# Marketing Analysis Toolkit: Break-even Analysis

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1 R E V : M A R C H 2 5, T H O M A S S T E E N B U R G H J I L L A V E R Y Marketing Analysis Toolkit: Break-even Analysis Introduction Marketing managers are often called on to make recommendations for or against programs that cost money to implement. Before expenditures are made, managers want to be sure that they will be getting a return on their investment; they want to ensure that the money will be well spent and will lead to incremental profits for the firm. One way of assessing this is by calculating the break-even point. The break-even point calculates the number of incremental units the firm needs to sell to cover the cost of the program. If the firm sells less than the break-even point volume, it is losing money it is not selling enough to recoup its investment. If the firm sells more than the break-even point volume, it is making money it is selling more than enough to cover its investment. Managers use break-even analysis to assess the financial feasibility of marketing investments. Once a break-even point is calculated, managers need to evaluate whether it is feasible that the firm will be able to sell that quantity of product. Marketing managers use break-even analysis to assess many different types of marketing programs. For example, a firm may want to assess how many incremental units of product it must sell to recoup the cost of a \$10 million advertising campaign. Or a firm may want to assess how many incremental units of product it must sell to recoup the cost of a \$5 million sales promotion. Or a firm may want to assess how many incremental units of a new product it must sell to cover the cost of lost sales of an existing product due to intra-firm product cannibalization. Break-even analysis can also be used to determine how many purchases a customer (or customer segment) will have to make before the firm realizes a profit, given the costs of acquiring that customer (or customer segment). The Break-even Formula The break-even point is the unit quantity that yields zero profits to the firm where the firm breaks even on its fixed-cost investment. Hence, the break-even point is the unit quantity that generates sales revenues coming into the firm that are exactly equal to the total costs being spent by the firm. The key to break-even analysis is setting up an equation with Total Revenue on one side of the equation and Total Costs on the other side, such that Total Revenue = Total Costs. In order to calculate the break-even point, one has to find a unit quantity that makes both sides of the equation equal. Remember that the unit quantity sold affects both sides of the equation because total revenue Professor Thomas Steenburgh and Senior Lecturer Jill Avery prepared this note as the basis for class discussion. Copyright 2010, 2011, 2016 President and Fellows of Harvard College. To order copies or request permission to reproduce materials, call , write Harvard Business School Publishing, Boston, MA 02163, or go to This publication may not be digitized, photocopied, or otherwise reproduced, posted, or transmitted, without the permission of Harvard Business School.

2 Marketing Analysis Toolkit: Break-even Analysis is calculated by multiplying the quantity sold by the selling price per unit, and because total costs are calculated by first multiplying the quantity sold by the variable cost per unit, and then adding fixed costs. Hence, the break-even equation looks like this: Total Revenue = Total Costs Price per unit * BEQ = (Variable Costs per unit * BEQ) + Fixed Costs (where BEQ is the break-even quantity) *Note: The price per unit that goes into the Total Revenue calculation is not necessarily the price at which a consumer purchases the product (i.e., the retail price). For firms that do not sell directly to consumers, the price per unit received by the firm is the price at which the firm sells the product to its distribution channel partners. We can reorder the above equation to solve for the break-even point algebraically. BEQ = Fixed Costs Price per unit Variable Costs per unit Or, since Price per unit Variable Costs per unit = Contribution Margin per unit: BEQ = Fixed Costs Contribution Margin per unit Hence, to calculate a break-even point to understand how many units of a product we need to sell to cover our costs, we need to know the fixed costs of the program and the amount of profit we make from each unit we sell. Graphical Representation of the Break-even Point Graphically, the break-even point is the point where the Total Revenue curve intersects the Total Cost curve. Let s take a look at how the curves are built. Imagine a company that makes flip-flops. The company sells the flip-flops at a price of \$ The variable costs to make the flip-flops are \$ The fixed costs to advertise the flip-flops are \$2,000. What is the break-even quantity of flipflops the company must sell to break even on its advertising expense? First, determine the fixed costs. No matter how many flip-flops are sold, the cost of advertising remains the same. Thus, the company s fixed costs are \$2,000. Second, build the Variable Cost curve. Draw this curve by multiplying the potential number of flip-flops sold by \$ Third, draw the Total Cost curve by adding the fixed costs to the variable costs. Thus, the Total Cost curve is parallel to the Variable Cost curve, and the distance between the curves at any point is equal to the fixed costs. Fourth, build the Total Revenue curve. Draw this curve by multiplying the potential number of flip-flops sold by \$

