Winter Pricing at a Bugibba Hotel
A 60-room three-star hotel in Bugibba reports 92% occupancy in July at an average room rate of €180, but only 45% in November at €95. The owning company is pressing the manager to raise winter revenue and the manager is considering a 15% cut in the November rate, to about €81. A consultant estimates the price elasticity of demand for November leisure bookings at -1.6, and for July peak bookings at -0.4. Variable cost is €55 per occupied room-night (housekeeping, laundry, breakfast, utilities). Fixed costs are about €40,000 a month and do not change with occupancy. November has 30 nights. The manager is paid a bonus based on gross profit, while the owning company reports on total revenue. Both know the July figure is the one that carries the year.
1. Calculate the effect of the 15% November price cut on room-nights sold, total room revenue and total contribution (revenue minus variable costs). Is the cut a good idea?
Read the worked answer
Now: occupancy 45% of 60 rooms = 27 rooms, over 30 nights = 810 room-nights.
- Revenue = 810 × €95 = €76,950
- Contribution = 810 × (€95 - €55) = 810 × €40 = €32,400
After a 15% cut: price = €95 × 0.85 = €80.75. With PED = -1.6, quantity rises by 1.6 × 15% = 24%.
- Room-nights = 810 × 1.24 = 1,004.4 (occupancy 55.8%)
- Revenue = 1,004.4 × €80.75 = €81,105 - up about €4,155
- Contribution = 1,004.4 × (€80.75 - €55) = 1,004.4 × €25.75 = €25,863 - down about €6,537
So the cut raises revenue and destroys profit. Both answers are correct; they answer different questions. Because demand is elastic, the percentage rise in rooms (24%) beats the percentage fall in price (15%), so revenue rises. But the margin per room-night collapses from €40 to €25.75 - a 36% fall - and 24% more volume cannot cover that. Fixed costs are unchanged, so profit falls by roughly €6,537 a month. For the manager, paid on profit, the cut is clearly bad.
2. Explain why cutting the July rate would be a mistake, using the elasticity figure and the occupancy figure.
Read the worked answer
Two independent reasons point the same way.
First, elasticity. At -0.4, demand is inelastic, so a price cut reduces revenue: a 10% cut to €162 would add only 4% in room-nights. Revenue would change by roughly (1 - 1.10 × 1.04) = -5.6%. Inelastic demand is an argument for raising the rate, not cutting it.
Second, capacity. 92% occupancy on 60 rooms is about 55 rooms sold, leaving 5 rooms of headroom. A 4% increase in demand needs only about 2.2 extra rooms, so the rooms exist - but there is no slack to grow into, and the hotel is already near the point where further demand cannot be served. Selling those few remaining rooms at €162 instead of €180 gives up €18 on a room that might have sold at full rate to a late booker.
Contribution makes it concrete: today, 55 rooms × (€180 - €55) = €6,875 a night. After the cut, 57.2 rooms × (€162 - €55) = €6,120. Lower profit on higher occupancy. The July lever is price up, carefully, not down.
3. The owner judges performance by revenue; the manager is paid on gross profit. Which target should guide the November decision, and what extra information would change your answer?
Read the worked answer
Gross profit should guide the decision, because contribution is what remains to cover the €40,000 of fixed costs and then become profit. Revenue is an intermediate variable; a hotel can go bankrupt filling rooms at €81.
But the manager's figure is incomplete. Guests also spend in the bar and restaurant. Let extra margin per occupied room-night be x. The cut is worthwhile only if: 1,004.4 × (25.75 + x) > 810 × (40 + x) 25,863 + 1,004.4x > 32,400 + 810x 194.4x > 6,537, so x > €33.6
Ancillary margin would have to exceed about €33.60 per room-night - implausibly high for a three-star winter guest. Even a generous €12 does not rescue the cut (€37,916 against €42,120).
What would change the answer: a large fixed-cost element in housekeeping that makes short-run marginal cost lower than €55; a group booking that fills a block of rooms; a view that winter volume protects staff the hotel needs in July; or an owner explicitly willing to buy market share at a loss for brand reasons. Absent those, the manager is right and the owner's revenue target is the wrong instrument.