## The Break-Even Point when selling multiple products

Break-even 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 break-even 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 break-even point.  Moreover, businesses selling multiple products will determine their break-even point using the following Break Even formula:

Break Even in Units        =                         Fixed Costs

WA Selling Price - WA Variable Costs

As you can see, the break-even 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.

• The weighted average selling price considers all the selling prices of all the products a company sells and reduces them (all selling prices) into one single selling price.
• The weighted average product cost (variable costs) considers all the costs of all the products a company sells and reduces them (all product costs) into one single product cost.

To illustrate the break-even 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 break-even 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:

•
1. The selling price for each pen

1. The variable costs for each pen

1. The sales percentage (%) forecast for each pen. The sales percentage forecast is simply the percentage of total sales Johnny anticipates for each type of pen. Moreover, he estimates 40% of his customers will purchase the Elite Pen while 60% of customers are expected to purchase the Ball Point Pen. One further note, the sales percentage forecast must always add to 100% (40% +60% = 100%).

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 break-even 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 break-even (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 break-even. 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 break-even 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 break-even. 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.

1. The sales in units were arrived at by multiplying the total number of units needed to break-even by each product's sales percentage forecast (40% and 60% multiplied by 11,765).

1. The sales in dollars was arrived at by multiplying each pen's selling price by each pen's corresponding unit sales (4,706 x \$20 and 7,059 x \$10.00).

1. The variable costs in dollars were arrived at by multiplying each pen's variable cost by each pen's corresponding unit sales. (4,706 x \$5 and 7,059 x \$3.00).

1. The contribution margin of \$120,003 is calculated by subtracting the total variable costs from the total sales (\$164,710 - \$44,707 = 120,003).

1. The pen company's fixed costs of \$120,003 are then subtracted from the contribution margin of \$120,003 to arrive at the Net Income Before Taxes of \$0.00 (\$120,003 - \$120,003).

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;

Break-even 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.

•
1. The sales in units was arrived at by multiplying the total number of units needed to break-even by each product's sales percentage forecast (40% and 60% multiplied by 14,265).

1. The sales in dollars was arrived at by multiplying each pen's selling price by each pen's corresponding unit sales (5,706 x \$20 AND 8,559 x \$10).

1. The variable costs in dollars was arrived at by multiplying each product's variable cost by each product's corresponding unit sales (5,706 x \$5 AND 8,559 x \$3).

1. The contribution margin of \$145,503 is calculated by subtracting the total variable costs from the total sales (\$199,710 - \$54,207 = 145,503).

1. The pen company's fixed costs of \$120,003 are then subtracted from the contribution margin of \$145,503 to arrive at the Net Income Before Taxes of \$25,500 (\$145,503 - \$120,003).

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 Break-even Analysis can be used to answer many important business questions such as;

1. What sales level is required to earn a desired Net Income?
2. What net income would be earned if selling prices were reduced?
3. What would the effect on net income be if costs were reduced?
4. What effect would machines replacing workers have on net income?
5. What would the effect on net income be if the sales mix changed?
6. What would the effect on net income be if selling prices increased?

In summary, the break-even 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".

Categories: Financial