The four YP factors valuers use, perpetuity, fixed term, deferred and quarterly in advance, worked on one rent, with the error each one prevents.
Years' purchase (YP) is the multiplier that turns an annual rent into a capital value: 1 ÷ yield for an income in perpetuity, and (1 − (1 + i)−n) ÷ i for an income that lasts n years. At 6 per cent, a 500,000 rent forever is worth 16.6667 YP, or 8,333,333; the same rent for fifteen years is worth only 9.7122 YP, or 4,856,124. Paid quarterly in advance, as most UK leases are, the perpetuity factor rises to 17.2871.
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 →
YP is the oldest tool in the valuer's kit and the one most often misapplied, because the same word covers four different factors. Each is a present value of 1 per year, and each answers a different question: how long the income lasts, when it starts, and how often it arrives. Getting the factor wrong moves the value by far more than any argument about the yield.
| Input | Value |
|---|---|
| Annual net rent | 500,000 |
| Yield (all risks or target rate) | 6.0% |
| Fixed term of a leasehold or lease income | 15 years |
| Deferral of a reversion | 5 years |
1. YP in perpetuity. A freehold let at market rent, with the rent assumed to continue forever. The factor is simply the reciprocal of the yield.
YP perpetuity = 1 ÷ i = 1 ÷ 0.06 = 16.6667
Value = 500,000 × 16.6667 = 8,333,333
Excel: =1/0.06, or =PV(0.06,1000,-1) as a check
2. YP for a fixed term. An income that stops: a leasehold interest, a profit rent, or a lease with no expectation of renewal. It is the annuity factor.
YP for n years = (1 − (1 + i)−n) ÷ i
1.06−15 = 0.417265, so YP = 0.582735 ÷ 0.06 = 9.7122
Value = 500,000 × 9.7122 = 4,856,124
Excel: =PV(0.06,15,-1)
Fifteen years of income is worth 58.3 per cent of the same income forever. The rest of the perpetuity value sits in years 16 onward.
3. YP in perpetuity deferred. An income that starts later: the reversion to market rent in a term and reversion valuation, or a ground rent that steps up. Take the perpetuity factor and discount it back by the deferral.
PV of 1 in 5 years = 1.06−5 = 0.747258
YP perpetuity deferred 5 years = 16.6667 × 0.747258 = 12.4543
Check: 16.6667 − YP 5 years (4.2124) = 12.4543
Value of 500,000 from year 6 onward = 6,227,151
The check is worth doing on every valuation. A deferred perpetuity is just the full perpetuity less the years you do not get, and if the two routes disagree, one of the formulas has a wrong exponent.
4. YP quarterly in advance. The first three factors assume one payment a year, received at the end of the year. Rent usually arrives in four instalments at the start of each quarter, which is worth more.
YP quarterly in advance (perpetuity) = 1 ÷ (4 × (1 − (1 + i)−0.25))
1.06−0.25 = 0.985538; 1 − 0.985538 = 0.014462; × 4 = 0.057847
YP = 1 ÷ 0.057847 = 17.2871, value 8,643,557
For fifteen years: 0.582735 ÷ 0.057847 = 10.0738, value 5,036,903
| Income | YP | Value |
|---|---|---|
| Perpetuity, annual in arrears | 16.6667 | 8,333,333 |
| Perpetuity, quarterly in advance | 17.2871 | 8,643,557 |
| Fifteen years, annual in arrears | 9.7122 | 4,856,124 |
| Fifteen years, quarterly in advance | 10.0738 | 5,036,903 |
| Perpetuity deferred five years | 12.4543 | 6,227,151 |
Quarterly in advance adds 310,224, or 3.72 per cent, to the perpetuity value at the same quoted yield. Put the other way: a buyer who pays 8,643,557 for this rent and calls it a 6 per cent yield is computing 500,000 ÷ 8,643,557 = 5.785 per cent on the conventional annual basis. Two valuers who agree on 6 per cent but disagree on the payment convention are 3.7 per cent apart before either has opened the rent roll.
