Break-even analysis is a tool used by managers to estimate either the quantity they need to sell at a given price to cover all costs or the price they must charge to cover all costs for a given quantity of output. Break-even analysis is often used when managers are considering new INVEST-MENTs or new PRODUCTs.
Break-even quantity (BEQ) is estimated using the formula BEQ = FC ÷ (P – AVC), where FC is total fixed costs, P is price per unit, and AVC is average variable cost per unit. Break-even analysis assumes a manager can estimate:
- the initial fixed costs (equipment, buildings, licenses; any cost that is required to get started but does not change with the level of output),
- the average variable cost (materials, labor, energy) in the range of output being considered.
If these costs can be estimated, a manager can then determine how many units must be sold at various prices to break even. For example, if FC is $1000 and AVC is $10, then at:
P = $20, BEQ = 100
P = $30, BEQ = 50
P = $40, BEQ = 33.3
Break-even analysis allows a manager to create a hypothetical DEMAND curve. Using the information from the BEQ analysis, managers then determine whether they think they can sell at least that quantity at a given price. Managers may then employ sales forecasting techniques to compare the results of BEQ analysis with potential market demand.
In the above formula, P–AVC is often called the contribution margin. For each unit produced and sold, the difference between price and the average variable cost (if the difference is negative, the product should not be produced) contributes to “covering” fixed costs, and when all fixed costs are covered, ultimately contributes to profit. Break-even price (BEP) is estimated using the formula BEP = (FC ÷ Q) + AVC, which says that the BEP equals average total cost. Using this same example above, if FC are $1000 and AVC is $10 then at:
Q = 50, BEP = $30
Q = 100, BEP = $20
Q = 200, BEP = $15
Managers can use BEP analysis to answer the question, “If we produce and sell 100 units, what price do we have to get in order to at least break even?”
Retail store managers frequently use break-even analysis when considering new products. In RETAILING, firms often “keystone” products—that is, price their products at twice the cost to the store. If a manager orders 100 spring shirts at $10 each and prices them at $20 each, then they must sell at least 50 shirts to break even.
Another way to use break-even analysis is when considering ADVERTISING options. If a magazine ad costs $500, the product advertised sells for $10, and the average variable cost is $5, then the advertisement would need to generate 100 additional sales to break even.
