21 Break Even Point Analysis
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Transcript of 21 Break Even Point Analysis
Key determinants of operating incomeKey determinants of operating income
Purchasing and selling pricesselling prices
Sales revenue – operating costs = operating income
Structural determinants
Volumesdeterminants
Structural factorsStructural factors
i d i i• Maximum production capacity• ExperienceExperience• Specialization• Standardization• Industry• Industry• Vertical/horizontal integration• ...
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Price levelsPrice levels
h i i• Purchasing prices– Price of inputs bought from suppliersp g pp
• Selling pricesi f ld– Price of output sold to consumers
• Both prices depend on internal factors (e.g. p p ( gpower of the firm in negotiating with suppliers or setting selling prices) and external factorsor setting selling prices) and external factors (e.g. industry trends, competition levels)
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VolumesVolumes• For given structural determinants and cost g
structure, the operating profits is determined by volumesvolumes
• Different volumes influence operating profits by changing both total costs (via variable costs) and revenuesa d eve ues
• We use the break even point (BEP) analysis to d t d th l ti hi b t lunderstand the relationship between volumes
and operating profits• Before BEP, let’s recap the nature of costs
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Costs CostsVolume range
being considered
Total variable costs
Total variable costs
Volumes
a. linear relationship variable costs/volumes
Volumes
b. actual relationship variable costs/volumes
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Question: Why non-linearities?
Costs CostsVolume range
being considered
Total fixed costs
Total fixed costs
Total fixed costs
Volumes
a. linear relationship fixed costs/volumes
Volumes
b. actual relationship fixed costs/volumes
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Question: Why step-wise increases?
A note on labor costsA note on labor costs
• If labor can be easily increased/decreased or reallocated across business units, then labor ,would be a variable cost
• However in practice labor is regulated and• However, in practice, labor is regulated and labor laws create hiring/firing costs
• In this case, labor costs are variable but they also entail some fixed cost componentalso entail some fixed cost component– In the Scaltrini solution, we classify them as semi-
variable costsvariable costs
Costs
Total costs
V i bl tVariable costs
Fixed costs
Volumes
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120
80
100
60
80 Average unit cost cost
40
0
20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 301 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Volumes produced
• It decreases due to fixed-cost absorption economies (i.e. fixed costs distributed over more units ot output), although variable costs increase• However the shape is determined by the importance of fixed and variable costs
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• However, the shape is determined by the importance of fixed and variable costs for the firm
Exampleh f l ld ( / l )What if only 30K pieces sold (2/3 or original projection)?
Average price per meal
Projected volume (300x150) = 45 000
16.00 Average price per meal
Projected volume (300x100) = 30 000
16.00
Projected volume (300x150) = 45,000
Total sales revenue 720,000
Variable unit cost per meal 4 00
Projected volume (300x100) = 30,000
Total sales revenue 480,000
Variable unit costs per meal 4 00Variable unit cost per meal
Projected volume = 45,000
4.00 Variable unit costs per meal
Projected volume = 30,000
4.00
Total variable costs 180,000Cost 1 expert pizza cook4 workers at average cost of 32,500
80,000130,000
Total variable costs 120,000Cost 1 expert pizza cook4 workers at average cost of 32,500
80,000130,000
Salaries and wages 210,000
Rent 60,000General Costs 70,000Depreciation 35,000
Salaries and wages 210,000
Rent 60,000General Costs 70,000Depreciation 35,000
Output sold is 1/3 lower but operating income is not just 2/3 lower but it’s negative! Why?
p ,Advertising 30,000Operating income 135,000
Depreciation 35,000Advertising 30,000Operating income -45,000
Output sold is 1/3 lower, but operating income is not just 2/3 lower but it s negative! Why? Some costs don’t drop (i.e. 5 worker is minimum number to run the restaurant), fixed costs remain unchanged
ExampleExample
(a) (b) (c) (d) (e) (f) (g)
Total and unit costs
(a) Q
(b) Variable cost (VC) per unit
(c) Total VC
(a x b)(000 €)
(d)Fixed
cost (FC)(000 €)
(e) Total costs
(c +d)000 €)
(f)Total cost per unit
(e / a)
(g)Fixed cost per unit(d / a)
25,000 4.00 100 405 505 20.20 16.20
30,000 4.00 120 405 525 17.50 13.50
45,000 4.00 180 405 585 13.00 9.0060,000 4.00 240 405 645 10.75 6.75
What can we do?What can we do?
