Whitepaper | Time value of carbon and ‘discounted carbon flow’ (DCF)
Implied carbon discount rates were calculated. Time value of carbon is currently undervalued
The term “time value of carbon” is not new. While generally being used and/or cited in the context as developed by Larry Strain’s in his whitepaper (1), there are various examples of earlier use (2).
There is overwhelming alignment in the significance of the time value of carbon within those using this terminology because of the elegance behind the concept. Everyone seems in agreement that extracting one atom of carbon from the atmosphere today is worth more than if extracted later (the rate of this decay in value being referred as the “carbon discount rate”). Despite this alignment, adoption of carbon discount rates into everyday vocabulary or modern-day climate policies seems mixed.
Certain firms, most notably Generation Investment Management, have been working hard at developing awareness and offering relevant insights on the time value of carbon (3). Personally, this is how I came across this subject; during a conference and listening in on a panel discussion. The realization shook me. Operating BXVentures, a venture studio dedicated to cleantech (4), I hadn’t yet come across the time value of carbon but had almost instinctive understanding of the time value of money. Why was is so? I felt compelled to vocalize the matter. I also felt unsatisfied with the current approach to discuss the concept. This became the basis for this whitepaper and for proposing an alternative approach to calculating the time value of carbon using a ‘discounted carbon flow’ model based on the fundamental financial principles of discounted cash flow.
A quick note to readers. An analysis and methodology to calculate carbon discount rates will now be presented. Such calculations will leverage various data sources pertaining to climate change, including United Nation’s Intergovernmental Panel on Climate Change (IPCC) Representative Concentration Pathways (RCP), global carbon budgets and specific emission forecasts. These sources, and the proposed methodology, are discussed in the following sections. Results and implications are presented thereafter. The overwhelming conclusions are two-fold. Undervaluing the time value of carbon cripples our ability to combat climate change, and the carbon needs to be valued ever more dynamically.
Review of existing data
The IPCC has created a flagship set of scenarios, labelled Representative Concentration Pathways or RCP, from which predictions of the increase in average global temperature have been made possible by using forecasts of future emissions (5). Developed in the 2010s, these scenarios have proven very useful to guide climate policy. They have also served the global community for setting limits to the total stocked atmospheric carbon (i.e. total amount of accumulated carbon in the atmosphere) and peak emission needed to be observe in order to achieve specific climate change objectives. The figure below illustrates such forecasts and projected increase in average global temperature in time for the flagship scenarios (labelled RCP 2.6, 4.5, 6.0 and 8.5).
RCP scenarios are influential projections which have helped shaped global climate policies. In the table below, the key outputs of such scenarios are presented, including the target increase in average global temperature and approximate year in which global CO2 emissions are supposed to peak.
To better understand how the total stocked atmospheric carbon evolves in time, various studies have been conducted on the global carbon budget (6). Such budgets represent the biosphere’s annualized capacity to absorb all carbon related fluxes and activities and quantifying the amount of additional carbon injected into (or remove from) the atmosphere on a yearly basis. The inputs to the yearly global carbon budget are global CO2 emissions, land-use change (emissions), land uptake (sink) and ocean uptake (sink), as illustrated below.
Developing long-dated forecasts for each of the inputs to the global carbon budget is part of the process by which all RCP scenarios are created. Out of all these inputs, global CO2 emissions forecasts (up to year 2100) are the most widely available (7). The following graph illustrates the global CO2 emissions forecasts as predicted in each of the RCP scenarios (RCP 2.6, 4.5, 6.0 and 8.5).
By combining the long-term forecasts for land-use change, land uptake and ocean uptakes, as explored in various scientific studies (8), all of the inputs of the global carbon budget could be estimated yearly between now and the year 2100.
Having laid out all of the fundamental building blocks required to calculating the time value of carbon, the proposed methodology will be presented in the following section.
Academic models describing the time value of carbon already exist (9). The motivation behind proposing this new methodology comes from the conviction that using a simple financial model might be both powerful and impactful. Time value of money is widely understood and frequently used. There is no reason why time value of carbon could not be as prevalent.
The proposed methodology consists of three steps.
Step 1: Write the stocked atmospheric carbon (SAC) as a mathematical formula and time series made from the global carbon budget forecasts.
This step includes collecting any and all required data and forecasts. Yearly net additions or reductions to SAC are calculated from yearly global carbon budgets. From here, the RCP scenarios (RCP 2.6, 4.5, 6.0 and 8.5) are reconstructed as a time series of total SAC. Finally, this time series is converted into a mathematical formula which sums the total SAC up to 2020 (evaluated to be 875 GtC (10)) with the yearly net global carbon budget outputs, as expressed below:
Step 2: Decide which ‘carbon’ to calculate its time value (i.e. to discount).
