Price per bed is the output of a valuation, not the method: two 400-bed schemes show why.
Value student accommodation on capitalised net operating income, then divide by beds: price per bed is an output, not a method. Value per bed equals NOI per bed divided by the yield grossed up for purchaser's costs, so an illustrative scheme earning £7,200 a bed at a 5.50 per cent yield is worth £122,574 a bed. Apply that figure to a neighbouring scheme earning £5,400 a bed and it is overvalued by 39.4 per cent.
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 →
Two blocks of 400 beds in the same city. Scheme A is studio-heavy, close to campus, let on 51-week tenancies. Scheme B is mostly cluster flats a bus ride away, let on 44 weeks. Scheme A has just sold, and the agent for Scheme B quotes the sale as a price per bed. Both cases are illustrative, as are the yields; purchaser's costs are taken at 6.8 per cent.
| Line | Scheme A | Scheme B |
|---|---|---|
| Tenancy length | 51 weeks | 44 weeks |
| Revenue per bed | £10,900 | £8,600 |
| Operating costs and fee per bed | £3,700 | £3,200 |
| NOI per bed | £7,200 | £5,400 |
| NOI margin | 66.1% | 62.8% |
| Net initial yield (illustrative) | 5.50% | 5.75% |
Scheme B's costs per bed are lower in pounds but higher as a share of revenue, because a building costs nearly as much to run for 44 weeks of income as for 51. That is the first reason a bed is not a bed.
1. NOI. Scheme A: 400 × £7,200 = £2,880,000. Scheme B: 400 × £5,400 = £2,160,000. Build each from bed-weeks, not from the rate card, as in how to calculate student housing NOI.
2. Capitalise. Divide by the yield for the gross value: £52,363,636 for A at 5.50 per cent, £37,565,217 for B at 5.75 per cent.
3. Net of purchaser's costs. A UK net initial yield is struck on the price plus the buyer's costs, so divide again by 1.068: £49,029,622 for A and £35,173,425 for B. The mechanics are set out in net initial yield with purchaser's costs.
4. Only now, per bed. £49,029,622 / 400 = £122,574 for A; £35,173,425 / 400 = £87,934 for B.
Value per bed = NOI per bed / (NIY × (1 + purchaser's costs))
Scheme A: 7,200 / (0.055 × 1.068) = £122,574
Scheme B: 5,400 / (0.0575 × 1.068) = £87,934
Excel: =NOIperBed/(NIY*(1+Costs))
Price Scheme B at Scheme A's £122,574 a bed and it is worth £49,029,622. That is £13,856,198, or 39.4 per cent, above its value on its own income. Turned round, a buyer paying that price for Scheme B is buying at a net initial yield of 4.12 per cent, 163 basis points below the yield the market applies to it. Nothing in the per-bed figure warns of this, because it has quietly assumed that Scheme B earns what Scheme A earns.
The gap compounds two effects. Scheme B's NOI per bed is 75.0 per cent of A's: seven fewer weeks, a lower rate and a thinner margin. Its yield is a quarter of a point higher. Together they put its value per bed at 71.7 per cent of A's, a difference of £34,640 a bed.
Price per bed still has two honest uses: checking a price against the replacement cost of a new bed, and comparing schemes whose NOI per bed is already known to be similar. As a valuation method on its own, it is a yield with the income left out.
| NOI per bed | 5.00% | 5.50% | 6.00% | 6.50% |
|---|---|---|---|---|
| £5,000 | £93,633 | £85,121 | £78,027 | £72,025 |
| £6,000 | £112,360 | £102,145 | £93,633 | £86,430 |
| £7,000 | £131,086 | £119,169 | £109,238 | £100,835 |
| £8,000 | £149,813 | £136,193 | £124,844 | £115,241 |
Read across and down: on Scheme A, £100 more NOI per bed is worth £1,702 of value per bed, and a 25 basis point move in yield, from 5.50 to 5.75 per cent, is worth £5,329. A scheme at £5,000 of NOI and 5.00 per cent is worth the same per bed as one at £6,000 and 6.00 per cent. Two beds at the same price can carry entirely different risks.
Per-bed comparisons fail most often on tenancy length. A bed let for 51 weeks sells 16 per cent more bed-weeks than one let for 44, and the summer income a 44-week scheme earns rarely closes the gap once its own costs are taken off. A per-bed price struck on a 51-week scheme and applied to a 44-week one carries that 16 per cent straight into value. The same is true of a block with a large nomination agreement, where rent and tenancy length are both set below the direct-let market, and of a scheme whose all-inclusive rent leaves the owner carrying energy costs that a comparable passed to students.
The discipline is the same as on any income-producing asset: rebuild the comparable's NOI per bed, derive the yield it was bought on, and apply a yield, not a price, to the subject.
The book takes a 520-bed scheme from rent roll to bid, and the free workbook for this case runs the value on both the asking price and the price that leaves the target return.
There is no good price per bed in isolation, only a price that the income supports. At illustrative yields of 5.00 to 6.50 per cent and 6.8 per cent purchaser's costs, £6,000 of NOI per bed supports between £112,360 and £86,430 a bed. Compare the price with the replacement cost of a new bed as a second check.
Divide NOI per bed by the price per bed grossed up for purchaser's costs. A scheme earning £5,400 a bed bought at £122,574 a bed with 6.8 per cent costs is on a net initial yield of 4.12 per cent. If the market yield for that scheme is 5.75 per cent, the price is too high.
A 51-week bed sells 16 per cent more bed-weeks than a 44-week bed, while the building costs almost as much to run. In the example the 51-week scheme earns £7,200 of NOI per bed against £5,400, and is worth £122,574 a bed against £87,934 once a slightly higher yield on the weaker scheme is applied.
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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