Uncertainties on the global availability and affordability of alternative marine fuels are stalling the shipping sector’s decarbonization course. Several candidate measures are being discussed at the International Maritime Organization, including market-based measures (MBMs) and environmental policies such as carbon taxes and emissions trading systems, as means to decarbonize. Their implementation increases the cost of fossil fuel consumption and provides fiscal incentives to shipping stakeholders to reduce their greenhouse gas emissions reductions. MBMs can bridge the price gap between alternative and conventional fuels and generate revenues for funding the up-scaling of alternative fuels’ production, storage and distribution facilities and, thus, enhance their availability. By estimating the fuels’ implementation and operational costs and carbon abatement potential, this study calculates marginal abatement costs and estimates the level of carbon pricing needed to render investments nto alternative fuels cost-effective. The results can assist policymakers in establishing robust and effective maritime decarbonization policies.
Main
In light of the global attention placed on climate change mitigation, in July 2023 the International Maritime Organization (IMO) adopted the Revised IMO Strategy aiming at, among others, reaching net-zero greenhouse gas emissions (GHG) from international shipping by/around 2050 and taking up zero and near-zero GHG emission technologies, fuels and/or energy sources by at least 5% striving for 10% by 2030 (ref. 1). However, the results of the fourth IMO GHG Study show that, under a business as usual (BAU) scenario, carbon dioxide (CO2) emissions from shipping in 2050 are expected to be 90–130% of 2008 levels2. In combination with estimates from the United Nations Conference on Trade and Development on expected growth in global trade volumes, it becomes clear that, without any solid regulatory intervention, emissions from shipping will notpeak and decline but might instead continue to rise3.
To leverage its decarbonization targets, the Revised IMO Strategy proposes several candidate measures classified into short, medium and long term, to be agreed upon and implemented by 2023, between 2023 and 2030, and between 2030 and 2050, respectively. Market-based measures (MBMs), also known as economic measures, belong to the set of medium-term measures and enforce the ‘polluter-pays’ principle that aims at internalizing the external costs of emissions. By increasing the cost of fossil fuels, they provide fiscal incentives to stakeholders to reduce consumption and thus GHG emissions. Their implementation also gathers revenues that can accelerate a maritime energy transition by funding research and development projects and by subsidizing first movers or green ships that comply with the carbon elimination regimes4,5,6,7.
There is an increasing number of studies advocating that, to harness the decarbonization potentials, technologcal measures and especially the uptake of alternative marine fuels are unavoidable8,9,10,11,12,13,14,15. However, the lack of global availability and sufficient supply of these fuels hamper the energy transition. MBMs can accelerate the up-scaling of zero-carbon technologies by closing the price gap between conventional and alternative fuels.
Marginal abatement costs (MACs) and marginal abatement cost curves (MACCs) have been widely applied in assessing the economics of climate change mitigation policies16. Their development allows policymakers to illustrate the relationship between an abatement measure’s emissions reduction potential, measured in metric tons (MT) of carbon dioxide equivalent (CO2e), and its associated cost for reducing CO2e emissions by one unit (USD per MT of CO2e). CO2e accounts for other GHGs besides CO2 and translates their potency in relation to CO2 on the basis of their global warming potential (GWP). This study considers the 100-year time horizon GWP relative o CO2 (ref. 17).
The prospect of MAC calculations is manifold. They can provide insights on policy-making guiding principles, assist in realizing the impacts of various mitigation options that may not bear the upfront implementation costs but have the capacity to support GHG abatement efforts and compare some mitigation technologies relative to their cost-effectiveness along with their abatement spectrum18. So far, they have been used in environmental theory and energy economics to indicate in a straightforward way the carbon price (that is, the MAC) associated with a specific reduction level or the carbon price resulting from an emissions cap in a cap-and-trade system19,20,21,22.
