Student Council Break-Even and a Discount Ticket Offer
Tubman University's Student Council is planning a cultural night in the main hall and must decide whether the event is financially safe. The hall rents for L$4,500; security costs L$1,200; printing costs L$300 regardless of attendance. Catering costs L$120 per attendee, and the caterer requires a non-refundable L$700 deposit, counted toward the catering bill. Tickets sell for L$250, and the hall holds 200 people. A local business has pledged L$2,000, but only if at least 150 tickets are sold. The council has L$6,000 in its account and cannot end the semester with a deficit. The treasurer expects to sell 150 full-price tickets. A student group then offers to buy 40 tickets at L$180 each if the council guarantees the event will proceed. The council must decide within a week, before the deposit is due.
1. Calculate the break-even attendance (ignoring the sponsor) and the profit if all 200 tickets sell at full price with the sponsor paid.
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Fixed costs: hall L$4,500 + security L$1,200 + printing L$300 = L$6,000. The deposit is part of catering, so it does not add a new cost. Contribution per ticket: L$250 − L$120 = L$130. Break-even: L$6,000 ÷ L$130 = 46.15, so 47 tickets. At 46 tickets contribution is L$5,980, a L$20 loss; at 47 it is L$6,110, a L$110 surplus. Break-even must always be rounded up.
Sold-out case: revenue = 200 × L$250 = L$50,000, plus L$2,000 sponsor (the 150-ticket threshold is met) = L$52,000. Costs = L$6,000 + 200 × L$120 = L$30,000. Profit = L$22,000.
The council's L$6,000 reserve equals fixed costs, but the reserve is not needed at break-even because ticket revenue covers variable costs as sales occur. The real cash risk is unsold capacity and the non-refundable deposit if the event is cancelled.
2. The council expects to sell 150 full-price tickets. Should it accept the group's offer of 40 tickets at L$180 each? Show the comparison.
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Compare the two worlds at 150 full-price sales.
Without the offer: revenue = 150 × L$250 + L$2,000 = L$39,500. Costs = L$6,000 + 150 × L$120 = L$24,000. Profit = L$15,500.
With the offer: attendance = 190, still under the 200 capacity, so no full-price buyer is turned away. Revenue = 150 × L$250 + 40 × L$180 + L$2,000 = L$37,500 + L$7,200 + L$2,000 = L$46,700. Costs = L$6,000 + 190 × L$120 = L$28,800. Profit = L$17,900.
Decision: accept. Each discounted ticket still contributes L$60 (L$180 − L$120), so 40 tickets add L$2,400 with no offsetting loss. The offer also secures the sponsor threshold and reduces the risk of a low-turnout loss. Conditions: confirm the group's payment arrives before the deposit is due, and cap total sales at 200.
3. Suppose the council instead expects 180 full-price sales. Does the answer change? Explain the principle you used.
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At 180 expected full-price sales the answer flips.
Without the offer: revenue = 180 × L$250 + L$2,000 = L$47,000; costs = L$6,000 + 180 × L$120 = L$27,600; profit = L$19,400.
With the offer: 180 + 40 = 220 exceeds the 200-seat capacity, so 20 full-price buyers must be displaced. Revenue = 160 × L$250 + 40 × L$180 + L$2,000 = L$40,000 + L$7,200 + L$2,000 = L$49,200; costs = L$6,000 + 200 × L$120 = L$30,000; profit = L$19,200.
Decision: decline, or renegotiate. The deal adds 40 × L$60 = L$2,400 of contribution but sacrifices 20 × L$130 = L$2,600 of full-price contribution, a net loss of L$200.
Principle: a discount is worthwhile only when it fills capacity that would otherwise be empty. The test is not 'is L$180 above cost?' (it is) but 'does this ticket displace a better-paying one?' The group would need to pay at least L$185 to break even on the displaced seats; asking L$190, or limiting the offer to seats beyond the projected 180, would make it worthwhile.