| Yield | Perpetuity | 15 years | Deferred 5 yrs | Qtly in advance |
|---|---|---|---|---|
| 4.0% | 25.0000 | 11.1184 | 20.5482 | 25.6219 |
| 5.0% | 20.0000 | 10.3797 | 15.6705 | 20.6212 |
| 6.0% | 16.6667 | 9.7122 | 12.4543 | 17.2871 |
| 7.0% | 14.2857 | 9.1079 | 10.1855 | 14.9054 |
| 8.0% | 12.5000 | 8.5595 | 8.5073 | 13.1190 |
The columns move at different speeds. From 4 to 8 per cent the perpetuity factor halves, from 25.0000 to 12.5000, while the fifteen-year factor falls by less than a quarter, from 11.1184 to 8.5595. A short income is far less sensitive to the yield than a long one, which is why the yield argument matters most for freeholds and long reversions, and least for short leaseholds. The deferred factor is the most sensitive of all: it loses 59 per cent of its value over the same range, because the yield both capitalises the income and discounts the wait.
Long leaseholds converge on the perpetuity. At 6 per cent, YP for 25 years is 12.7834 (76.7 per cent of the perpetuity), for 50 years 15.7619 (94.6 per cent) and for 100 years 16.6175 (99.7 per cent). Beyond about fifty years the difference is smaller than the error in the yield.
Applying a perpetuity factor to an income that stops. A valuer who capitalises a fifteen-year profit rent at 1 ÷ 6 per cent reports 8,333,333 instead of 4,856,124, an overstatement of 3,477,209 or 71.6 per cent. It happens most often with income that looks permanent but is not: a headlease with fifteen years left, an over-rent that will fall away at expiry, or a sale and leaseback rent above market. The over-rented slice should be valued for its term only, then the market rent in perpetuity behind it.
The second mistake is quieter: mixing a yield derived from quarterly in advance comparables with an annual in arrears formula, or the reverse. The valuation then carries a 3 to 4 per cent error that nobody sees, because every input looks right. Decide the convention once and state it next to the yield.
A third, in markets that quote yields net of purchaser's costs: capitalising at 6 per cent gives the gross value, 8,333,333. A buyer paying 6.8 per cent costs on top can offer only 7,802,747 for the property itself. The detail is in how to calculate the net initial yield with purchaser's costs.
The book works yields on a ten-unit estate where several of these factors meet in one rent roll; the free workbooks for the case carry the income account and six entry yields as live formulas. Where term and reversion and hardcore diverge, see term and reversion vs the hardcore method.
1 divided by 0.05, which is 20.0000. A rent of 500,000 capitalised at 5 per cent in perpetuity is worth 10,000,000. Paid quarterly in advance the factor rises to 20.6212, because each quarter's rent arrives at the start of the period rather than at the end of the year.
Multiply the YP by the present value of 1 for the deferral period, (1 + i) to the power minus d. At 6 per cent, YP in perpetuity deferred five years is 16.6667 x 0.747258 = 12.4543. The same figure comes out as the perpetuity factor less YP for five years, 16.6667 less 4.2124, which is a useful check.
Arithmetically it is a multiple of rent, but it is built from a yield and a duration, so it carries a time value. A gross rent multiplier is an observed price over gross rent with no term in it. At 6 per cent, YP is 16.6667 for a perpetual income and 9.7122 for fifteen years: a GRM cannot tell those two incomes apart.
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.
Get the book on Amazon →Free companion files
Also on Amazon UK · Amazon Germany · Amazon France · Amazon Canada
Reading guide: real estate investing, finance and fund management → · All 1340 articles →
If this book helped, or didn’t, a few lines on Amazon are worth more than they look: they are what the next reader goes on. Write a review. The workbook stays free either way.