There are two main methods for constructing MACCs21. First, the so-called model-based approach generates a linear cost-effectiveness trend line relative to the abatement potential. In shipping, this has been used to evaluate different carbon mitigation measures23,24,25,26,27, including operational and technlogical mitigation measures. Both the second and fourth IMO GHG studies involve MACCs relying on a model-based approach2,28, and CE Delft has published their shipping model-based MACCs29,30. Model-based MACCs tend to demonstrate macroeconomic responses on international trade more precisely and capture the interdependencies between different mitigation measures. However, they often are criticized for lacking transparency, technical detail and clarity in their findings16.
The second method for producing MACCs is the so-called expert-based approach, which uses a step-form visualization of the various mitigation measures and ranks them accordingly by demonstrating the economic and technical merits of reducing GHG emissions. The technique provides a MAC comparison of the assessed mitigation measures, transparency on the calculations of the associated costs and a simpler representation of the relationship between cost-effectiveness and abatement potential. More specifically, the expert-base model is constructed using several mitigation measures from lowest to highest cost-effectiveness, forming multiple steps that represent the MAC over the whole lifetime of the mitigation measure. In shipping, this approach has been used to study various maritime carbon mitigation measures’ interdependencies and propose methods to rank them systematically.
Many studies develop “expert-based” MACCs and consider a number of measures to quantify the effect of interdependencies between operational and technical standards towards 2030 (refs. 24,31). Fuel prices and discount rates influence the preference for a mitigation measure32, and in shipping, measures with negative MAC are frequently implemented33. The results highlight that MACs and the associated MACCs can be effective tools in forecasting any mitigation measure implementation rate33. By calculating the abatement cost of various e-fuels, it was found that dual-fuel marine engines ensure flexibility and robustness in fuel selection ad can set the scene for growing supplies of e-fuels at lower risks34. The development of MACCs for operational and technical measures such as trim and ballast optimization, main engine auto-tuning, liquefied natural gas (LNG) and Flettner rotors showed that the investigated measures with negative abatement cost should only be considered as medium-term solutions as they do not lead to fossil fuel independence35. A comprehensive review of MAC methodologies showed that MACs and the associated MACCs can be a reliable tool to rank the mitigation options relative to a baseline rather than focusing on complex methods and the absolute value of the individual measures22.
We note that MACCs are to be considered on a cumulative basis, with measures ranked in non-decreasing order of MAC and in which all measures that have a MAC less than or equal to zero are to be chosen in combination. This method is not suitable if the measures under consideration are mutually exclusive and cannot be used in cobination, such as alternative fuels. This study aims to close the research gap on utilizing MACs to assess the cost-effectiveness of alternative marine fuels and their supporting technologies. We rank the alternative fuels from the lowest to the highest MAC and identify the required carbon pricing level that renders these fuels’ costs comparable to a baseline fuel. We assume that each fuel will be used independently as the only choice to cover the vessel’s energy requirements, and thus emissions abatement potential is not to be considered in a cumulative manner. The analysis estimates the net present cost of implementing and utilizing alternative marine fuels and their abatement potential for several case studies of newbuilding and existing vessels, obtaining inputs from Table 1. Table 2 summarizes our inputs on alternative fuel production prices as of today’s cost estimations, drawing from a more comprehensive analysis presented in Supplementary Table 1. The utilization of MACs allowsfor identifying the required level of MBMs in the form of carbon pricing for closing the price gap between conventional and alternative fuels.
Table 1 Case study: vessel newbuilding, opportunity and retrofitting cost parameters
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Table 2 Fuel prices and well-to-wake (WtW) emissions
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The rest of this study is organized as follows: Results section contains the outcomes of the MAC calculations, followed by a brief interpretation of the results. Discussion and conclusion section highlights the key findings of the analysis. This study’s methodology and data set are presented in Methods section.
