A shadow carbon price is not a cash cost. Run through the hold and the exit multiple, it is a valuation adjustment, and the test of whether a decarbonisation plan is worth its capex.
To apply an internal carbon price to a deal, charge the shadow price on the target's Scope 1 and 2 emissions in every year of the hold, capitalise the exit-year charge at the exit multiple, and discount both at the deal's cost of capital. On an illustrative company with 25.0 million euros of EBITDA and 20,000 tonnes of CO2e, a shadow price rising from 100 to 150 euros a tonne reduces a 225.0 million entry value by 25.91 million, 11.5 per cent. A 6.0 million plan that cuts emissions by 40 per cent recovers 4.18 million of it.
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 →
The target is a fictional mid-market manufacturer bought at 9.0x EBITDA. EBITDA is held flat so that only carbon moves. None of its emissions is covered by an emissions trading scheme in the base case. The shadow price path is the fund's own illustrative policy, not a forecast of any market.
| Input | Value |
|---|---|
| EBITDA, million euros | 25.0 |
| Entry and exit multiple | 9.0x |
| Entry enterprise value, million euros | 225.0 |
| Scope 1 / Scope 2 market-based, tCO2e a year | 12,000 / 8,000 |
| Carbon intensity, tCO2e per million of EBITDA | 800 |
| Internal carbon price, years 1 to 5, euros a tonne | 100, 110, 120, 135, 150 |
| Discount rate | 10% |
| Decarbonisation plan: capex in year 1 / emissions cut from year 2 | 6.0m / 40% |
Shadow carbon costt = (Scope 1 + Scope 2)t × internal pricet
Year 1: 20,000 × 100 = 2.00 million, 8.0 per cent of EBITDA; year 5: 20,000 × 150 = 3.00 million, 12.0 per cent
Excel: =Emissions*Price/10^6, one column a year
| Year | Price | No plan, tCO2e | No plan, cost | With plan, tCO2e | With plan, cost |
|---|---|---|---|---|---|
| 1 | 100 | 20,000 | 2.00 | 20,000 | 2.00 |
| 2 | 110 | 20,000 | 2.20 | 12,000 | 1.32 |
| 3 | 120 | 20,000 | 2.40 | 12,000 | 1.44 |
| 4 | 135 | 20,000 | 2.70 | 12,000 | 1.62 |
| 5 | 150 | 20,000 | 3.00 | 12,000 | 1.80 |
Exit haircut = year-5 shadow cost × exit multiple = 3.00 × 9.0 = 27.0 million
Valuation adjustment = Σ costt / 1.10t + exit haircut / 1.105 = 9.15 + 16.76 = 25.91 million
Carbon-adjusted value = 225.0 − 25.91 = 199.1 million, or 7.96x reported EBITDA
The assumption that does the work is the exit: 64.7 per cent of the adjustment comes from supposing that the next buyer will price carbon the way you do. On the hold alone the adjustment is 9.15 million, 4.1 per cent of the value. Against an equity cheque of half the enterprise value, the full adjustment is 23.0 per cent of the fund's money.
With plan: 6.22 (hold costs) + 10.06 (exit haircut of 16.2, discounted) + 5.45 (capex of 6.0 in year 1, discounted) = 21.73 million
Value of the plan = 25.91 − 21.73 = 4.18 million
The plan removes 8,000 tonnes a year, 32,000 over the hold, at 750 euros of capex per annual tonne. It is worth doing at the fund's price, but notice why: priced on the hold alone, without the exit, it loses 2.52 million. A decarbonisation plan in a five-year hold is mostly an exit argument, which is the same conclusion an ESG value creation plan reaches when it is measured in enterprise value.
| Year-1 price | Year-5 price | Adjustment, no plan | Share of EV | Value of plan |
|---|---|---|---|---|
| 50.0 | 75.0 | 12.96 | 5.8% | -0.64 |
| 75.0 | 112.5 | 19.43 | 8.6% | 1.77 |
| 100.0 | 150.0 | 25.91 | 11.5% | 4.18 |
| 125.0 | 187.5 | 32.39 | 14.4% | 6.59 |
| 150.0 | 225.0 | 38.87 | 17.3% | 9.00 |
The plan breaks even when the whole path is scaled to 56.6 euros in year 1 rising to 84.9 in year 5. That is the number to put in the investment committee paper: not "the plan is worth 4.18 million" but "the plan pays as long as the fund believes carbon will cost more than about 57 euros a tonne now and 85 at exit".
How the programme's value carries from enterprise value to equity and IRR is worked in the free workbook for this book. The cost per tonne of individual abatement measures is in how to calculate abatement cost per tonne, and the exit value of a full programme in what an ESG value creation plan adds.
One set by the fund and written down, rising over time, and tested rather than asserted. The illustrative path runs from 100 to 150 euros a tonne over five years. The decision it supports should be checked at lower prices: the illustrative 6.0 million decarbonisation plan breaks even when the path is scaled to 56.6 euros rising to 84.9.
Only where carbon is already paid, under the EU ETS or a carbon tax, and that part is already in EBITDA. For the rest it is a shadow cost: a way to price the risk that regulation, customers or the next buyer will charge for emissions. In the illustrative case 64.7 per cent of the adjustment comes from assuming the exit buyer prices carbon too.
At least Scope 1 and market-based Scope 2, the emissions the company controls and a buyer will diligence. For emissions already under an ETS, charge only the gap between the shadow price and the price paid: 5,000 covered tonnes at a 70 euro ETS price take the year-5 shadow cost from 3.00 million to 2.65 million.
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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