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An example illustrating the financials of the Fund

Let us examine the financing sources and uses of the Fund and the incentives of participating countries through an example. The following three-country example is based on the following assumptions. (For a discussion of the financing related issues please see this blog entry ).

  1. The agreement comes into effect and the Fund starts operations in 2017.

  2. The price of carbon is set at USD 50 per ton of CO2e in 2017 prices. All figures in the example are in 2017 real values.

  3. The three countries A, B and C are assumed to have an equal share, 18 GtCO2e, of total carbon emissions amounting to 54 GtCO2e globally in 2016.

  4. Total emission benchmarks are assumed to be flat at 18 GtCO2e, the 2016 level, for all three countries for the entire period until 2050. To put this assumption into perspective, the sum of unconditional INDCs by 2030 is 56 GtCO2e (UNEP 2015), which roughly equals current global emission levels.

  5. The marginal cost of abatement compared to initial emission levels is a linear function of the size of emission cuts and declines over time. This decline reflects that a more gradual decarbonization can be achieved at a lower cost than a rapid one. MAC(i) = k(i) * q(i) / t, where MAC(i) is the marginal cost of abatement for country i; k(i) is a constant specific to country I; q(i) is the quantity of abatement by country i; and t is the number of years passed. k(A) is assumed to be 150 USD/t, k(B) is 175 USD/t and k(C) is 200 USD/t meaning that country A can cut emissions at a lower cost than B and C.

  6. Countries optimize their abatement i.e. they cut emissions until the marginal cost of abatement equals the carbon price.

  7. Real interest expense is assumed to be 1.5% p.a. Compared to current market conditions this implies a rise in interest rates.

  8. Global GDP is assumed to be USD 85 trillion in 2017 and is assumed to grow by 3% p.a. in real terms in the future.

  9. The Fund is assumed to have an annual payment cap of USD 1,000 billion in 2017 real terms.

  10. The allocation of the Fund’s liabilities, i.e. countries’ future contributions to the Fund, is based on their respective share of aggregate emission benchmarks. In our example, this means that each country carries one third of future liabilities.

  11. In order to limit an unsustainable build-up of the Fund’s debt, liabilities (including related interest costs) incurred more than 20 years earlier are assumed to be repaid through contributions by participants as opposed to through new debt issuance by the Fund.

Note that these assumptions lead to results that are broadly consistent with a path of keeping global warming below 2 °C with a probability of >66%. Such a path requires that global emissions are cut to 42 GtCO2e by 2030 and to 23 GtCO2e by 2050 (UNEP 2015). In our example, global emissions amount to 42 GtCO2e by 2030 and to 24 GtCO2e by 2050. Clearly, the level of abatement is dependent on the carbon price and the abatement cost function of countries among others. Estimating the abatement cost function, calibrating the carbon price and thus targeting a certain level of abatement is beyond the scope of this example. Its focus is to discuss the features of the proposed framework and the incentives it creates.

The following tables summarise the results of this example.

The example uses a scenario with high financing needs by the Fund. Emission benchmarks are kept flat at current levels until 2050, implying limited willingness by countries to contribute to global mitigation without financial incentives. At the same time, actual emissions are assumed to be cut to levels that are consistent with a 2 °C warming path and the carbon price is set at a meaningful level. Even under this high financing need scenario, the Fund’s cumulative liabilities peak at a level below 10% of global GDP. This, of course, is a significant level of debt, and in order to motivate countries to join and act, it has to be, as they will be the beneficiaries of the annual payments. To the extent more ambitious benchmarks can be agreed, the financing requirements could be reduced. However, even this level of debt could be financed by private investors, especially if we consider the gradual rise in the Fund’s debt over 30 years. To put these financing requirements into perspective, global non-financial sector debt increased by USD 50 trillion during the six and half years between the fourth quarter of 2007 and the second quarter of 2014 (MGI 2015). This represents an approximately 25 percentage point increase as a proportion of global GDP.

The impact of the annual payment cap for the Fund, which becomes effective after 24 years, and the contributions from countries from year 21 onwards can also be seen in the example. Both have a limiting effect on the build-up of the Fund’s liabilities.

The following tables illustrate the perspective of individual countries.

The above table illustrates that the country with lowest marginal abatement cost, country A, achieves the highest abatement level. It can also be seen that abatements increase overtime, as the abatement cost function assumes that the longer the adjustment period, the lower the marginal cost of abatement for any given quantity.