Results
This section presents the results of the analysis for our case studies. In Figs. 1–5, the y axis illustrates the estimated MAC or the net present value (NPV) per MT of CO2e abated, while on the x axis the width of each column represents the emission abatement potential of each alternative fuel relative to the baseline. Furthermore, the results in the data tablesare ranked from the lowest to the highest MAC and contain the total amount of CO2e averted by implementing the alternative fuel over the vessel’s lifetime, the percentage of GHG emissions reductions achieved relative to using the baseline fuel and the level of carbon pricing that renders the fuels’ cost viable. A lower and upper bound of fuel prices are considered to capture the uncertainty of the expected alternative marine fuel production prices and their dependence on exogenous inputs such as the prices of renewable electricity and carbon capture and storage (CCS). These results are mainly utilized to facilitate a straightforward interpretation of the relationship between cost-effectiveness and abatement potential and to compare some mitigation technologies with respect to their MAC and abatement spectrum.
Fig. 1: MACs and GHG abatement potential of alternative marine fuels for a newbuilding vessel.
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a, Based on a 200 USD per MT of CO2 cost of carbon capture and storage anda 100 USD MWh−1 cost of electricity47. b, As for a, but for a 20 USD MWh−1 cost of electricity.
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Figure 1a shows the MACs of alternative fuels for a newbuild Supramax bulk carrier vessel in a high fuel price scenario, assuming a lifespan of 25 years and a discount rate of 3%. The results indicate that investments into an internal combustion engine (ICE) LNG vessel have a negative MAC and thus constitute cost-effective investment choices under high fuel price expectancy. The results are attributed to the expectation that LNG prices will be low in the future (compared with very low sulfur fuel oil (VLSFO)). When the increase in capital expenditure is not high enough to compensate for the difference in the long-term operational cost savings attributed to the low LNG prices, then the MAC of the alternative fuel will be positive. The LNG ship’s abatement potential is limited to only 8% of GHG emissions reductions for a well-to-wake (WtW) scope and GWP100. This isufficient reduction in absolute emissions could be complemented by other operational measures, such as speed reduction, to reach the desired emissions levels. Furthermore, Fig. 1a shows that investments into bio-methanol can become cost-effective after imposing a carbon price of around 40 USD per MT of CO2e and can achieve 65% GHG reductions. The same rationale is followed for all other fuel choices within the scope.
Figure 1b shows the MACs of alternative marine fuels for the newbuilding Supramax bulk carrier assuming a lifespan of 25 years and a discount rate of 3% for a low fuel price scenario. In this case, investments into (liquefied petroleum gas) LPG vessels have the lowest MAC and would require a carbon price of approximately 95 USD per MT of CO2e to become economically viable. The results differ from the high price scenario for various reasons, such as the lower marginal difference in the relevant fuel cost between LPG and diesel and between LNG and diesel, the higher abatemnt potential of LPG versus LNG and the marginal difference in the capital cost of a newbuilding LPG vessel and a conventional diesel vessel. However, the emissions reduction potential of an LPG vessel is approximately 20%. Blue ammonia, on the other hand, which follows LPG in Fig. 1b, can achieve emissions reductions up around 60% and, from a financial perspective, would require a carbon price of 150 USD per MT of CO2e to become financially attractive.
Figures 2–5 present our results for the retrofitting case. We consider the same Supramax bulk carrier retrofitted after 5 or 10 years, respectively, for two fuel price development scenarios. The results show that, on the one hand, the ranking of the preferred fuels considered is not influenced notably by the vessel’s age but the derived MAC increases with the vessel’s age. This is expected as it shows that retrofitting a relatively younger vessel with alternative fuels has greater return on investment potential and higher total abatemen capabilities. In terms of the MBMs, lower MACs are translated to lower levels of carbon pricing.
Fig. 2: MACs and abatement potentials of alternative fuels for a retrofit of a 5-year-old diesel ICE vessel.
