A reversionary building has two easy yields and neither describes it; the equivalent yield weights each rent by when it arrives, and averaging gets it wrong by over a million.
The equivalent yield is the single discount rate at which the passing rent to the reversion, plus the market rent in perpetuity after it, equals the price including purchaser's costs. It has no closed form: solve it with Goal Seek. On an illustrative 18,000,000 purchase at 1,000,000 of rent, reverting to 1,250,000 in three years, the equivalent yield is 6.28 per cent, against a net initial yield of 5.20 and a reversionary yield of 6.50. Averaging the two, 5.85 per cent, would overpay by 1,372,578.
Worked in full in Commercial Real Estate Investing by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A reversionary property has two incomes, the rent it is let at and the rent it would let at today, and so it has two easy yields. Neither describes the investment. The equivalent yield does, because it weights each income by when it arrives and for how long. It is also the number a valuer uses to compare one reversionary asset with another, which is why it is worth computing rather than reading off a schedule.
| Input | Value |
|---|---|
| Net price to the vendor | 18,000,000 |
| Purchaser's costs (illustrative) | 6.8% |
| Gross price, including costs | 19,224,000 |
| Passing rent | 1,000,000 |
| Estimated rental value (ERV), today | 1,250,000 |
| Years to the reversion | 3 |
| Net initial yield: rent ÷ gross price | 5.20% |
| Reversionary yield: ERV ÷ gross price | 6.50% |
The reversion is a rent review or a lease expiry at which the rent moves to the ERV. The equivalent yield takes the ERV at today's level: it assumes no rental growth. That assumption is the definition, not a weakness, and it is why the equivalent yield is a comparison tool and not a forecast of return.
Gross price = rent × YP for n years at r + ERV × YP in perpetuity at r × (1 + r)−n
YP for n years = (1 − (1 + r)−n) ÷ r; YP in perpetuity = 1 ÷ r
The equation is solved for r. In Excel: put the trial rate in one cell, compute =Rent*(1-(1+r)^-n)/r+ERV/r*(1+r)^-n in another, then Data, What-If Analysis, Goal Seek: set the value cell to 19,224,000 by changing r. Value falls steadily as r rises, so there is one answer.
| Line | Factor | Value |
|---|---|---|
| Term: 1,000,000 × YP 3 years | 2.6590 | 2,658,981 |
| YP in perpetuity | 15.9110 | |
| Present value of 1 in 3 years | 0.8329 | |
| Reversion: 1,250,000 × YP in perpetuity deferred 3 years | 13.2520 | 16,565,019 |
| Gross price | 19,224,000 |
The reversion is 86.2 per cent of the value. That is the practical point: an equivalent yield on a short reversion is mostly a statement about the ERV. If the ERV is 10 per cent too high, the equivalent yield is materially too high with it, and the asset looks cheaper than it is.
Because the higher income starts later. A simple average of 5.20 and 6.50 is 5.85 per cent. Value the same income stream at 5.85 per cent and it is worth 20,689,914 gross, 19,372,578 net: 1,372,578 more than the price that actually produces a 6.28 per cent equivalent yield. The average treats the reversion as half the story when it is most of it, and it ignores how long the term lasts.
The equivalent yield is also the internal rate of return on the purchase if rents never grow. Hold the asset ten years at zero growth, sell at the same equivalent yield on the ERV, and the IRR is 6.28 per cent. That is the cleanest way to explain it to a committee: it is an IRR with growth switched off.
| Years to reversion | ERV 1,100,000 | ERV 1,250,000 | ERV 1,400,000 |
|---|---|---|---|
| 1 | 5.69% | 6.42% | 7.14% |
| 3 | 5.64% | 6.28% | 6.90% |
| 5 | 5.60% | 6.17% | 6.71% |
| Reversionary yield | 5.72% | 6.50% | 7.28% |
The nearer the reversion, the closer the equivalent yield gets to the reversionary yield; the further away, the closer it drifts to the net initial yield. The ERV moves it far more than the timing does. Two buildings with the same equivalent yield can rest on very different ERV evidence, and that is the line to test.
The same arithmetic runs in reverse on an over-rented building. With an ERV of 900,000 against 1,000,000 of passing rent and five years to run, the equivalent yield is 4.79 per cent: below the net initial yield, above the reversionary yield of 4.68, and a warning that the income will fall at the reversion. A simple equivalent yield on an over-rented asset hides the risk that matters most, which is whether the tenant is still there to pay the over-rent.
UK valuations usually assume rent paid quarterly in advance. The same price and the same rents, received quarterly in advance, give a true equivalent yield of 6.53 per cent, annual effective, against 6.28 per cent annual in arrears: money received sooner means a higher return for the same price. Neither is wrong; quoting one beside a comparable computed on the other is. State the convention, and state whether the yield is on the price with or without purchaser's costs.
The equivalent yield, 6.28 per cent here, is the only one of the quoted yields that weights each rent by when it arrives, and the only one that can sensibly be set beside an exit yield. Most of its value sits in the ERV, so test that first. Commercial Real Estate Investing computes six entry yields for one estate and shows which compares with the exit; the free workbooks for that case carry them all as live formulas. For the exit side of the same question, see how to calculate the break-even exit yield.
The reversionary yield is the ERV divided by the gross price, as if the market rent were received today. The equivalent yield discounts the passing rent until the reversion and the ERV after it at one rate. On an illustrative asset the reversionary yield is 6.50 per cent and the equivalent yield 6.28, because the higher rent starts three years later.
Only if rents never grow. The equivalent yield assumes the ERV stays at today's level, so it equals the IRR of a purchase held at zero growth and sold at the same yield. On an illustrative ten-year hold that IRR is 6.28 per cent, exactly the equivalent yield. With rental growth the IRR is higher.
It is the equivalent yield computed on rent received quarterly in advance, as UK leases usually pay, rather than annually in arrears. Receiving the same rent sooner raises the yield for the same price: on an illustrative asset the true equivalent yield is 6.53 per cent against 6.28 per cent annually in arrears.
This article is one calculation from Commercial Real Estate Investing. 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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