*3.1. The Pay-Off Method Based Analysis*

For the pay-off method case, instead of assuming variations in many input parameters of the investment, we elect to let only the biofuel blend vary. This means that we calculate, ceteris paribus, the net present value of an investment with three different biofuel blend scenarios.

We assign the "30% biofuel blend" as be the base case scenario and consider two extreme scenarios, "standalone conventional fuel production", and "pure biofuel production". This way, we isolate the effect of different policies on the decision with respect to the fuel blend only. The resulting fuzzy NPV distribution demonstrates the effect of different fuel blends on the NPV. In the case of no policy support, Figure 3, only fossil fuel production is profitable. Investment in biofuel facilities deteriorates the profitability compared to only fossil fuel production. Already 30% share of biofuel makes the operations unprofitable, whereas pure biofuel production is in deeply negative territory.

Paying a financial subsidy for every liter of biofuel produced shifts the profitability of the 30% blend scenario and the biofuel only scenario, Figure 4. The 30% blend scenario becomes profitable. Pure biofuel production lags behind and still remains unprofitable, due to the heavier cost structure. Profitability of the fossil fuel production remains unchanged and remains the most profitable option.

The combination of tax-relief for biofuel and penalties for not reaching the blending target creates a very different picture, Figure 5. The tax-relief has a similar effect on the 30% blend scenario and the biofuel only scenario, as financial incentives. The 30% blend scenario is profitable, while the biofuel-only production remains in the negative profitability zone. In contrast to financial benefits, the fossil fuel only scenario becomes deeply unprofitable

due to the penalties. Only penalties create this effect since in the previous policy situations (Figures 3 and 4) the fossil fuel production is profitable. Thus, the combination of penalties and tax-relief generates a two-fold effect, making biofuel blend production attractive to the investors, while discouraging fossil fuel only production. *Sustainability* **2022**, *14*, 147 7 of 15 - Biofuel only - 30% biofuel blend - Fossil fuel only

**Figure 3.** Pay-off net present value (NPV) distribution of fuel production with different fuel blends under no support. **Figure 3.** Pay-off net present value (NPV) distribution of fuel production with different fuel blends under no support. due to the heavier cost structure. Profitability of the fossil fuel production remains unchanged and remains the most profitable option.

**Figure 4.** Pay-off net present value (NPV) distribution of fuel production with different fuel blends under financial incentive. **Figure 4.** Pay-off net present value (NPV) distribution of fuel production with different fuel blends under financial incentive. *Sustainability* **2022**, *14*, 147 8 of 15

Overall, use of the fuzzy pay-off method, when only the change in the critical parameter is analyzed, enables a clear demonstration of the effects of different policies. Overall, use of the fuzzy pay-off method, when only the change in the critical parameter is analyzed, enables a clear demonstration of the effects of different policies.

of the operations compared to all other factors. Therefore, to further analyze the policy effects, we should have a method that is able to capture the interplay of several sources of uncertainty simultaneously, for this we turn to Monte Carlo simulation and the simulation

However, the system studied is surrounded by uncertainties, and the critical one is

Simulation decomposition is based on the Monte Carlo simulation. The same underlying assumptions and NPV cash-flow model that is used for the pay-off method-based analysis is utilized for the simulation. The variation of input variables is allowed for mul-

The fossil fuel production is assumed to be preexistent, and its size is now considered fixed, while the size of the biofuel production is relaxed and ranges from 0 to 1000 million liters per year that corresponds to the variation of the share of the biofuel in the fuel blend from 0 to 46%. For simplicity, the investment cost is assumed to be a linear function of the production quantity. Thus, we are not looking at a separate pure biofuel production any-

The second source of uncertainty is the price of the final product. We assume it to be independent of the fuel-mix sold and to vary in the upper range from the current level from 1.0 to 1.5 EUR/liter. Clearly, the biofuel blends are expected to be sold at a premium compared to fully fossil fuel, however, a natural fuel-price variation exists among countries [54] and fuel-producers might be willing to consider different price-levels independently of their production-blend. Both sources of uncertainty are modeled with a uniform distribution. The uniform distribution, compared to, e.g., a normal distribution, places more weight on the extreme values and thus, creates a more detailed picture of the

For the decomposition, we break down the biofuel production-size into two ranges– below the 30% share blend (0–500 million liters per year) and to equal or above 30% (500– 1000 million liters per year). The price-range is divided into three equally "wide" pieces, see Table 2. The overall number of all possible combinations of these two variables' states

more, but at the fossil fuel production supplemented with biofuel.

decomposition method.

tiple variables simultaneously.

extent of policy effects.

or scenarios is six.

*3.2. Simulation Decomposition Based Analysis* 

However, the system studied is surrounded by uncertainties, and the critical one is the fuel-price uncertainty that, according to [50], has a major influence on the profitability of the operations compared to all other factors. Therefore, to further analyze the policy effects, we should have a method that is able to capture the interplay of several sources of uncertainty simultaneously, for this we turn to Monte Carlo simulation and the simulation decomposition method.
