Theater Season: Break-Even with a Student Discount
A community theater is planning a 20-performance season in a 240-seat auditorium, giving a total capacity of 4,800 tickets. Fixed season costs are $48,000 for rent, staff, and performance rights. Each ticket sold adds $6 in variable costs for printing, ticketing fees, and front-of-house supplies. The theater currently charges $28 per ticket and expects average occupancy of 65%. The board is considering a student discount: 30% of tickets would sell at 15% off the regular price, while the other 70% would sell at $28. Assume the same total number of tickets is sold under either pricing plan unless stated otherwise. The board has no reserve fund and will cancel the season if it cannot cover all costs. It receives no other revenue.
1. Calculate the season break-even number of tickets and the occupancy rate required at the regular $28 price. Show rounding.
Read the worked answer
Contribution per full-price ticket = $28 − $6 = $22. Break-even tickets = fixed costs ÷ contribution = $48,000 ÷ $22 = 2,181.82. Since fractional tickets are not sold, the theater needs 2,182 tickets. Capacity is 20 × 240 = 4,800. Required occupancy = 2,182 ÷ 4,800 = 0.4546, or about 45.5%. At 2,181 tickets, contribution is $47,982, which is $18 short, so rounding up is necessary.
2. Under the discount plan, what is the new break-even number of tickets and occupancy rate, assuming the same sales mix? Does the discount make break-even easier or harder?
Read the worked answer
Discounted price = $28 × 0.85 = $23.80. Weighted average price = 0.70($28) + 0.30($23.80) = $19.60 + $7.14 = $26.74. Contribution per ticket = $26.74 − $6 = $20.74. Break-even tickets = $48,000 ÷ $20.74 = 2,314.37, so 2,315 tickets. Occupancy = 2,315 ÷ 4,800 = 48.2%. The discount makes break-even harder: each ticket contributes $1.26 less, so the theater must sell 133 more tickets than at full price to cover the same fixed costs.
3. If the discount raises total sales to 3,600 tickets at 75% occupancy with the same 70/30 mix, what season profit or loss results? Would the theater be better off selling 3,000 tickets at full price?
Read the worked answer
At 3,600 tickets and the 70/30 mix, total contribution = 3,600 × $20.74 = $74,664. Profit = $74,664 − $48,000 = $26,664. At 3,000 full-price tickets, contribution = 3,000 × $22 = $66,000; profit = $66,000 − $48,000 = $18,000. The discount plan is better by $26,664 − $18,000 = $8,664, provided the 3,600 tickets and the assumed mix actually occur. If the discount mostly cannibalizes full-price sales rather than adding attendance, the advantage shrinks.