What does it mean when a company breaks even? It means that profit is exactly equal to zero or its revenues exactly equal its costs. Now using our handy profit formula, it means that revenues minus variable costs minus fixed costs are equal to zero. And for starters, there are two important aspects of breakeven analysis: first determining the breakeven quantity or the number of units that a company needs to sell to breakeven or have profit exactly equal to zero, and then number two, determining the breakeven price or the price at which the company wants price its products or services to breakeven. Let's take a look. The breakeven point or breakeven quantity is an important concept to managers. As sales levels below that point, the organization incurs a loss and only when sales increase beyond that level would the organization report a profit. For given a price, a variable cost per unit and total fixed costs, we can determine how many units the company needs to sell to breakeven. Consider our T-shirt maker. The company prices its T-shirts at $10, variable cost per unit is $4, total fixed costs for $40000. How many T-shirts does a company need to sell to breakeven? Let's start with our handy profit formula. Substituting price times units for revenues and variable cost per unit times unit for variable costs and rearranging a bit, we see we can determine the breakeven quantity by dividing total fixed costs by the contribution margin per unit. For the T-shirt maker that's $40000 divided by $6 per T-shirt or 6667 T-shirts. So the T-shirt maker must sell 6667 T-shirts to breakeven. Think about it this way. The company has total fixed cost of $40000. Every time the company sells a T-shirt it receives $6 in contribution. The $10 minus price minus the $4 variable cost that it can use to help cover fixed cost. The sales of one unit -$6, a second unit another $6, a third unit another $6 and so on and so on and so on. So how many of these $6 increments does it take to get to $40000? Oh 6667, you guessed it. Once it sells 6667 units, its total contribution margin is $40000. $6 per T-shirt times 6667 T-shirt. So what exactly- that total contribution margin exactly covers its fixed costs and breaks even, and then every additional unit at sales after that increases profit by $6. So in summary then, the contribution margin per unit represents the incremental profit for each unit sold and the total contribution represents the total amount available to cover the fixed cost and then generate a profit. Okay, let's change this up a bit. Suppose a T-shirt maker knows that the variable cost per unit is $4, total fixed cost of $40000, and it projects demand for 6667 units. So it doesnt know the price yet. What price does it need to charge to breakeven? So here, rather than solving for the breakeven number of units given a price, we are solving for a breakeven price given a certain number of units. Again, we can write out that handy profit formula, algebraically solve for the breakeven price and here the break even price is $10. Now, that makes sense doesn't it? Let's think about this. We're looking for a price that is sufficient to cover all the costs. The total fixed costs plus the total variable costs, or the $40000 fixed cost plus the variable cost and here, that is $10.
