Both halves of a property's return share one denominator, and the capital half is the value change after the capex that bought it.
Divide the quarter's NOI, and separately the change in value net of capital expenditure, by the same time-weighted denominator: opening value plus half the capex, minus half of any sale receipts, minus a third of the NOI. Chain-linked over four quarters, a building bought at 50,000,000 that earned 2,635,000 of NOI and rose to 51,200,000 after 900,000 of capex returned 5.35 per cent income and 0.59 per cent capital, 5.97 per cent in total, not the 7.67 per cent a quick calculation gives.
Worked in full in Real Estate Fund Management by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Income return and capital return are the two halves of every property performance report, from a single asset's quarterly pack to the benchmark a fund is measured against. The split matters because the two halves are paid for differently: income is cash a fund can distribute, capital return is an appraisal movement that only becomes cash on sale. The arithmetic is short, but two lines in it are routinely dropped, and both push the reported number up.
| Quarter | Opening value | NOI | Capex | Closing value |
|---|---|---|---|---|
| Q1 | 50,000,000 | 650,000 | 300,000 | 50,200,000 |
| Q2 | 50,200,000 | 655,000 | 200,000 | 50,400,000 |
| Q3 | 50,400,000 | 660,000 | 250,000 | 50,700,000 |
| Q4 | 50,700,000 | 670,000 | 150,000 | 51,200,000 |
| Year | 50,000,000 | 2,635,000 | 900,000 | 51,200,000 |
Values are the appraised market values at each quarter end. NOI is the property-level figure after operating expenses and before capex and debt service, built the way NOI on a commercial property is built. Capex is everything capitalised into the asset in the quarter: refurbishment, tenant improvements, leasing costs.
Denominator = BMV + ½ Capex − ½ Sales − ⅓ NOI
Income return = NOI ÷ Denominator
Capital return = (EMV − BMV + Sales − Capex) ÷ Denominator
Total return = Income return + Capital return
In Excel, with the quarter in a row: =NOI/(BMV+0.5*Capex-0.5*Sales-NOI/3) and =(EMV-BMV+Sales-Capex)/(BMV+0.5*Capex-0.5*Sales-NOI/3). This is the quarterly convention used by the US NCREIF property index; other index providers use monthly periods with a simpler denominator, but the logic is the same.
Each adjustment to the denominator has a reason. Capex spent during the quarter was invested for about half of it, so half is added. Sale proceeds left about halfway through, so half is removed. NOI arrives monthly and is assumed to be taken out as it arrives, so on average a third of the quarter's NOI is not in the asset; that third is deducted.
Quarter 1, worked in full:
| Quarter | Gain net of capex | Denominator | Income | Capital | Total |
|---|---|---|---|---|---|
| Q1 | −100,000 | 49,933,333 | 1.30% | −0.20% | 1.10% |
| Q2 | 0 | 50,081,667 | 1.31% | 0.00% | 1.31% |
| Q3 | 50,000 | 50,305,000 | 1.31% | 0.10% | 1.41% |
| Q4 | 350,000 | 50,551,667 | 1.33% | 0.69% | 2.02% |
| Year, chain-linked | 300,000 | 5.35% | 0.59% | 5.97% |
The annual figures are chain-linked, not added: (1 + 1.10%) × (1 + 1.31%) × (1 + 1.41%) × (1 + 2.02%) − 1 = 5.97 per cent. The income and capital components are chain-linked the same way, which is why 5.35 plus 0.59 is 5.94 and not 5.97: the missing 2.34 basis points is the cross term of compounding two streams, and a report that forces the components to add up is either not compounding them or allocating the residual somewhere.
The reading of the year is the useful part. The building's value went up 1,200,000, which looks like a 2.4 per cent capital gain. But 900,000 of capex was spent to produce it. Net of that spend, the capital return is 300,000 on roughly 50,000,000, and almost all of the total return is income. An asset manager who presents 2.4 per cent of appreciation has reported the capex as performance.
Capital return is not appreciation. Appreciation is the change in value. Capital return is the change in value less the money spent to cause it. On a building in a heavy refurbishment year the two can have opposite signs, as Q1 shows.
| Annual capex | Income | Capital | Total |
|---|---|---|---|
| 0 | 5.36% | 2.41% | 7.87% |
| 450,000 | 5.36% | 1.50% | 6.91% |
| 900,000 (base) | 5.35% | 0.59% | 5.97% |
| 1,800,000 | 5.34% | −1.20% | 4.09% |
Doubling the capex to 1,800,000 while the valuer moves the building by the same amount turns the capital return negative. The income return barely moves, because capex enters its denominator at only half weight. That asymmetry is why capex discipline shows up almost entirely in the capital line.
Partial sales work the other way. If 2,000,000 of land is sold in Q3 and the closing values fall by the same amount, to 48,700,000 and 49,200,000, the sale proceeds are added back to the capital gain and half of them leave the denominator. The year then shows 5.44 per cent income, 0.62 per cent capital and 6.08 per cent total: the sale itself is neutral, and the slightly higher figures come from earning the same NOI on a smaller capital base.
The quick version divides the year's NOI and the year's value change by the opening value: 2,635,000 ÷ 50,000,000 = 5.27 per cent of income and 1,200,000 ÷ 50,000,000 = 2.40 per cent of capital, 7.67 per cent in all. It overstates by 1.70 points. The 900,000 of capex counted as a gain, 1.80 per cent of the opening value, more than explains the gap; the opening-value denominator and the lack of compounding pull the other way by a little. That denominator also ignores the timing of money in and out, which matters more in quarters with large capex or sales.
The second mistake is to compare a property's total return calculated this way with a fund's net return. The property figure is unlevered and before fees. Appraisal-based returns are also smoothed; unsmoothing appraisal-based returns shows how much volatility the quarterly series hides.
Use one denominator for both halves, deduct capex from the capital gain, and chain-link the quarters. Here that turns 7.67 per cent into 5.97 per cent and shows a year that was income, not growth. The free workbooks for this book separate in-place operations from value creation in the budget and the variance analysis, which is the same distinction the income and capital split makes after the fact.
Because annual returns are chain-linked from quarters, and each component is compounded separately. Compounding two streams leaves a cross term. In the worked example the components chain-link to 5.35 per cent income and 0.59 per cent capital, which add to 5.94 per cent, while the total chain-links to 5.97 per cent. The 2.34 basis point gap is that cross term, not an error.
From capital return. NOI is before capex, so the income return is unaffected except through the denominator, where half of the capex is added. The capex is subtracted from the change in value: a building that rises 1,200,000 after 900,000 of spending has a capital gain of only 300,000. Treating the whole rise as appreciation overstates the return by 1.80 per cent of value in this case.
Multiply one plus each quarterly return and subtract one. With quarterly totals of 1.10, 1.31, 1.41 and 2.02 per cent the annual total return is 5.97 per cent. Adding the four quarters instead would understate it slightly; averaging the quarters and multiplying by four does the same. Each component is linked the same way, so the annual income return is 5.35 per cent.
This article is one calculation from Real Estate Fund Management. 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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