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a, Based on a 200 USD per MT of CO2 cost of CCS and a 100 USD MWh−1 cost of electricity48. b, As for a, but for a 20 USD MWh−1 cost of electricity.
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Figures 2 and 3 show the alternative marine fuel MACs for our first retrofit case study of a vessel equipped with a diesel ICE. Bio-methanol appears to be the most preferred solution due to the low retrofitting costs for upgrading the engine to burn methanol, the expected low-price differential of bio-methanol and VLSFO and the large emissions abatement potential that bio-methanol can achieve. Also, if the production costs of ammonia decrease to 56 USD kWh, the implementation of a carbon price of approximately 200 USD per MT of CO2e would make retrofits to ammonia economically viable. Compared withthe newbuilding scenario, the reduced lifespan and the lower price range between LNG and diesel do not result in high enough operational cost savings to cover the retrofitting costs. Thus, LNG appears to be further down in the ranking of preference for alternative fuels. A switch to e-diesel is the most cost-intensive choice, whereas for green liquid hydrogen a levy of approximately 600 USD per MT of CO2e is required.
Fig. 3: MACs and abatement potentials of alternative fuels for a retrofit of a 10-year-old diesel ICE vessel.
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a, Based on a 200 USD per MT of CO2 cost of CCS and a 100 USD MWh−1 cost of electricity48. b, As for a, but in a low fuel price scenario of 20 USD MWh−1 cost of electricity.
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Figures 4 and 5 show our results for our Supramax bulk carrier case study that is built with a dual fuel LNG ICE running on a diesel cycle. We highlight that, in this analysis, LNG constitutes the baseline fuel, and owing to the engine’s dual fuel technoogy, calculations on retrofitting to diesel are not examined. The model runs for two distinct vessel age stages and both high and low bounds of alternative fuel price expectancy. Figure 4 shows that, in a high-price scenario, a switch to bio-LNG would require a carbon price of 150 USD per MT of CO2e to become cost-effective, similar to the carbon price required for incentivizing the same fuel for an older vessel (Fig. 5a). Green ammonia has a higher MAC but larger emissions reduction potential. Overall, in high fuel price expectancy, it is mainly the operational costs and the fuel’s abatement potential that have the most substantial effects on MACs, while only for investments in hydrogen systems does the high initial capital outlay have a greater influence on cost viability.
Fig. 4: MACs and abatement potentials of alternative fuels for a retrofit of a 5-year-old LNG ICE vessel.
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a, Based on a 200 USD per MT of CO2 cost of CCS and a 100 USD MWh−1 cost of electricity48. b, As fr a, but for a 20 USD MWh−1 cost of electricity.
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Figures 4b and 5b show that, in a low fuel price expectancy scenario, investments in ammonia ICEs seem to become more financially appealing. There are only marginal changes in the fuels’ MAC ranking depending on their age at the time of the retrofit. Green liquid hydrogen, which can achieve 100% GHG emissions reduction, can become cost-competitive with LNG when a carbon price of 300 USD per MT of CO2e is implemented.
Fig. 5: MACs and abatement potentials of alternative fuels for a retrofit of a 10-year-old LNG ICE vessel.
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a, Based on a 200 USD per MT of CO2 cost of CCS and a 100 USD MWh−1 cost of electricity48. b, As for a, but for a 20 USD MWh−1 cost of electricity.
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Discussion and conclusions
This study focused on the developments of MACs to rank alternative marine fuel solutions according to their cost-effectiveness and calculate the level of carbon pricing needed toclose the price gap between alternative and conventional marine fuels. We first considered the capital costs arising from the installation onboard of the relevant power and fuel storage systems for facilitating the alternative fuels, for both a newbuilding and a retrofit scenario. Second, we estimated the operational costs from the utilization of these fuels during the vessel’s lifetime including bunkering and opportunity costs. Our analysis demonstrated our case study vessel in a newbuilding/design stage and in an existing stage where the ship is built with either a diesel or an LNG dual fuel ICE.