While this should be straightforward, there are various ‘carbon’ inputs from which to chose and that choice will directly affect the outcome of any calculation. In this methodology, the ‘carbon’ subject to discounting is chosen to be the net carbon (addition or reduction) as calculated yearly from the global carbon budget. This choice is supported by the fact that this is the same net carbon from which climate change scenarios are built and global policies are based on.
Step 3: Rewrite the stocked atmospheric carbon (SAC) time series as a discounted cash flow.
It is impossible to calculate the time value of carbon without calculating a discount rate. To calculate the carbon discount rate, the SAC formula is rewritten as a ‘discounted carbon flow’ instead of as a simple sum of a time series. This ‘discounted carbon flow’ is analogous in every respect to a classical financial discounted cash flow except for using net carbon flows instead of net cash flows. Using RCP 8.5 as reference (since it is associated to the “Business-as-usual” scenario), the yearly addition or reduction to SAC under RCP 8.5 becomes the discounted term. Continuing with our financial analogy, this is analogous to adding net present 'impact' values of future carbon flows. As a result, the new formula for the total SAC for the proposed model is:
In this expression, the discount rate 'x' represents to the year-on-year change in value of excess carbon when delaying its removal (i.e. staying in a RCP 8.5 business-as-usual) as solved to achieve a specific RCP objective (e.g. RCP 2.6/4.5/etc.). Using this approach, different implied carbon discount rates can be calculated for chosen RCP scenarios.
Implied carbon discount rates were calculated in four scenarios. In all cases, a strong fit was observed between the reproduction of stocked atmospheric carbon curves using the ‘discounted carbon flow’ model and the original RCP time series. The graphical results are presented below.
As seen in the figure above, the use of a single carbon discount rate effectively tracks the time evolution of expected stocked atmospheric carbon curves, effectively reproducing RCP 2.6 and RCP 4.5 scenarios until they reach their peak. Practically, this implies that the tracking of progress against RCP objectives could be managed through the use of a single independent variable: the implied carbon discount rate. Note that the difference between implied RCP 2.6 and RCP 2.6D comes from artificially delaying the start of CO2 emission reduction from 2020 to 2025 to see the impact on the implied carbon discount rate.
Moreover, the use of a single carbon discount rate is a perfect fit for creating a stocked atmospheric carbon curve which has a hard maximum limit. As illustrated in the implied 1 TtC (1 trillion tons of carbon) curve, the carbon discount rate can be used to dial up or down the maximum limit of total stocked atmospheric carbon in the far future. Therefore, as depth of knowledge is gained into the maximum stocked carbon capacity of the atmosphere, the carbon discount rate could become a powerful tool for managing such hard limit.
The real-life ramifications of these carbon discount rates can be significant. For instance, this methodology offers a ‘half-life’ for carbon (i.e. period in years by which the value of carbon emissions will have doubled, or equivalently, the value of carbon reduction will have halved). The implied carbon discount rates and carbon half-life for various RCP scenarios are listed in the table below.
The conclusions to draw from these tabulated results are somber. If humanity wants to keep the projected increase in global temperature below 2 degrees C by year 2100 (i.e. RCP 2.6, RCP 2.6D or 1TtC), the carbon discount rate cannot not be less than 8.4% and may be as high as 28.0% (if global emissions finally peak in 2025). To put in perspective, this would imply that the value of one atom of carbon may double in as little as 2.81 years but no more than 8.59 years.
This proposed model does have its limitations. Since this approach works best in excess global carbon budget scenarios, the implied reproductions of RCP 2.6, 2.6D and 4.5 are stopped before the curve starts decreasing. This does not mean that the value of carbon no longer evolves in time, it simply means that it has entered into a new regime of deficit global carbon budgets. Such regimes have not yet been investigated. It is also worth noting that this methodology was never expected to work in scenarios where the total stocked atmospheric carbon never stops increasing. For that reason, no reproductions were attempted for both RCP 6.0 and RCP 8.5. Finally, this analysis was done using publicly available and outdated data sets. Gaining access to more recent data would further strengthen the results and insights. It will be a pleasure to discuss building upon this model with different stakeholders.
The potential ramification of this methodology and these results will be discussed for three potential sectors with significant interest.
Cleantech investor implications
Discounted cash flow (DCF) models are widely used by investors. Their construction, including the analysis of underlying discount rates, is carefully examined as part of most due diligence process. Given they significantly impact future cashflows, discount rates are generally seen as one of the most important inputs for valuations and DCF analysis.
