Breakeven Point for Businesses Selling Multiple Products
Recall The Cigar Company sold only Cuban Cigars, The XYZ Company sold only one type of calculator, and the "Computers Are Us company sold only one type of computer. All of the examples we examined thus far had one thing in common; they all sold only one type of product having a single selling price and a single variable cost. Most businesses, however, sell multiple (many) products, each having their own selling price and product cost (or variable cost). How can these businesses calculate a breakeven point, when the formula allows for only one selling price and one variable cost? Below discusses how simple the process is.
Businesses selling multiple products must reduce all the selling prices down to one selling price. Similarly, businesses selling multiple products must reduce all the product costs (variable costs) for each product down to one product cost (variable cost). This is accomplished by calculating a weighted average selling price and a weighted average product cost (variable cost). Further, when the weighted average selling price and weighted average variable cost are calculated, only then can a business, selling multiple products, determine their breakeven point. Moreover, businesses selling multiple products will determine their breakeven point using the following Break Even formula:
Break Even in Units = Fixed Costs
WA Selling Price  WA Variable Costs
As you can see, the breakeven point formula for businesses selling multiple products is similar to the formula used by businesses selling a single product. The only difference is the term "weighted average" placed in front of the selling price and variable cost. It is important to understand the concept of weighted averages.
To illustrate the breakeven point for a company selling multiple products, let's assume the following example:
Johnny Smith is establishing a manufacturing company that makes two brands of writing pens; The Elite Pen and the Ball Point Pen. He plans to sell the pens to retailers all across the county. Johnny will sell the Elite Pen to retailers for $20.00 and the Ball Point Pen for $10.00. Through market research, Johnny estimates 40% of his customers (retail outlets) will purchase the Elite Pen, while the remaining 60% of customers (retail outlets) will purchase the high quality Ball Point Pen. The cost to manufacture each Elite Pen is estimated to be $5.00, while the cost to manufacture each Ball Point Pen is forecasted at $3.00 . These manufacturing costs are the only variable costs incurred by the company. Johnny has calculated his weighted average selling price to be $14.00 and his weighted average variable cost to be $3.80. In addition, Johnny forecasts the company's fixed costs for the upcoming year at $120,003 (assumed). Using the information presented above, calculate Johnny's breakeven point (IE how many pens will Johnny have to sell in order to cover his fixed costs and achieve a net income before taxes of Zero?)
Break Even in Units = Fixed Costs
WA Selling Price  WA Variable Costs
= $120,003
$14.00  $3.80
= $120,003
$10.20
= 11,765 units or pens
Therefore, the pen manufacturing company must sell 11,765 pens in order to break even or achieve a net income before taxes of ZERO.
In the above example, the weighted average selling price of $14.00 and weighted average variable costs of $3.80 were given. Let's now show you how these were calculated. Under the assumption section of this example, we provided you with three important pieces of information necessary in calculating the weighted average selling price and the weighted average variable cost. They are as follows:
The three above items can be organized as follows.
Elite Pen  Ball Point Pen  
Selling Price Per product  $20.00  $10.00 
Variable Cost Per Product  $ 5.00  $ 2.00 
Sales Percentage Forecast  40%  60% 
Below shows how Johnny calculated his weighted average selling price of $14.00 and his weighted average variable costs of $3.80
Step 1  determine weighted average selling price
The first step is to calculate the weighted average selling price. To do this, we simply multiply each product's selling price by its corresponding sales percentage forecast. The resulting figure will be called the ADJUSTED FACTOR. The adjusted factors are then added together to arrive at the weighted average selling price. Here's how it's accomplished;
(A) Selling Price 
(B) Sales % Forecast 
(A x B) Adjusted Factor 

Elite Pens  $20.00  40%  $ 8.00 (C) 
Ball Point Pens  $10.00  60%  $ 6.00 (D) 
100%  
Weighted Average Selling Price  $14.00  


The letter A = The Selling Price The letter B = The Sales Percentage (%) Forecast The Adjusted Factor = A x B (Selling Price X the Corresponding Sales % Forecast) The letter C = The Adjusted Factor for the Elite Pen The letter D = The Adjusted Factor for the Ball Point Pen The Weighted Average Selling Price = C + D (The sum of the Adjusted Factors) 
As you can see, Johnny's Weighted Average Selling Price is $14.00; the same value used in our example. Now lets calculate the weighted average variable cost.
Step 2  determining the weighted average variable cost.
Calculating the weighted average variable cost involves the exact procedures as calculating the weighted average selling price. Moreover, simply multiply each pens's variable costs by their corresponding sales percentage forecast. The resulting figure will be called the ADJUSTED FACTOR. The two adjusted factors are then added together to arrive at the weighted average variable costs. Here's how it accomplished;
(A) Variable Costs 
(B) Sales % Forecast 
(A x B) Adjusted Factor 