Our findings show that biofuels demonstrate high technical potential for being used as zero-carbon bunker fuels as their future cost projections are relatively lower than for e-fuels. For newbuilding vessels, investments into bio-methanol can achieve 65% GHG emissions reductions and will become financially attractive after a carbon price of 37 USD per MT of CO2e. However, ensuring their lare-scale supply is likely to be constrained by the limited availability of biomass as well as the competing demands from other transportation sectors36.
The adoption of green liquid Hydrogen would require a carbon price of 243–704 USD per MT of CO2e to become cost competitive. The low estimates are based on the expected decrease in future costs of renewable electricity owing to the rapid and widespread deployment of renewable energy technologies. This decrease is expected to stem from economies of scale that will be realized as renewable energy projects become more prevalent. Figure 6 summarizes our results on the range of estimated carbon prices needed to incentivize the adoption of alternative marine fuels and their supporting technologies and on the percentage of GHG emissions reductions achieved on a WtW basis through the adoption of each fuel.
Fig. 6: Summary of the range of carbon prices and the percentage of GHG emissions reduction achieved for each alternative fuel.
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Te upper bound of carbon prices is based on a 200 USD per MT of CO2 cost of CCS and a 100 USD MWh−1 cost of electricity. The lower bound is based on a 200 USD per MT of CO2 cost of CCS and a 20 USD MWh−1 cost of electricity. The intensity of the green shading represents the GHG emissions reduction potential of each alternative fuel.
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For existing ships equipped with a diesel ICE, investments into biofuels can be a promising solution in a high fuel price scenario, whereas in a low fuel price scenario, the retrofitting costs to ammonia systems do not influence the resulting MAC more than the operational costs and the abatement potential of the fuel in the denominator. For an existing vessel with a dual fuel LNG engine, retrofitting to ammonia seems to be a better solution regardless of the fuel price expectancy, mainly because ammonia shares some of the technical design specifications of LNG and requires fewer modifications during the retrofit.
From a policy perspective, ny choice on the level of carbon pricing in the case of a global fixed fuel levy regime should consider the average age of the global fleet at the time of enforcement. The analysis showed that, in high fuel price expectancy, it is mainly the operational costs and the fuel’s abatement potential that have the most significant effects on MACs, while only for investments in hydrogen systems does the high initial capital outlay have a greater influence on cost viability. Early investments have greater potential for returns in a newbuilding or retrofit case. As mentioned above, our results involve assumptions for fuel prices to capture the volatility of the bunker price and the uncertainty of the overall demand for these fuels.
This study did not consider the indirect network effect that relates to the interdependence between the demand and supply of alternative marine fuels, that is, between the adoption of these fuels by multiple ship owners and the investment in fuel production and bunke infrastructure from fuel suppliers. The choice of alternative fuels will be ultimately shaped not only by their MAC but by other factors such as fuel availability, provision of adequate bunkering infrastructure in many ports of the world, policy decisions such as subsidies, exemptions or rebates and other external factors, whose analysis lies beyond the scope of this paper. While the marine fuel versus production/infrastructure problem does show similarities to the electric cars versus charging infrastructure problem37, there are decisive differences between the two: the high number of competing fuels in combination with the fleet heterogeneity, as well as various factors that are less amenable to an objective quantification (for example, safety preferences and the effect of singular events such as accidents).
Last but not least, and even though our study used a Supramax bulk carrier as a case study, the methodology can be applied to any ship type. Each ship has its distinct featuresand special constraints, thus one would expect the numerical values of the MACs and required levies to differ across ship types. However, we conjecture that the main thrust of our results will remain the same as outlined herein.
