## MACC and its development

For overall presentation of cost effectiveness of results as well as potential CO_{2} reductions for a ship or a fleet and for management purposes, development of MACC (Marginal Abatement Cost Curves) for the company fleet or ships will be
a useful way of communicating the results and priorities on the basis of each EEM and as a whole. Additionally and apart from ship energy audit, the economic assessment of the EEMs is of utmost importance in CO_{2} reduction activities.
Many organisations including IMO have carried out studies in this area. The basic requirement is that how much it costs to reduce CO_{2} emissions when different measures are implemented. Off course the answer will be specific for each
ship.

Marginal Abatement Cost Curve (MACC) is used to show potential CO_{2} reduction of various EEMs versus associated costs/benefits in a very visual and simple way. The MACC shows the reduction potential (tonne/year) and abatement cost ($ spent/tonne
CO_{2} reduction) on one diagram. A typical one developed for international shipping as a whole is shown in figure below as example. The X axis represents CO_{2} reduction potential and Y axis shows the relevant costs per
unit of CO_{2} abatement (MariEMS 2017).

Figure 19: Typical MACC for international shipping (MariEMS 2017).

To develop the MAC curve as in figure above but for a single ship, the following steps need to be taken:

- Step 1 – Identify EEMs and their energy saving potentials in terms of for example percent reduction in the ship’s fuel consumption. This is best to be done via an energy audit or review as explained above. From fuel consumption reduction, one can
calculate the CO
_{2}reduction level using relevant emission factor and normalize to an annual value. This will provide a number that later on could be used for X axis. - Step 2 - Calculation of the cost-effectiveness of individual measures: Cost-effectiveness is by definition the ratio of costs to saving levels both measured financially. There are various financial methods to estimate the cost effectiveness including
payback period, IRR and NPV as discussed earlier. However, and for CO
_{2}studies, a far better method is use of Marginal Abatement Costs (MAC). The relevant calculations can be done as outlined below. The MAC calculation per unit of CO_{2}reduction will be used for Y axis. - Step 3 – Ranking and putting in order the EEMs from lowest MAC to highest MAC (i.e. lowest cost EEM to highest cost EEMs).
- Step 4 – Plotting the MACC. Use the ranking system, each EEM represented by a rectangle where its vertical side is the MAC and the horizontal side is the CO
_{2}reduction level. These rectangles will be next to each other.

Simple formula for MAC development: The following formulas can be used to estimate the X and Y axis value for the MACC.

Where:

*ΔCj*is the change of annual cost of for the implementation of EEMj, estimated as per equation (1)*Kj*is the capital cost of the EEMj, discounted by the interest rate and written down over the service years of the technology or the remaining lifetime of the ship, whichever is shortest;*Sj*is the service or operating costs related to the application of EEMj.*ΣOj*is the opportunity cost related to lost service time and/or space due to the installation of the EEMj such as the cost of days off hire for the vessel (MariEMS 2017).