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 = 10− − 𝑃𝑟𝑜𝑓𝑖𝑡 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 =7.500 𝑋 𝐵𝑟𝑒𝑎𝑘𝑒𝑣𝑒𝑛 = 𝑇𝑜𝑡𝑎𝑙 𝐹𝑖𝑥𝑒𝑑 𝐶𝑜𝑠𝑡 𝐶𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑀𝑎𝑟𝑔𝑖𝑛 = =5.000 𝑢𝑛𝑖𝑡𝑠
New Situation: Annual selling volume unit , monthly selling volume unit. Annual fixed cost TL, Monthly fixed cost TL. 𝑓=10 ∗1.2=12 𝑇𝐿 𝑈𝑛𝑖𝑡 𝐶𝑜𝑛𝑡.𝑀𝑎𝑟𝑔𝑖𝑛=12−4=8 TL 𝑃𝑟𝑜𝑓𝑖𝑡 𝑁𝑒𝑤 = 𝑓−𝑎 𝑥 −𝑏 𝑃𝑟𝑜𝑓𝑖𝑡 𝑁𝑒𝑤 =8 𝑥 − →𝑥=6.250 𝑃𝑟𝑜𝑓𝑖𝑡 𝑁𝑒𝑤 = 𝑋 𝐵𝑟𝑒𝑎𝑘𝑒𝑣𝑒𝑛 = 𝑇𝑜𝑡𝑎𝑙 𝐹𝑖𝑥𝑒𝑑 𝐶𝑜𝑠𝑡 𝐶𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑀𝑎𝑟𝑔𝑖𝑛 = =3.750 𝑢𝑛𝑖𝑡𝑠

24. Cost-Volume-Profit (CVP) Analysis Parameter changes in Profit Function
Changes in Contribution Margin Parameters
Changes in Unit Variable Cost
Example: ABC Co. has sold unit in 20X1 while the selling price is 10 TL. The annual total fixed cost is TL. Unit contribution margin is 6 TL. Company expects %40 increase in unit variable cost. Required: Except unit variable cost, assume that the remaining parameters will be constant, compute the monthly breakeven point and the profit accordingly.

25. Cost-Volume-Profit (CVP) Analysis Parameter changes in Profit Function
Changes in Contribution Margin Parameters
Changes in Total Fixed Cost
Changes in total fixed cost causes change in breakeven point.
As the total fixed cost increases, the breakeven point increases to high volumes.
As the total fixed cost decreases, the breakeven point decreases to low volumes.

26. Cost-Volume-Profit (CVP) Analysis Parameter changes in Profit Function
Changes in Contribution Margin Parameters
Changes in Total Fixed Cost
Example: ABC Co. has sold unit in 20X1 while the selling price is 10 TL. The annual total fixed cost is TL. Unit contribution margin is 6 TL. Company expects %20 decrease in annual total fixed cost. Required: Except annual fixed cost, assume that the remaining parameters will be constant, compute the monthly breakeven point and the profit accordingly.