Methods
Data set
The development of fuel prices depends on various exogenous inputs, such as the price of renewable electricity, the price of CCS and the global and sufficient availability of these fuels. Given the high level of uncertainty in the evolution of alternative fuel prices, our data set consists of a high and low price expectancy scenario. Fossil fuel prices were based on historical trajectories, while the bio-fuel prices depend on the cost of biomass. E-fuel prices rely on the levelized cost of renewable electricity (as well as the cost of CO2). The two different price scenarios are intended to capture the uncertainty with respect to the named exogenous factors.
Our case study focuses on a 63,000 deadweight (DWT) Supramax bulk carrier of 7,500 kW aximum brake power. The analysis assumes that the vessel has an energy output of 43,500 MWh per year, which remains constant and thus additional fuel storage space will be required to account for the lower energy density of the alternative fuels. For calculating the opportunity cost associated with the revenues lost due to cargo space being used as fuel storage capacity, we keep the total displacement of the ship constant (at 78,750 MT) for all power systems and thus reduce the respective cargo carrying capacity. As performed in ref. 38, for the first 58,000 DWT, we assume an average utilization of 90%, while for the next 5,000 DWT we estimate an average utilization of 25%. According to the aforementioned utilization of deadweight ranges, we assume a charter rate of 25,000 USD per day, which is distributed proportionally among them39.
Firstly, our analysis focuses on a newbuilding scenario, ranks the alternative marine fuels according to their MAC and evaluates the carbon price neededto render these investments cost-effective. In estimating the newbuilding price over the past years, our VLSFO reference configuration has a capital cost (CAPEX) of roughly 30 million USD (mUSD)40. We deduct the cost of a VLSFO power system and instead use the alternative fuel power system’s cost per unit of brake power as estimated in ref. 34. We use a system-based41 cost estimation approach with cost factors per unit power for our case study vessel of 7,500 kW installed power. We estimate the newbuilding costs as shown in Table 1. Second, this study estimates the MACs for a retrofit scenario and uses the same system-based cost factors as for newbuilds plus an additional penalty of 3.6 mUSD to account for shipyard costs and lost income during retrofitting.
Our second scenario involves a newbuilt vessel equipped with a conventional diesel ICE that seeks to switch to an alternative fuel at 5 or 10 years of age. We aim to calculate the carbon price that will incentivize the retrofit. Th analysis is conducted for two different price scenarios to account for the uncertainty on the evolution of alternative fuel bunker prices. Retrofitting to alternative marine fuels entails various technical modifications onboard. We assume that additional tanks of up to 1,600 m3 can be installed on deck in the aft part of the ship to accommodate the new fuel. The case differs from other shipping segments, and decisions on the instalment of the alternative fuel storage tanks depend on the type and initial design of the vessel.
In the case of retrofitting to methanol, we assume that the fuel tanks can be integrated into the ship’s structure. Retrofitting would require modifications to the fuel supply system regardless of the alternative chosen42. On the other hand, in the case of retrofitting to LNG or ammonia, the advanced requirements for main engine modifications and the installation of additional tank capacity will lead to a relatively higher retrofitting cost compared with methanol For LPG, we assume that retrofitting costs are similar to methanol, while for hydrogen, owing to its unique properties and relatively low technological readiness, retrofitting costs are considered the most expensive.
Moreover, we calculate the MACs for an existing vessel equipped with an LNG ICE. Considering the current record on the orderbook for LNG newbuilding vessels (and their 25 year life expectancy), it is very likely that LNG ICE ships will seek to comply with the more stringent forthcoming regulations before 2050, and retrofitting will become a viable solution. It is only the LNG dual fuel engine operating on a diesel cycle that can deliver GHG emissions reductions on a WtW, and this study will consider this engine technology9,43.
MAC calculations
MAC calculations require determining each project’s financial details and the expected GHG abatement volume over the project’s lifetime. The analysis follows the four steps below:
1.
Conduct a comprehensive survey of the various echnologies and their costs required to facilitate the adoption of alternative marine fuels for a case study vessel.
2.
Calculate the MAC of these alternatives for various stages of the vessel’s lifetime and different scenarios on the evolution of fuel prices.
