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56/3335–8FE Reference Handbook 10.4 · Engineering Economics · Break-even analysis
1. Simple Interest2. Single-Payment Compound Amount (F/P)3. Single-Payment Present Worth (P/F)4. Uniform-Series Compound Amount (F/A)5. Sinking-Fund Factor (A/F)6. Capital-Recovery Factor (A/P)7. Uniform-Series Present Worth (P/A)8. Effective Interest Rate9. Arithmetic Gradient Present Worth (P/G)10. Net Present Worth11. Benefit–Cost Ratio12. Straight-Line Depreciation13. Geometric Gradient Present Worth14. Capitalized Cost (Perpetual PW)15. Payback Period16. Break-Even Quantity17. Equivalent Uniform Annual Worth18. Internal Rate of Return vs MARR19. MACRS Depreciation20. Declining-Balance Depreciation21. Inflation and Real Interest22. Expected Value of Alternatives

Handbook formula

Break-Even Quantity

Break-even is the production (or demand) quantity where total revenue equals total cost. Contribution margin is (p − v) per unit. Below Q_BE the firm loses; above, it profits. Two alternatives break even when their AW or NPW are equal (solve for Q, n, or i).

Fixed cost per period
Variable cost per unit
Price per unit
Break-even quantity

Step-by-step solved example

FC = $20,000, v = $15/unit, p = $40/unit. Find Q_BE. Profit at Q = 1,000?

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Quantity where revenue meets fixed + variable cost.

  1. 1. Contribution

    p − v = 25 $/unit. Q_BE = 20000/25 = 800 units.

  2. 2. Profit

    Profit = (p−v)Q − FC = 25×1000 − 20000 = $5,000.

Answer: Q_BE = 800 units; profit = $5,000 at Q = 1,000

10 practice questions

0/10 correct

1.If p = v, Q_BE is

2.FC = $9,000, p = $30, v = $12. Q_BE =

3.Increasing price p, other things equal, makes Q_BE

4.Profit = (p−v)Q − FC. At Q = Q_BE profit is

5.Two machines: pick the higher-FC / lower-v option when expected Q is

6.Units of Q_BE are

7.If FC doubles and (p−v) doubles, Q_BE

8.Break-even n between two alternatives is found by setting

9.Contribution margin is

10.A linear TC and linear TR intersect at most