The rate-or-occupancy trade solved for the beds a rent cut has to win, and why the answer depends on how many beds are already sold.
A rent cut pays only if it wins enough extra beds to replace the rent given up on beds that would have let anyway. On an illustrative 500-bed scheme let at £190 a week for 44 weeks and expected to reach 92 per cent occupancy, a 5 per cent cut applied to every bed gives up £192,280 of rent and needs 28.1 more beds: occupancy must rise from 92.0 to 97.6 per cent just to stand still. A 7.5 per cent cut would need 100.7 per cent, so no amount of demand repays it.
Worked in full in Student Housing Real Estate by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A 500-bed purpose-built scheme sells its rooms for the coming academic year on 44-week tenancies at an average rate of £190 a week. On the current booking pace the letting team expects 460 beds, 92 per cent. It is January, before the main booking season, and the question on the table is whether to cut the rate card to fill the last 40 beds. Each occupied bed carries £1,100 a year of costs that an empty bed does not: utilities on an all-inclusive rent, cleaning, consumables and agent commission. Everything else is fixed. All figures are illustrative.
| Item | Value |
|---|---|
| Beds | 500 |
| Tenancy length | 44 weeks |
| Average rate | £190.00 a week |
| Expected occupancy at full rate | 92.0% (460 beds) |
| Variable cost per occupied bed | £1,100 a year |
| Valuation yield | 5.50% |
A bed let for the year earns 44 × £190 = £8,360 and contributes £7,260 after its variable cost. A point of occupancy is 5 beds: £41,800 of rent, £36,300 of net operating income and, at 5.50 per cent, £660,000 of value. That is the prize the discount is chasing, and it is large, which is why letting teams are tempted.
Student housing re-sells its whole rent roll every year from one rate card. A cut published on the January rate card applies to every bed sold from then on, including the 460 that would have let at £190. That is the cost.
Rent given up = beds that would have let × weeks × weekly cut
460 × 44 × (190.00 − 180.50) = 460 × 44 × 9.50 = £192,280
Each extra bed now earns the lower rate: 44 × £180.50 = £7,942, less £1,100, a contribution of £6,842. Divide the rent given up by it.
Extra beds needed = rent given up / (weeks × new rate − variable cost)
192,280 / 6,842 = 28.1 beds
Required occupancy = (460 + 28.1) / 500 = 97.6%, a gain of 5.6 points
Excel: =(Let*Weeks*Rate*Cut)/(Weeks*Rate*(1-Cut)-VarCost) for the beds, then =(Let+B)/Beds
The cut is only worth making if the letting team believes it turns a 92 per cent year into one above 97.6 per cent. Put as an elasticity, 28.1 beds on 460 is a 6.1 per cent volume gain for a 5 per cent price cut: demand must respond 1.22 times as strongly as the price moves. A scheme forecasting 92 per cent usually has a reason, a room type or a location, that 5 per cent does not fix.
| Cut | New rate £ | Rent given up £ | Extra beds needed | Occupancy needed |
|---|---|---|---|---|
| 2.5% | 185.25 | 96,140 | 13.6 | 94.7% |
| 5.0% | 180.50 | 192,280 | 28.1 | 97.6% |
| 7.5% | 175.75 | 288,420 | 43.5 | 100.7% |
| 10.0% | 171.00 | 384,560 | 59.9 | 104.0% |
There are only 40 empty beds. Beyond a cut of roughly 7 per cent the break-even sits above full occupancy: the scheme loses money even if it lets every room. A 10 per cent cut that does fill the building still costs £127,600 of NOI, £2,320,000 of value. And a 5 per cent cut that only reaches 95.0 per cent, 475 beds, loses £89,650 a year.
The cost of a discount is driven by how many beds it touches. If the lower rate is offered only to beds still unsold, the beds already contracted at full rate are out of the calculation.
| Beds already contracted at £190 | Beds exposed to the cut | Rent given up £ | Extra beds needed | Occupancy needed |
|---|---|---|---|---|
| 0 | 460 | 192,280 | 28.1 | 97.6% |
| 300 | 160 | 66,880 | 9.8 | 94.0% |
| 400 | 60 | 25,080 | 3.7 | 92.7% |
A cut made late, on the last 60 expected beds and the 40 unsold, needs only 0.7 points to pay. The same percentage put on the rate card in January needs 5.6. That is the arithmetic behind late, targeted offers on specific room types rather than headline cuts, and why the RevPAB of a scheme that discounts early is usually lower than its occupancy suggests.
The timing table assumes students who booked at £190 do not ask for the lower rate. Where they can see it, some will, and every one who is matched moves the case back towards the first row.
The common mistake is pricing the discount on the empty beds alone: 40 beds at £180.50 look like £317,680 of new rent, which seems to dwarf a 5 per cent cut. It ignores the £192,280 given up on the 460 beds that were coming anyway. The second mistake is counting the extra beds at their rent rather than their contribution: an all-inclusive rent carries energy and cleaning with every bed filled, £1,100 a bed here. Both mistakes push the break-even occupancy down and make the cut look safe. The fixed-cost side of the same scheme is worked in what occupancy a student housing scheme needs to break even.
The book's model runs the rate-and-occupancy trade on its 520-bed Leeds scheme, and the free workbook for this case lets you put in your own rate card, booking pace and cost per bed.
One point is 1 per cent of the beds for the full let. On a 500-bed scheme at 190 pounds a week for 44 weeks, that is 5 beds and 41,800 pounds of rent; after 1,100 pounds of variable cost per bed it adds 36,300 pounds of NOI, worth 660,000 pounds of value at an illustrative 5.50 per cent yield.
Divide the rent given up on beds that would have let anyway by the contribution of one extra bed at the new rate. A 5 per cent cut on 460 let beds gives up 192,280 pounds; each extra bed contributes 6,842 pounds, so 28.1 beds are needed, 5.6 points of occupancy.
Late discounts touch fewer beds. A 5 per cent cut made when 400 of the expected 460 beds are already contracted at full rate gives up only 25,080 pounds and needs 3.7 extra beds, 0.7 points of occupancy, against 5.6 points for a cut published on the rate card in January. The risk is that earlier bookers ask for the lower rate.
This article is one calculation from Student Housing Real Estate. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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