3.
Rank order the MACs, and correlate MAC and the fuels’ abatement potential
4.
Estimate the required level of carbon pricing that renders the alternative fuels cost-competitive with the baseline fuel.
Supplementary Table 2 defines the various symbols and variables used in this analysis. For alternative fuel A and baseline fuel B, both carbon coefficients CfA and CfB and fuel prices PfA and PfB are normalized by unit energy (per kWh) to allow for direct comparison of alternative fuels on a common denominator basis. The common denominator is the energy required to propel the ship over its lifetime (equivalently, on an annual basis). For our study, we assume that this energy is known and fixed, equal to Fc, and expressed in kWh Furthermore, we assume that introducing the alternative fuel will not change the pattern of trade or service speed of the vessel over its lifetime. The main reason we make this assumption is to be able to isolate the impact of the main (strategic) ship owner decision, the choice of alternative fuel on CAPEX, operating expenses (OPEX), CO2e and MACs. Other operational decision variables such as the vessel’s speed and trade pattern are assumed to remain constant on an ‘everything else being equal’ basis. It is realized, of course, that the choice of alternative fuels may impact these other decision variables as well. This is considered a higher order effect that remains beyond the scope of this study.
Also, we shall only compare fuels that have CfA < CfB, so that they have a (positive) emissions reduction potential and serve the initial goal of reducing the sector’s GHG emissions. ΔCAPEX(A) represents the difference in the capital costs for implementing the alternative fuel A. In the nwbuilding scenario, the value represents the difference in newbuilding costs whereas, in the retrofit scenario, the cost of retrofitting. We note that both PfA and PfB are considered exogenous inputs. These are the costs that the ship operator (ship owner or charterer) needs to bear for purchasing the fuel and usually derive as the sum of the fuel production, transportation and storage costs. Owing to the high level of uncertainty regarding future prices of alternative marine fuels, this study has performed a literature survey on the various estimations published so far and presents them in Supplementary Table 1. The final purchasing cost is also hard to predict. For instance, the latest rise in LNG prices does not correlate with an increase in the production cost of LNG but is attributed to a radical decrease in LNG supply. The definition of the MAC of alternative fuel A is described in the following equations: $$mathrm{MAC}(mathrm{A})=frac{{{Delta }}mathrm{NCOST}(mathrm{A})}{{Delta }}mathrm{CO}_{2{{{ m{e}}}}}(mathrm{A})},$$ (1) $${{Delta }}mathrm{NCOST}(mathrm{A})={{Delta }}mathrm{CAPEX}(mathrm{A})+mathop{sum }limits_{t=1}^{R}frac{{{Delta }}mathrm{OPEX}(mathrm{A})+mathrm{OppC}(mathrm{A})}{{(1+i)}^{t}},$$ (2) $${{Delta }}mathrm{OPEX}(mathrm{A})=(mathrm{Pf}_{mathrm{A}}-mathrm{Pf}_{mathrm{B}}) imes {F}_{mathrm{c}},$$ (3) $${{Delta }}mathrm{CO}_{2{{{ m{e}}}}}(mathrm{A})=(mathrm{Cf}_{mathrm{B}}-mathrm{Cf}_{mathrm{A}}) imes {F}_{mathrm{c}} imes R,$$ (4) $$mathrm{MAC}(mathrm{A})=frac{{{Delta }}mathrm{CAPEX}(mathrm{A})}{{{Delta }}mathrm{CO}_{2{{{ m{e}}}}}(mathrm{A})}+frac{1}{{{Delta }}mathrm{CO}_{2{{{ m{e}}}}}(mathrm{A})} imes mathop{sum }limits_{t=1}^{R}frac{(mathrm{Pf}_{mathrm{A}}-mathrm{Pf}_{mathrm{B}}) imes {F}_{mathrm{c}}+mathrm{OppC}(mathrm{A})}{{(1+i)}^{t}}.