OpenSpecEngineering

Finds how many units a product must sell to cover its fixed costs, and the sales revenue at that point. It also gives the volume for a profit target and, for a sales forecast you enter, the profit, the margin of safety and the degree of operating leverage. Engineers, plant managers and estimators use it to test a price, judge a new product line or compare a make-or-buy choice.

The break-even equations

CM = p − v    Q_BE = F / CM    R_BE = F / (CM/p)

F is the total fixed cost for the period, p the selling price per unit and v the variable cost per unit. CM is the contribution margin, what each unit sold adds toward the fixed cost and then profit, and CM/p is the contribution margin ratio. Q_BE is the break-even volume and R_BE the break-even revenue [1], [2]. For a target profit P_T, the volume is (F + P_T)/CM.

Profit = CM·Q − F    MOS = Q − Q_BE    DOL = CM·Q / Profit

Q is the expected sales volume. The margin of safety (MOS) is how far sales can fall before the product loses money, given in units and as a percent of Q. The degree of operating leverage (DOL) is the percent change in profit for a 1 % change in sales [1]. It is shown only when the expected profit is positive. Leave Target Profit at 0 for the plain break-even point, and enter 0 for Expected Sales Volume to skip the forecast rows.

Inputs and limits

• Enter all money values in one currency and for one period, such as a year. The fixed cost and the sales volume must cover the same period.
• The price must be higher than the variable cost, or no volume breaks even.
• The model is linear: price and unit cost stay the same at every volume, and fixed cost does not step up with capacity [3]. Check that the break-even volume is within what the plant can make.
• Volumes come out fractional. Round a break-even volume up to the next whole unit.
• Count only costs that change with volume as variable cost: material, direct labor paid per piece and energy per unit. Rent, salaries and depreciation are fixed.

Worked example

A shop plans to make a pump bracket. Tooling, a machine lease and overhead cost 120,000 a year. Each bracket sells for 85 and costs 52 in material and labor. The owner wants a 30,000 profit and forecasts 6,000 sales a year.

1. Enter Total Fixed Cost (F) 120000.
2. Enter Selling Price per Unit (p) 85 and Variable Cost per Unit (v) 52.
3. Enter Target Profit 30000 and Expected Sales Volume 6000.
4. Press Solve. The Solution shows: Contribution margin per unit: 33
   Contribution margin ratio: 38.8235 %
   Break-even volume: 3,636.36 units
   Break-even revenue: 309,091
   Volume for target profit: 4,545.45 units
   Profit at expected volume: 78,000
   Margin of safety: 2,363.64 units
   Margin of safety: 39.3939 %
   Degree of operating leverage: 2.53846

Check: 120,000/33 = 3,636.4, so the shop must sell 3,637 brackets to break even. At 6,000 brackets, 33 × 6,000 − 120,000 = 78,000. A DOL of about 2.5 means a 10 % drop in sales cuts profit by about 25 %.