three ways to run a break-even analysis

woman working on calculator in front of two computer monitorshow to tell what the profit should be.

by ed mendlowitz
77 ways to wow!

break-even analysis is a budgetary process designed to tell you how much sales are needed to break even, and how much you will make or lose if you exceed or fall short of this “break-even” sales amount. properly used, it can become a very potent tool.

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in a break-even analysis, all costs and expenses must be separated into “fixed” and “variable” categories. designations such as “costs of goods sold,” “selling” or “general and administrative” are irrelevant.

fixed costs are those that will occur, whether or not there are sales, or no matter what the sales volume. rent, office administrative and telephone are examples of items that are generally considered fixed.

variable costs are costs incurred because a sale was made. materials purchased and commissions are considered variable costs.

fixed items should be stated in dollars and variable costs as a percentage of sales. if a product sells for $100 and has a variable cost of $60, then the variable percent is 60 percent. on the same token, $40 is available to recover fixed costs and earn a profit. this is referred to as the profit contribution percent. the amount represented by that percent determines what is available to recover fixed costs and provide a profit. arithmetically it is done by subtracting the variable percent from 100 percent. in the example in this paragraph, the profit contribution percent (“pcp”) is 100% – 60% or 40%. to determine the break-even point, the fixed-cost dollar amount is divided by the pcp.

multiplying sales amounts over the break-even point by the pcp will tell what the profit should be. multiplying sales under the break-even point by the pcp will tell the dollars lost.

this calculation assumes that the fixed costs will not change from period to period. if they do, then adjustments must be made in the formula. for example, if there is a major repair, the break-even analysis can tell how much additional sales are needed to recover that cost. just divide the additional cost by the pcp.

generally, the break-even point should stay about the same from month to month. however, users should be aware and sensitive to extraordinary items and changing conditions and adjust the formula accordingly. in reality, the fixed costs are fixed for a range of sales. for instance, a 20 percent upward or downward shift in sales should not cause any change in the fixed costs. however, a 50 percent shift would, either requiring greater expenditures for increases or contracting of costs for decreases. an example could be shown with rent. an upward change that appears to become the norm would cause expanding into additional or larger facilities.

a confusing cost is most advertising costs because advertising is usually described as a percentage of sales. however, it is always committed to before the sales are made, making its expenditure independent of the sales volume. therefore, it is a fixed expense.

however, as with a lot of things there are exceptions. if advertising fees or commissions are paid based on search engine sales, then they become a variable cost because the amount paid is solely based on sales volume.

so, the lesson here is that nothing should be assumed, and the underlying activity needs to be thought out and understood thoroughly before classification decisions are made or acted upon.

three forms of break-even analysis compared

note that some items have fixed and variable elements and these should be broken into components and classified accordingly. an example could be direct labor, where a base of the labor force would never be reduced.

for example: a direct labor force of 100 people might include 20 people as the rock-bottom minimum that would always be retained, as long as the operation is in effect. therefore, the costs of those 20 people would be considered as fixed (and those dollars would be recorded as fixed) and anything over that, i.e., the 80 people would be variable and shown as a percentage of sales. accordingly, if sales increase then the variable labor would be added to, and if sales drop, the variable portion would decrease, but the fixed portion would not change.

following is a comparison between a conventional form of financial statement and break-even form.

 

break-even analysis – illustration 1

manufacturing co., inc.  
break-even analysis – monthly amounts
    conventional format   break-even format
    $ %   $ %
sales 1,000,000 100.00%
cost of goods sold
inventory – beginning*
purchases 230,000 23.00% 23.00%
direct labor ** 250,000 25.00% 70,000 18.00%
indirect labor 34,000 3.40% 34,000
rent 40,000 4.00% 40,000
utilities 18,000 1.80% 18,000
insurance 7,000 0.70% 7,000
factory maintenance and supplies 14,000 1.40% 14,000
depreciation 30,000 3.00% 30,000
less inventory – end*
total cost of goods sold 623,000 62.30%
gross profit 377,000 37.70%
selling, general and administrative
sales manager 25,000 2.50% 25,000
sales commissions 80,000 8.00% 8.00%
shipping salaries 40,000 4.00% 16,000 2.40%
other selling costs 25,000 2.50% 25,000
officers’ payroll 80,000 8.00% 80,000
office payroll 40,000 4.00% 40,000
rent and utilities 7,500 0.75% 7,500
telephone 9,000 0.90% 9,000
other general and administrative 11,000 1.10% 11,000
depreciation 7,500 0.75% 7,500
total sg&a 325,000 32.50%
net income before interest and taxes 52,000 5.20%      
  totals       434,000 51.40%
 * inventory is not calculated for this simplified illustration
 ** all labor costs above include taxes and fringes
proof of break-even analysis
profit contribution percent (100% – variable percent) 48.60%
fixed costs 434,000
break-even sales (fixed costs ÷ profit contribution percent) 893,004
sales for month 1,000,000
excess over break-even sales 106,996
multiplied by profit contribution percent (monthly profit) 52,000
profit per conventional format         52,000
difference or proof 0

