This is “Breakeven Analysis”, section 2.4 from the book Managerial Economics Principles (v. 1.0).
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A scan of Figure 2.1 "Graphs of Revenue, Cost, and Profit Functions for Ice Cream Bar Business at Price of $1.50" shows that the ice cream bar venture could result in an economic profit or loss depending on the volume of business. As the sales volume increases, revenue and cost increase and profit becomes progressively less negative, turns positive, and then becomes increasingly positive. There is a zone of lower volume levels where economic costs exceed revenues and a zone on the higher volume levels where revenues exceed economic costs.
One important consideration for our three students is whether they are confident that the sales volume will be high enough to fall in the range of positive economic profits. The volume level that separates the range with economic loss from the range with economic profit is called the breakeven pointThe volume of business that separates economic loss from economic profit; the quantity at which the revenue function and the cost function are equal.. From the graph we can see the breakeven point is slightly less than 35,000 units. If the students can sell above that level, which the prior operator did, it will be worthwhile to proceed with the venture. If they are doubtful of reaching that level, they should abandon the venture now, even if that means losing their nonrefundable deposit.
There are a number of ways to determine a precise value for the breakeven level algebraically. One is to solve for the value of Q that makes the economic profit function equal to zero:0 = $1.2 Q − $40,000 or Q = $40,000/$1.2 = 33,334 units.
An equivalent approach is to find the value of Q where the revenue function and cost function have identical values.
Another way to assess the breakeven point is to find how large the volume must be before the average cost drops to the price level. In this case, we need to find the value of Q where AC is equal to $1.50. This occurs at the breakeven level calculated earlier.
A fourth approach to solving for the breakeven level is to consider how profit changes as the volume level increases. Each additional item sold incurs a variable cost per unit of $0.30 and is sold for a price of $1.50. The difference, called the unit contribution marginThe difference between the price per unit and the variable cost per unit; price per unit - variable cost per unit., would be $1.20. For each additional unit of volume, the profit increases by $1.20. In order to make an overall economic profit, the business would need to accrue a sufficient number of unit contribution margins to cover the economic fixed cost of $40,000. So the breakeven level would beQ = fixed cost/(price per unit − variable cost per unit) = $40,000/($1.50 − $0.30) = 33,333.3 or 33,334 units.
Once the operating volume crosses the breakeven threshold, each additional unit contribution margin results in additional profit.
We get an interesting insight into the nature of a business by comparing the unit contribution margin with the price. In the case of the ice cream business, the unit contribution margin is 80% of the price. When the price and unit contribution margins are close, most of the revenue generated from additional sales turns into profit once you get above the breakeven level. However, if you fall below the breakeven level, the loss will grow equally dramatically as the volume level drops. Businesses like software providers, which tend have mostly fixed costs, see a close correlation between revenue and profit. Businesses of this type tend to be high risk and high reward.
On the other hand, businesses that have predominantly variable costs, such as a retail grocery outlet, tend to have relatively modest changes in profit relative to changes in revenue. If business level falls off, they can scale down their variable costs and profit will not decline so much. At the same time, large increases in volume levels beyond the breakeven level can achieve only modest profit gains because most of the additional revenue is offset by additional variable costs.