Marketing Arithmetic Note
This is an introductory note that provides a basic explanation of marketing arithmetic. You should expect to see the following concepts covered in much more detail throughout your course of studies in the business curriculum. Please use this note in conjunction with other concepts the text covers. Consider the connections between the concept of supply and demand (Chapter 2’s microeconomics), the marketing concepts in Chapters 13-15, and the accounting terms we will cover in later Chapters. You should note that although the concepts address similar issues such as the price for a product, the perspectives are very different. Academic disciplines such as economics and marketing see and use very similar words (e.g. price) but see the business world in very different ways.
Marketing arithmetic is a term used to describe the relationship between the cost, profit and price of a product. The following equation describes this relationship.
cost + profit = price
Please note that it is possible to have a negative profit if costs exceed the price charged for a product. The balance of this note describes each of these three portions of the equation in turn.
Variable and fixed costs are the two basic types of costs we will consider in this note. Variable costs are those costs that vary directly with the number of products that you produce. These include costs such as material, labor involved in making the product, sales commissions on each product, energy costs, shipping, handling and distribution, and packaging. Fixed costs are those costs that a business incurs just to open the doors. Plant, equipment, insurance, advertising, staff labor, and general management are types of fixed costs.
Companies usually produce many different products using some or all of the components included as fixed costs. Therefore, we need to modify the simple equation used above. One way to look at this equation is to calculate the amount of money each line of products contributes to the fixed costs. Contribution is the amount of money left after subtracting the variable costs from price. For example, our company made and sold 100 widgets with a price of $50.00. The total sales equal $5,000. The variable costs (per widget) were as follows:
Material$3.00
Labor 2.00
Commission .50
Shipping .50
Packaging1.00
Per widget variable costs$7.00
With a per widget selling price of $50.00 and a per widget variable cost of $7.00, the per widget contribution equals $43.00 ($50.00 – 7.00). The total variable costs are $700.00 ( $7 X 100 widgets) and therefore the total contribution is $4,300.00 ($5,000.00 – 700.00).
Break even occurs when all of the costs for a given product equal its price. Break even analysis takes a different approach than contribution in that it assumes that you know the fixed costs associated with producing a product. Let us assume that we know that the fixed costs for producing each of our 100 widgets were as follows:
Plant $50.00
Equipment 5.00
Insurance 1.00
Advertising 1.00
staff labor 2.00
general management 3.00
fixed costs $ 62.00
Adding our fixed costs per widget ($ 62.00) to the variable costs per widget ($7.00) gives us a total cost per widget of $69.00. To break even the company needs to charge at least $69.00 and sell every widget.
Now we can combine the contribution and break even concepts. Assume that, instead of knowing our per widget amount for fixed costs, we were trying to calculate how many widgets we had to produce and sell just to cover our fixed costs. Assume that we know our total fixed costs equal $7800.00. If the contribution to fixed costs is $39.00 per widget, how many widgets would we have to sell to break even? You can calculate the break even number of widgets we need to sell by dividing the total fixed costs by the contribution. In this case we arrive at 200 widgets or $7800.00/ $39.00 per widget.
We can continue to develop different break even analyses by adjusting our variable and fixed costs. We would want to do develop these additional analyses to help us make decisions. For example, if we were to increase our advertising by $2.00 per widget, would we be able to increase the number of widgets we actually sell and realize a larger overall profit. We will work on exercises in class to provide additional examples.
Our ability to sell these additional widgets also depends on people willing to buy them. Market share and market share analysis are two concepts that deal with a special variation of the equation first shown in this note. These concepts assume that we can calculate how many buyers there are for our product and similar products made by other companies. We express market share as a percentage of the total sales for a product. (You will find that this is a very simplified definition of market.) For example, the total amount of money spent on buying widgets was $100,000.00 in 1998. If our company’s sales for widgets was $20,000.00, we would say our market share was 20% or $20,000/100,000. Market share analysis studies the potential growth of the widget market (total number of people willing to buy widgets in any given year) and the potential of our company to increase its market share. Once again, we will work through some examples in class to reinforce these concepts.
Profit is the next concept we should address. Profit is the amount of money remaining after paying all of the variable and fixed costs. Profit assumes that we charged and received enough money to cover or pay for these costs. Margin is a term usually used to express the percent of profit associated with an individual product. You can calculate margin as a percentage of price or cost. For example, our infamous widget sells for $10.00 and costs (variable and fixed) $7.00. Margin (or profit margin) expressed as percent of the selling price would be 30% or $3.00/10.00.
Sometimes you calculate margin based on cost. This usually occurs with retailers adding their ‘markup’ or ‘profit margin’ to the cost of the product from the wholesaler. Assume that the wholesaler sold us the widget for $6.00 and we had a 40% markup or profit margin. Our original equation indicates that price = cost + profit. We know that price = 100%, our cost is $6.00 and we want a 40% profit. We can show the equation as:
price = cost + profit
OR
100% = $6.00 + 40%
By subtracting 40 % from each side, we determine that cost equals 60% of the selling price.
(100 – 40) or 60 % = $6.00
If the $6.00 cost equals 60% of the selling price, we can determine 100% of the selling price using the following ratio.
$6.00 (cost) = 60% of the selling price
actual unknown selling price100% of the selling price
Some multiplication tells us that the actual selling price is $10.00. A quicker way to calculate the selling price is to divide the cost by (1- the percentage). In this example we would divide $6.00 by (1 – 0.40). This would give us $6.00 / 0.6 or $10.00.