Film Festival Budget and Sponsor Threshold
A student society is planning a one-night film festival. The venue costs $850, and film licensing costs $300. Each attendee costs $4 in snacks and printed materials. Tickets sell for $12. A sponsor has pledged $500, but only if at least 150 tickets are sold; otherwise the sponsor pays nothing. The venue holds 220 people. The society has $1,200 in cash and must keep a $200 reserve. Without advertising, they expect 140 attendees. With $250 of advertising, they expect 190 attendees. Advertising is paid whether or not the event proceeds. The society wants to finish with at least $600 profit for next year's activities. A local business has offered to pay the $500 sponsorship in advance if the society signs a confirmation before the event, but only if the expected attendance is at least 150. The treasurer is unsure whether the event is financially safe, whether advertising is worth it, and whether the group can cover costs before ticket money arrives.
1. Calculate the break-even attendance without advertising and explain why the sponsor condition makes the break-even non-linear.
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Without advertising, fixed costs are 850 + 300 = 1,150. Contribution per ticket is 12 − 4 = 8. If the sponsor pays nothing, break-even attendance N satisfies 8N = 1,150, so N = 143.75, meaning 144 tickets. At 144, the sponsor still pays nothing because 144 is below 150, so profit is 8(144) − 1,150 = 2.
At 150, the sponsor pays 500, so profit jumps to 8(150) − 1,150 + 500 = 550. The break-even is therefore not a single smooth line: for N below 150, sponsor = 0; for N at least 150, sponsor = 500. There is a discontinuity at 150: moving from 149 to 150 adds $8 in contribution plus $500 in sponsor money.
Capacity is sufficient because 220 is greater than 144. However, the cash constraint matters: available cash is 1,200 − 200 reserve = 1,000. Fixed costs of 1,150 exceed available cash by 150 before any ticket revenue, so the event is not cash-safe unless the sponsor pays in advance or suppliers accept payment after ticket sales. The treasurer must separate accounting break-even from cash-flow feasibility.
2. Compare the expected profit with and without advertising, including the sponsor condition, and state which option is better on expected values.
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No advertising: expected attendance is 140, which is below 150, so the sponsor pays 0. Profit = 140(12 − 4) − 1,150 = 1,120 − 1,150 = −30.
With advertising: expected attendance is 190, which is at least 150, so the sponsor pays 500. Profit = 190(8) − 1,150 − 250 + 500 = 1,520 − 1,400 + 500 = 620.
The difference is 650 in favor of advertising, but most of the gain comes from crossing the 150-ticket sponsor threshold, not from the extra tickets alone. With advertising but no sponsor, profit would be 1,520 − 1,400 = 120; the sponsor adds 500. So the advertising decision is really a bet that attendance reaches 150.
At exactly 150 attendees with advertising, profit is 1,200 − 1,400 + 500 = 300. At 149 attendees, profit is 1,192 − 1,400 = −208. Expected value is higher with advertising, but the downside is worse if the estimate is wrong. On expected values alone, advertise; on risk, the margin is thin.
3. The society wants at least $600 profit and must decide by tomorrow. Recommend a course of action and identify the most important condition or risk.
Read the worked answer
With advertising, required attendance for $600 profit is: 8N − 1,150 − 250 + 500 ≥ 600, so 8N − 900 ≥ 600, so 8N ≥ 1,500, so N ≥ 187.5, meaning 188 tickets. The expected 190 is only two tickets above that, which is too thin for a $600 target.
Without advertising, even at capacity 220 with the sponsor, profit is 8(220) − 1,150 + 500 = 1,110, but expected attendance of 140 gives −30. Realistically, advertising is the only option that can reach $600, but it should be conditional on pre-sales.
Recommendation: spend the $250 only after confirming at least 160–170 paid pre-sales, because 150 is the sponsor cliff and 188 is the profit target. Ask the sponsor to pay the $500 in advance so the cash shortfall is covered; otherwise negotiate to pay the venue after ticket revenue. Set a pre-sale deadline and cancel or switch to a smaller venue if pre-sales are below 150. The key risk is not the average attendance estimate; it is the sponsor threshold and the cash timing. A plan that ignores either is financially unsafe.