Problem 1: A business has fixed costs of $5,000, a selling price of $25, and a variable cost of $10. What is the break-even point in units?
Solution: profit per unit = $25 − $10 = $15. BEP = $5,000 ÷ $15 = 333.33, rounded up to 334 units.
Problem 2: Using Problem 1, what is the break-even point in revenue?
Solution: BEP (revenue) = 334 × $25 = $8,350.
Problem 3: A company has fixed costs of $10,000, a selling price of $100, and a variable cost of $60. What is the break-even point?
Solution: profit per unit = $100 − $60 = $40. BEP = $10,000 ÷ $40 = 250 units.
Problem 4: A service business has fixed costs of $4,000, a selling price of $200, and a variable cost of $80. How many clients are needed to break even?
Solution: profit per client = $200 − $80 = $120. BEP = $4,000 ÷ $120 = 33.33, rounded up to 34 clients.
Problem 5: A Social Security recipient compares claiming at 62 ($1,500 a month) with claiming at 70 ($2,600 a month). What is the break-even age?
Solution: benefits collected from 62 to 70 = $1,500 × 12 × 8 = $144,000. Extra per year from waiting = $1,100 × 12 = $13,200. Break-even = 70 + ($144,000 ÷ $13,200) = 70 + 10.9 = 80.9 years.
Answers: 1. 334 units · 2. $8,350 · 3. 250 units · 4. 34 clients · 5. 80.9 years