Elite Pens  $5.00  40%  $ 2.00 (C) 
Ball Point Pens  $3.00  60%  $ 1.80 (D) 
100%  
Weighted Average Variable Cost  $ 3.80 (C+D)  
The letter A = The Variable Costs The letter B = The Sales Percentage (%) Forecast The Adjusted Factor = A x B (Variable Cost X the Corresponding Sales % Forecast) The letter C = The Adjusted Factor for the Elite Pen The letter D = The Adjusted Factor for the Ball Point Pen The Weighted Average Variable Cost = C + D (The sum of the Adjusted Factors) 
As you can see, Johnny's Weighted Average Variable Cost is $3.80; the same value we used in our example.
And that's it!!! The weighted average selling price is $14.00 and the weighted average variable cost is $3.80. And once again, the breakeven point for the pen manufacturing company is:
Break Even in Units = Fixed Costs
WA Selling Price  WA Variable Costs
Break Even in Units = $120,003
$14.00  $3.80
Break Even in Units = $120,003
$10.20
Break Even in Units = 11,765 units or pens
As shown in the above example, The Pen Company must sell a total of 11,765 pens in order to breakeven (Net Income of ZERO). The 11,765, however, doesn't tell us how many Elite Pens must be sold nor does it tell us how many Ball Point pens must be sold in order to breakeven. Is there any way to determine this? YES, we simply apply the Sales Percentage Forecast for each product (40% and 60%) to the number of breakeven units (11,765). Since Johnny forecasted 40% of customers will purchase the Elite Pen, then 40% of the 11,765 pens are expecting to sell. Similarly, since Johnny forecasted 60% of customers will purchase the Ball Point Pen, then 60% of the 11,765 pens are expecting to sell. Therefore, 4,706 Elite Pens (11,765 total pens x 40%) and 7,059 Ball Point Pens (11,765 total pens x 60%) must be sold in order to breakeven. Let's see if these figures are correct.
(A) Elite Pens 
(B) Ball Point Pens 
(A + B) Totals 

Sales in units  4,706 pens  7,059 pens  11,765 pens 
Sales at $20 and $10  $94,120  $70,590  $164,710 
Variable Costs at $5 and $3  $23,530  $21,177  $ 44,707 
Contribution Margin  $70,590  $49,413  $120,003 
Less:  $120,003  
Net Income Before Taxes ($120,003  $120,003)  $ 0.00 
As you can see, the Net Income Before Taxes would be ZERO, if the pen company sold 11,765 pens, consisting of 4,706 Elite Pens and 7,059 Ball Point Pens. The five points below depict how the above figures were calculated.
The above example determined the number of pens (Elite and Ball Point Pens) Johnny would have to sell in order to achieve a net income before taxes of ZERO. What if Johnny wanted to calculate the number of units needed to be sold in order to achieve a net income of lets say $25,500? The following formula is needed;
Breakeven for a Desired Income Level:
Fixed Costs + Desired Net Income Before Taxes
Weighted Average Selling Price  Weighted Average Variable Costs
= $120,003 + $25,500
$14.00  $3.80
= $145,503
$10.20
= 14,265 units or pens
Therefore, for Johnny to cover the company's forecasted fixed costs and achieve a net income before taxes of $25,500, he would have to sell 14,265 pens. Of the 14,265 pens sold, 5,706 would have to be Elite Pens and 8,559 would have to be the Ball Point Pen (14,265 x 40% sales percentage forecast = 5,706 Elite Pens and 14,265 x 60% sales percentage forecast = 8,559 Ball Point Pens). The following chart can be used to verify these figures.
(A) Elite Pens 
(B) Ball Point Pens 
(A + B) Totals 

Sales in units  5,706 pens  8,559 pens  14,265 pens 
Sales at $20 and $10  $114,120  $85,590  $199,710 
Variable Costs at $5 and $3  $28,530  $25,677  $ 54,207 
Contribution Margin  $85,590  $59,913  $145,503 
Less:  $120,003  
Net Income Before Taxes  $ 25,500 
As you can see, the Net Income Before Taxes would be $25,500 if the pen company sold 14,265 pens; consisting of 5,706 Elite Pens and 8,559 Ball Point Pens. The five points below depict how the above figures were calculated.
SUMMARY:
A Break Even Analysis, in its simplest form, is a tool used to determine the level of sales a business must earn in order to achieve neither a profit nor a loss. In other words, the point at which a business' Net Income Before Taxes is ZERO (revenues  expenses = 0). Once again, the Breakeven Analysis can be used to answer many important business questions such as;
In summary, the breakeven analysis formula, used by a company selling a single product, is similar to the formula used by a company selling multiple products. A company selling multiply products, however, must calculate a weighted average selling price and a weighted average product cost (variable cost). For a thorough explanation on calculating a weighted average selling price and a weighted average product cost, please refer to the financial section entitled "Weighted Averages".