3 Marketing Analysis Toolkit: Break-even Analysis Finally, find the point where the Total Revenue curve intersects with the Total Cost curve. This is the point at which Total Costs equal Total Revenues and therefore is your break-even point. For this example, the company would need to sell 200 units in order to break even. Use the formula to check the graph: BEQ = \$2,000/(\$24 \$14) = 200 units So, if managers believe that the incremental quantity of flip-flops sold as a result of the advertising campaign will be more than 200 units, the firm will recoup its investment in the advertising. This is indicated by the fact that the Total Revenue curve is greater than the Total Cost curve for all unit quantities greater than 200. At quantities less than 200 units, the firm will not recoup its investment because the Total Costs will be greater than the Total Revenues. 12,000 Total Revenue = \$24 per unit 11,000 10,000 9,000 Total Costs 8,000 Dollars 7,000 6,000 5,000 BEQ Fixed Costs = \$2,000 Variable Costs = \$14 per unit 4,000 3,000 2,000 1, Unit Sales Source: Casewriters. 3

5 Marketing Analysis Toolkit: Break-even Analysis BEQ = 66.7 units So the firm must be confident that it can sell at least 66.7 additional units at the lower price to justify the price decrease. (The total number of units that would need to be sold at the lower price is units.) Looking at the problem another way, the price reduction causes the company to lose \$200 on the products that it would have sold at the higher price. So we can think of \$200 as the fixed cost of the price decrease. Therefore, the company needs to sell an additional 66.7 units at a contribution margin of \$3.00 per unit to make up for this loss, as shown in the BEQ calculation below: BEQ = Fixed Cost = \$200 = 66.7 units Contribution Margin \$3.00 In the case of a price increase, a manager can use break-even analysis to calculate the amount of unit sales that can be sacrificed given the higher price point. When a price is increased, the firm gains money on each unit sold but may lose some of its existing unit volume, given the inverse relationship between price and demand. This decrease in unit volume may not compensate for the gained revenue on the existing demand. For example, suppose demand for a product is 100 units if the price is \$ A break-even analysis can be used to determine how much demand can be lost if the price is increased to \$ If the product has a contribution margin of \$5.00 at the \$10.00 price (and thus a contribution margin of \$7.00 at the \$12.00 price), then the break-even point is: Contribution Margin (at existing price) = Contribution Margin (at new price) \$5.00 * (100 units) = \$7.00 * (100 units + BEQ) BEQ = 28.6 units So the firm must be confident that it will lose fewer than 28.6 units to justify the price increase. (The total number of units that would need to be sold at the higher price is 71.4.) Looking at the problem another way, if the company is able to sell all of the original 100 units at the higher price, it would realize an additional \$200 in profits (we can think of this as a negative fixed cost, which means we can plug \$200 as the fixed cost of the program into the break-even formula). But the higher price will lead it to sacrifice some unit sales. The company would break even if it sacrificed 28.6 units; if the sales decrease was less than 28.6 units, the firms would make incremental profit from the price increase. BEQ = Fixed Cost = (\$5.00 \$7.00) * (100 units) = 28.6 units Contribution Margin \$7.00 3) To assess the feasibility of proposed short term variable marketing expenditures, such as the cost of a coupon promotion. Here, break-even analysis is used to determine the incremental number of units the company must sell to recoup its loss of profits from the sale of each product bought at a discounted price. If I am going to sell my products with a coupon that reduces the retail price by \$1.00, how many additional units of product do I need to sell to break even on my 5

6 Marketing Analysis Toolkit: Break-even Analysis coupon program investment? What the break-even formula is calculating here is how many units of product generate enough profit to cover the cost associated with the \$1.00 price break on the number of units sold with a coupon. For example, if I estimate that I will sell 50,000 units with a coupon, then I need to sell enough units to cover a \$50,000 marketing investment. 4.) To assess the feasibility of a new product introduction that will cannibalize existing product sales. Many new products a firm introduces to the market not only steal sales from competitors, but also steal sales from the firm s current offerings, a process known as cannibalization. Here, the cost of cannibalization is the decrease in profits the firm realizes as unit volume of the existing products goes down. Break-even analysis is used to determine the incremental number of units of the new product the firm must sell in order to recoup the cost of cannibalization. 6

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