The PCAF attribution factor worked on a four-company buyout portfolio, and why the ownership share overstates a leveraged fund's footprint.
Multiply each company's emissions by an attribution factor, the fund's equity divided by the company's total equity plus debt, and add the results. On an illustrative four-company buyout fund that gives 33,074 tonnes of CO2e, about 184 tonnes per million euros invested. Using the fund's ownership share instead gives 73,990 tonnes, an overstatement of 2.24 times, because in a leveraged company the lenders finance more of the emissions than the equity does.
Worked in full in The ESG Manager in Private Equity by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Financed emissions are the emissions a fund reports as its own because it provided the capital. The PCAF methodology that most limited partners ask for splits a company's emissions between all of its providers of capital in proportion to what each one financed. The arithmetic is short. The error that matters is almost always in the denominator, and in a buyout portfolio it runs in one direction.
| Company | Fund's share of equity | Total equity | Debt | Emissions |
|---|---|---|---|---|
| Industrial services | 70% | 60.0 | 90.0 | 24,000 |
| Software | 55% | 120.0 | 80.0 | 1,800 |
| Food manufacturer | 80% | 50.0 | 50.0 | 41,000 |
| Logistics | 45% | 70.0 | 105.0 | 52,000 |
| Total | 118,800 |
For private companies the convention is to use book values for both the numerator and the denominator. Whatever basis your reporting follows, the rule that cannot be broken is consistency: the fund's holding and the company's capital must be measured the same way, and in the same year as the emissions.
Attribution factor = fund's outstanding amount ÷ (company total equity + debt)
Financed emissions = attribution factor × company emissions, summed across the portfolio.
Industrial services: outstanding 70% × 60.0 = 42.0. Attribution 42.0 ÷ 150.0 = 0.28. Financed 0.28 × 24,000 = 6,720 tonnes.
In Excel, with ownership in B, equity in C, debt in D and emissions in E: =B2*C2/(C2+D2)*E2, then =SUM() down the column.
| Company | Outstanding | Attribution factor | Financed emissions | Ownership method | Overstatement |
|---|---|---|---|---|---|
| Industrial services | 42.0 | 0.28 | 6,720 | 16,800 | 2.50x |
| Software | 66.0 | 0.33 | 594 | 990 | 1.67x |
| Food manufacturer | 40.0 | 0.40 | 16,400 | 32,800 | 2.00x |
| Logistics | 31.5 | 0.18 | 9,360 | 23,400 | 2.50x |
| Fund | 179.5 | 33,074 | 73,990 | 2.24x |
The fund finances 27.8 per cent of its companies' combined 118,800 tonnes. Divided by the 179.5 million it has invested, that is an intensity of 184 tonnes per million euros. The ownership method would have reported 412.
A fund that owns 70 per cent of the industrial services company owns 70 per cent of its equity, but equity is only 40 per cent of the company's capital. The other 60 per cent is debt. The attribution factor is the product of the two, 0.70 × 0.40 = 0.28, and the lenders are allocated their own share of the same tonnes through their own reporting. Across this portfolio the lenders are attributed 66,820 tonnes and the minority shareholders 18,906; add the fund's 33,074 and you recover the 118,800 exactly. Report on ownership and the fund claims tonnes that its lenders also claim, and the system stops adding up.
The overstatement is not uniform. It equals one divided by the equity share of capital: 2.50 times at the two companies financed 60 per cent with debt, 1.67 times at the software company, which carries 40 per cent. A fund that reports on ownership will therefore look worst exactly where it uses the most leverage, which is also where its limited partners are least likely to be able to reconcile the figure to anything.
Hold the industrial services company's emissions at 24,000 tonnes and its total capital at 150.0, and vary only how the capital is split.
| Debt share of capital | Equity | Debt | Attribution factor | Financed emissions |
|---|---|---|---|---|
| 40% | 90.0 | 60.0 | 0.42 | 10,080 |
| 50% | 75.0 | 75.0 | 0.35 | 8,400 |
| 60% | 60.0 | 90.0 | 0.28 | 6,720 |
| 70% | 45.0 | 105.0 | 0.21 | 5,040 |
The consequence for year-on-year reporting: a company that deleverages and changes nothing about its operations will show rising financed emissions for the fund. Before an ESG manager explains a movement in the fund's total, it should be split into the part caused by emissions and the part caused by the attribution factor, and the second part labelled as such.
Two companies, the food manufacturer and the logistics business, carry 25,760 of the fund's 33,074 tonnes, or 77.9 per cent. The software company carries 594, or 1.8 per cent. A 10 per cent reduction at the food manufacturer removes 1,640 tonnes from the fund's total, 5.0 per cent, which is nearly three times what the fund would gain if the software company's emissions fell to zero. The financed emissions calculation is, among other things, the quickest way to decide where the ESG budget goes.
Financed emissions are the fund's share of each company's capital, applied to that company's emissions: 33,074 tonnes here, not 73,990. Keep the capital structure and the emissions in the same year, and when the total moves, say how much of the movement is leverage. The free workbook for this book carries the companion cases, including one on a fund-level target built from financed emissions, and a related article prices what an ESG programme adds at exit.
It is the fund's outstanding amount divided by the company's total equity plus debt, on the same basis and in the same year. A fund holding 70 per cent of a company with 60.0 of equity and 90.0 of debt has an outstanding amount of 42.0 and an attribution factor of 0.28, not 0.70, because the lenders financed the other part of the capital.
Because the attribution factor rises as equity becomes a larger share of capital. Holding emissions at 24,000 tonnes and capital at 150.0, moving the debt share from 60 to 40 per cent raises the fund's financed emissions from 6,720 to 10,080 tonnes. The movement should be reported as an attribution effect, not as an operational change.
Divide total financed emissions by the total outstanding amount. Here 33,074 tonnes over 179.5 million invested is 184 tonnes per million euros. Using ownership-based emissions would give 412, so the intensity inherits whatever error sits in the numerator, and comparisons between funds are only valid on the same method.
This article is one calculation from The ESG Manager in Private Equity. 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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