• Variations in volumes• Variations in costsVariations in costs• Variations in selling prices
• First question to ask is what is the output that• First question to ask is, what is the output that allows the firm to generate enough revenues to
it ti t ? B k i tcover its operating costs? Break even point
Break even point (BPE)Break even point (BPE)
• Q such that Revenues (R) = Total Costs• Lets call r the selling price of each unitLets call r the selling price of each unit
• Then, r×Q = VC×Q + FC, Q Q
r×Q-VC×Q = FC
Q×(r - VC) = FC
Qbreak-even = FC / (r – VC)i ib i i= unit contribution unit
Compute the BPECompute the BPE
+ Average price per mealx Hypothetical volume (300x112.5) = 33,750
16.00Costs and revenues
Sales
= Total sales revenue 540,000+ Average cost per meal x Hypothetical Volume = 33,750
4.00
revenue
Operating profit
= Total variable costs 135,000
Salaries and wages 210,000
Rent 60,000Fixed
Total costs540,000
General costs 70,000
Depreciation 35,000
Fixed costs
Operating loss
BEPAdvertising 30,000
Operating income 0,000Volumes
BEP33,750
Break even point (BPE)Break even point (BPE)
/ ( )Qbreak-even = FC / (r – VC)= unit contribution unit (MCu)
• How much does the production and sale of each it f t t t ib t t i fi d t ?
( )
unit of output contribute to covering fixed costs?• Often, contribution margin is expressed as a
f CM(%) MC /percentage of revenues: CM(%) = MCu/r• Using this term, we can compute the revenue-
based BPE: FC/CM(%)• Useful when e.g. reasoning in quantity doesn’t g g q y
make sense (diversified firm)
Operating riskOperating risk
• Varying degree of profitability that a firm will face particularly negative or positive net income, in relation to the fluctuation in production and sales volumes
• Linked to two components of the organization's economic structure: BPE and degree of the operating leverage
• Operating leverage is the size of the differentialOperating leverage is the size of the differential between revenues and total costs above and below the break-even pointb ea eve po t
Operating riskOperating risk
Costsdand revenues Sales revenue
Operating leverage
Total costs
p g g
Fixed costs
VolumesBEP VolumesBEP
Operating riskOperating risk
• Suppose that there are exogenous changes in volume:• If a firm has very rigid cost structure, i.e. high ratio of y g g
fixed costs to total costs– The firm will react badly to drops in volumes (less room to y p (
distribute fixed costs over units of output)– But the same firm will respond positively to increases in
volumes
• The opposite is true for a firm with a flexible coststructure, i.e. low ratio of fixed costs to total costs– If volumes drop, the firm can easily reduce costs– If volumes increase, the firm experience unavoidable cost
increases
Operating riskOperating risk
Computation of operating riskComputation of operating risk
• Ratio of total variable costs and fixed costs at the BEP
• The greater the value, the greater the operating risk• Operating risk is not necessarily a bad thing: itOperating risk is not necessarily a bad thing: it
amplifies losses (as we move in the area right to the BEP), but it amplifies profits (as we move in the areaBEP), but it amplifies profits (as we move in the area left to the BEP)
• Hence the choice of e g two plants with same BEP• Hence, the choice of, e.g. two plants with same BEP but different operating risk depends on our estimate of how much volumes sold would exceed the BEPof how much volumes sold would exceed the BEP, and on the manager’s degree of risk aversion
Profit pointProfit point
• So far, we have only focused on a BEP such that revenues cover operating costs (e.g. labor, p g ( g ,equipment etc.)
• But in practice firms incur in non operating• But in practice firms incur in non-operating costs related e.g. to financial charges and taxes
• These charges are negative components that need to be taken into account in theneed to be taken into account in the determination of net income (≠ operating income)income)
Profit point: examplep pLet’s go back to the example of the restaurant (under scenario 1)
Financial charges 24,000
Non-income taxes 6,000
Income tax rate (on pre tax income) 50%
Average price per meal
Projected volume (300x150) = 45,000
16.00
Income tax rate (on pre-tax income) 50%
Target net income 75,000Total sales revenue 720,000
Variable unit cost per meal 4.00
Target operating income 24,000+6,000+150,000= 180,000
Projected volume = 45,000
Total variable costs 180,000What is the sale revenue that can allow the
firm to reach the target?
,Cost 1 expert pizza cook4 workers at average cost of 32,500
Salaries and wages
80,000130,000
210,000We use a variation of the revenue based BEP:(FC+Target operating income)
CM(%) (r-VC)/r = 12/16
Rent 60,000General Costs 70,000Depreciation 35,000Advertising 30 000
= (405,000+180,000)0.75
( )Advertising 30,000Operating income 135,000