Based on this ‘discounted carbon flow’ model and the implied carbon discount rates, fresh avenues leveraging this new understanding of the time value of carbon in the context of cleantech investing and due diligence are made possible.
First, there is a growing subset of investors targeting ‘transformative’ projects, generally linked with precise (and significant) CO2 or % of total emission reduction objectives. This seems to be driven by the realization that large scale impact is needed urgently to change the current global emission trajectory. Using Breakthrough Energy Ventures as an example, they specifically target technologies with the potential to reduce emissions by 0.5Gtons per year (11). As an investor, it may be difficult to directly compare different large-scale projects with very different emission reduction profiles. Using the proposed time value of carbon methodology may simplify such comparisons and ultimately help investment decisions, as shown in the illustrative comparative table below of the net present ‘impact’ value for different carbon discount rates 'x'.
Second, the International Energy Agency (IEA) has stated that 40% of technologies needed to reduce emissions have not yet been commercially deployed (12). Likewise, many technologies may take longer to develop but may have significant future benefits in terms of emission reduction. In such scenarios, understanding the target policies, peak emissions and time value of carbon can improve investing decisions relative to ‘deeper’-tech or ‘earlier’-stage cleantech. Given that solutions of varying maturity and emission reduction profiles will be needed to abate global emissions, overlaying carbon discount rates onto impact models (analogous to exploring different tech for its peak-shaving capabilities) could become a useful investor tool for diversification. In essence, clean technology scouting could become dynamic and tailored for maximum impact against specific parts of future emission forecasts.
Carbon market & policy maker implications
Applying the results of the proposed methodology to the carbon markets also leads to an important conclusion. Not only do policy makers need to continue to increase the price of carbon every year but they need to accelerate the rate at which such prices are increasing.
Using Canada’s carbon markets as an example, as of year 2023, carbon is priced at CAD $65/ton and set to increase by CAD $15 per ton per year (13). At its current rate, the price of carbon will double in a little over 4 years, in line with the RCP 2.6 implied carbon discount rate of 16.8%. However, Canadian policy makers need to consider accelerating its price increases otherwise, by year 2027 (with a price of carbon of CAD $125 per ton doubling in roughly 8.5yrs) the policy’s implied carbon discount rate will have decayed to 8.4%, in line with the 1 TtC scenario instead of following RCP 2.6 (with an additional average global temperature increase moving from 1.7oC to 2.0oC).
Furthermore, delaying the start of carbon reduction will only drive the implied carbon discount rate up, as seen in the difference between RCP 2.6D and RCP 2.6. To combat this effect, efficient carbon markets could be setup to track carbon target policies (e.g. RCP 2.6 or 1 TtC) by reacting to updates in global carbon budgets as an indication of future implied carbon value. Similarly, policy makers could also setup dynamic carbon price policies based on fulfilling global carbon reduction commitments.
Academia and intergovernmental implications
There are various avenues by which academia and intergovernmental agencies could leverage this proposed methodology.
From academia’s perspective, there is an opportunity to elevate this new model from a whitepaper to a validated and peer-reviewed publication. By building upon and improving this easy-to-use methodology, an academic institution could position itself as its custodian, with the associated benefits of being active contributors to a new way to study climate change, future possible citations and other references.
From intergovernmental agencies’ perspective, the benefits are potentially ever greater. By feeding this model with up-to-date data and reporting on its results, such agencies could gain a new analysis tool from which to track progress against climate change objectives. In summary, the regular publication of official carbon discount rates as indices could become an influential climate change indicator for investors, carbon markets and policy makers alike.
Using this approach to calculating time value of carbon further strengthens the need for urgency and the immediate reduction of carbon emissions. The proposed ‘discounted carbon flow’ model is simple and easy to calculate. By presenting this financial analysis to carbon discount rates, the intent is to draw new stakeholders into seeing the value in investing their own time or capital into the cleantech ecosystem.
The time value of carbon is a discussion which needs to continue, evolve and grow. It has been very motivating to present this new angle to discuss climate change. I hope that I have inspired you to join the conversation.
This article was written by Marc Guilbert.
(8) Extract: https://pubs.acs.org/doi/10.1021/es506201r, https://doi.org/10.1007/s00382-007-0342-x, https://www.researchgate.net/publication/347125138_Forecasts_of_the_trend_in_global-mean_temperature_to_2100_arising_from_the_scenarios_of_first-difference_CO2_and_peak_fossil_fuel