 

 

break-even analysis – illustration 2

jan feb mar apr may fixed variable
sales 1,000,000 1,000,000 1,200,000 800,000 1,000,000
   
cost of sales    
inventory – beginning 1,000,000 1,000,000 1,000,000 928,800 1,000,000
purchases 250,000 250,000 300,000 200,000 250,000 25.0%
direct labor 200,000 200,000 200,000 200,000 200,000 200,000
indirect labor 30,000 30,000 30,000 30,000 30,000 30,000
payroll taxes and benefits 69,000 69,000 69,000 69,000 69,000 69,000
rent 30,000 30,000 30,000 30,000 30,000 30,000
utilities 20,000 20,000 24,000 16,000 20,000 2.0%
insurance 3,000 3,000 3,000 3,000 3,000 3,000
factory costs 20,000 20,000 20,000 20,000 20,000 20,000
depreciation 4,000 4,000 4,000 4,000 4,000 4,000
less inventory – end -1,000,000 -1,000,000 -928,800 -1,000,000 -1,000,000
total cost of sales 626,000 626,000 751,200 500,800 626,000
gross profit 374,000 374,000 448,800 299,200 374,000
gp% 37.4% 37.4% 37.4% 37.4% 37.4%
selling and shipping
sales manager 20,000 20,000 20,000 20,000 20,000 20,000
sales commissions 60,000 60,000 72,000 48,000 60,000 6.0%
shipping salaries 10,000 10,000 10,000 10,000 10,000 10,000
payroll taxes and benefits 27,000 27,000 30,600 23,400 27,000 9,000 1.8%
advertising 20,000 20,000 20,000 20,000 20,000 20,000
other selling costs 15,000 15,000 15,000 15,000 15,000 15,000
total selling and shipping 152,000 152,000 167,600 136,400 152,000
general and administrative 40,000 40,000 40,000 40,000 40,000 40,000
total selling, shipping, g&a 192,000 192,000 207,600 176,400 192,000
   
net income before taxes 182,000 182,000 241,200 122,800 182,000
470,000 34.8%
be sales 720,859
monthly sales 1,000,000
sales over break-even sales 279,141
profit 182,000

 

 

break-even analysis – illustration 3

  2016 2017 2018
(6 months)
fixed (based on 2018) variable %
sales 20,000,000 21,000,000 15,000,000
cost of sales:
inventory – beginning (did not include)
purchases 5,000,000 5,250,000 3,750,000 25%
direct labor and taxes and benefits 4,000,000 4,200,000 3,000,000 20%
indirect labor and taxes and benefits 800,000 840,000 441,000 441,000
factory costs and other overhead 3,000,000 3,150,000 1,653,750 1,653,750
depreciation 280,000 280,000 140,000 140,000
less inventory – end (did not include)
total cost of sales 13,080,000 13,720,000 8,984,750
gross profit 6,920,000 6,280,000 6,015,250
gp% 34.6% 29.9% 40.1%
selling, shipping, general and admin:
independent sales representatives 1,200,000 1,260,000 900,000 6%
sales salaries, taxes and benefits 900,000 945,000 496,125 496,125
shipping salaries, taxes and benefits 500,000 525,000 275,625 275,625
advertising 800,000 1,200,000 600,000 600,000
other sales and shipping costs 700,000 735,000 385,875 385,875
general and administrative 1,000,000 1,050,000 551,250 551,250
total selling, shipping, gen and admin 5,100,000 5,715,000 3,208,875
net income before interest and taxes 1,820,000 565,000 2,806,375
total fixed costs       4,543,625  
total variable costs         51%

 

proof: calculate the break-even sales (show your calculation)

1 – 51% = 49%

4,543,625 / 49% = 9,272,704 for 6 months = 18,545,408 for a year

 

proof: for above 6 months:

15,000,000 – 9,272,794 = 5,727,206 x 49% = 2,806,331 for 6 months

per above p&l = 806,375

diff.: 44 (ok per em)