The above table illustrates the cash flows between countries and the Fund. It also shows the gross profit of countries, which is simply the difference between the annual payments received from the Fund and contributions made to the Fund. We can see that country A receives higher payments than country B and C as a result of its higher abatement levels. However, the contribution of countries to the Fund follows a pre-determined formula based on the emission benchmarks and, accordingly, the contribution of the three countries are equal. Consequently, the gross profit differs among countries. The gross profit outcome could be made more equitable by setting individual emission benchmarks with reference to countries’ potential to curb emission i.e. their implied abatement cost function. In the above example this would imply a lower emission benchmark for country A be than for country B and C.

The table also shows discounted gross profits. This reflects the fact that decision makers place a higher value on near term cash flows than more distant ones, which is one of the premises of the proposed plan. The example assumes a discount rate of 5% p.a. In order to incorporate future liabilities in the discounted total, the example assumes that the Fund ceases to make payments to countries after 2050, but countries continue to make their contributions as before and repay the Fund’s liabilities over the period 2051-2070. Note that this assumption makes the example conservative as it ignores benefits that the continuation of the plan could offer.

As gross profit does not include the cost of abatement, it measures the benefit a country gets from joining the agreement compared to not participating in it with equal levels of abatement between the two scenarios. The example shows that all three countries, including country C, which receives the smallest payments in relation to its fixed contribution, derive a significant overall benefit from the Fund. The total discounted gross profit depends, of course, on the discount rate. However, the positive result for all countries is robust to changes in the discount rate. The rate would have to be as low as 2.2% p.a. for the impact on country C to turn negative. Collectively, the countries will derive a positive benefit as long as the interest paid by the Fund is lower than decision makers’ discount rate. It is fair to assume that the discount rate decision makers apply explicitly or implicitly is considerably higher and the limited climate action to-date is evidence of this. If future climate and co-benefits benefits were discounted at a rate of 2% or less, mitigation would be seen as very compelling. This could have helped overcome other hurdles and we should have seen a lot more abatement than we have seen to date.

The last table adds the abatement costs faced by countries to the calculation. The cost function and optimization criteria used imply that the total cost of abatement equals half of the product of emission reduction and carbon price. The net profit measure is also introduced, which is defined as the difference between gross profit and the total abatement cost. Thus, net profit compares the financial situation of countries if they join the agreement and reduce emissions with the alternative of not participating and not reducing emissions at all. This measure and comparison is relevant if we assume that zero climate change mitigation is an option considered. Further, it is important to note that while net profit incorporates abatement costs and financials benefits and costs linked to the Fund, they exclude all climate benefits, co-benefits and other advantages of climate action. Similar to gross profits, net profits are also discounted including the liabilities repaid by participants between 2051-2070.

The results of the example show that even net profits can be positive. Country A’s total discounted net profit is positive, while country B and C have a negative net profit. Again, these results depend on the discount rate. Assuming that future benefits and costs are discounted at a rate higher than 6.2% would result in all three countries ending up with positive discounted net profits. This means that depending on how governments value and discount future outcomes, the proposed plan could be more advantageous than no mitigation action at all even including the costs of abatement and, excluding climate benefits.

Clearly, the assumptions and details of the agreement used for the example should be the subject of further research and refinement. Nevertheless, the conclusion of the example can be summarized as follows:

  1. The proposed framework could create a significant and over the next decades increasing financing

need by the Fund. However, even in a scenario of keeping emission benchmarks at current levels while reducing actual emission by 55% by 2050, which is in line with the global warming target of 2 °C, the financing of the plan should be viable.

  1. From the perspective of countries, the scheme renders climate change mitigation more attractive as they derive a benefit from joining it compared to not participating.

  2. The benefits of countries – capturing near term financial rewards and pushing the financial costs into the future – are so large that under certain scenarios they can offset even the cost of abatement. How decision makers value the future is a key parameter in this regard. Assuming their implied discount rate is around 5-6% – which, arguably, is a conservative assumption given the political reality – means that even ignoring climate benefits and other advantages, the plan can be beneficial to participants.

The example demonstrates many of the benefits of the proposed framework. It makes commitment to an effective cooperation agreement more attractive for governments. Second, decoupling the allocation of financial costs from mitigation efforts, the countries’ interests change from free riding to curbing emissions. Finally, the more short-term focused decision makers are, the more attractive this approach and mitigation within its framework becomes.


UNEP (2015): The Emissions Gap Report 2015 . United Nations Environment Programme (UNEP), Nairobi, Internet:

MGI (2015): Debt and (not much) deleveraging. McKinsey Global Institute, February 2015, Internet:

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