$$ (5) The above methodology estimates the MAC of an alternative fuel A vis-à-vis baseline fuel B. Considering that alternative fuel soutions are deemed expensive investments, they are expected to have MAC > 0. As mentioned above, in the definition of MAC, investments with MAC < 0 are already cost-competitive, and at this point, the carbon abatement option is equally expensive as the baseline scenario from an investor point of view. To identify the abatement cost turning point that will achieve cost competitiveness of the alternative fuel, this study identifies the required level of the carbon price that renders the MAC to be zero. More specifically, considering the enforcement of carbon pricing at the level of Cp0, the following considerations are essential: The imposition of a carbon price is an additional operational cost for the ship that alters the MAC(A) to (mathrm{MAC}^{{prime} }(mathrm{A})) as follows: $$mathrm{MAC}^{{prime} }(mathrm{A})=frac{{{Delta }}mathrm{NCOST}^{{prime} }(mathrm{A})}{{{Delta }}mathrm{CO}_{2{{{ m{e}}}}}(mathrm{A})},$$ (6) where ({{Delta }}mathrm{NCOST}^{{prime} }(mthrm{A})) is the new net cost and ΔCO2e(A) is still given by equation (4). The new annual operational costs ({{Delta }}mathrm{OPEX}^{{prime} }(mathrm{A})) will be reduced by (CfB − CfA) × Fc × Cp0 owing to the emissions reductions achieved by alternative fuel A, and therefore $${{Delta }}mathrm{NCOST}^{{prime} }(mathrm{A})={{Delta }}mathrm{CAPEX}(mathrm{A})+mathop{sum }limits_{t=1}^{R}frac{{{Delta }}mathrm{OPEX}^{{prime} }(mathrm{A})+mathrm{OppC}(mathrm{A})}{{(1+i)}^{t}},$$ (7) $${{Delta }}mathrm{OPEX}^{{prime} }(mathrm{A})=(mathrm{Pf}_{mathrm{A}}-mathrm{Pf}_{mathrm{B}}) imes {F}_{mathrm{c}}+(mathrm{Cf}_{mathrm{B}}-mathrm{Cf}_{mathrm{A}}) imes {F}_{mathrm{c}} imes mathrm{Cp}_{0}.$$ (8) From equations (7) and (8), we identify the carbon price Cp0 for which (mathrm{MAC}^{{prime} }(mathrm{A})=0) or ({{Delta }}mathrm{NCOST}^{{prime} }(mathrm{A})=0). Since ΔCO2e = (CfB − CfA) × Fc × R is constant, we get $$egin{array}{l}frac{{{Delt }}mathrm{CAPEX}(mathrm{A})}{{{Delta }}mathrm{CO}_{2{{{ m{e}}}}}(mathrm{A})}+frac{1}{{{Delta }}mathrm{CO}_{2{{{ m{e}}}}}(mathrm{A})}\ imes mathop{sum }limits_{t = 1}^{R}frac{(mathrm{Pf}_{mathrm{A}}-mathrm{Pf}_{mathrm{B}}) imes {F}_{mathrm{c}}+(mathrm{Cf}_{mathrm{B}}-mathrm{Cf}_{mathrm{A}}) imes {F}_{mathrm{c}} imes mathrm{Cp}_{0} + mathrm{OppC}(mathrm{A})}{{(1+i)}^{t}}=0end{array}$$ or $$mathrm{MAC}(mathrm{A})-mathop{sum }limits_{t=1}^{R}frac{mathrm{Cp}_{0}}{R imes {(1+i)}^{t}}=0,$$ (9) $$mathrm{Cp}_{0}=frac{R imes mathrm{MAC}(mathrm{A})}{mathop{sum } olimits_{t=1}^{R}frac{1}{{(1+i)}^{t}}}.$$ (10) Equation (10) is n
