*3.2. Simulation Decomposition Based Analysis*

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 multiple variables simultaneously.

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

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 extent of policy effects.

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 or scenarios is six.


**Table 2.** Assumptions for Monte Carlo simulation and simulation decomposition.

In the absence of support (Figure 6) fossil fuel production with less than 30% of biofuel (sc1–3) is profitable in the high price region and partially profitable in the medium price region. Producing higher shares of biofuel in the blend becomes unprofitable in the lowprice region (sc4) and only slightly less profitable in the medium and high price regions (sc5,6). This happens, because at these high prices the standalone biofuel production becomes less unprofitable and therefore adding more production facilities does not harm the profitability of the current fossil-fuel production that much.

0%

1%

2%

PROBABILITY

3%

4%

**Figure 6.** Simulation decomposition for fuel production net present value (NPV) with different fuel blends and price uncertainty under no support. **Figure 6.** Simulation decomposition for fuel production net present value (NPV) with different fuel blends and price uncertainty under no support.

**Table 2.** Assumptions for Monte Carlo simulation and simulation decomposition.

the profitability of the current fossil-fuel production that much.

Biodiesel production size, million liters

**Parameter Range States** 

per year 0–1000 <30% [0, 500)

Price of fuel, €/liter 1.00–1.50 low [1.00, 1.17)

In the absence of support (Figure 6) fossil fuel production with less than 30% of biofuel (sc1–3) is profitable in the high price region and partially profitable in the medium price region. Producing higher shares of biofuel in the blend becomes unprofitable in the low-price region (sc4) and only slightly less profitable in the medium and high price regions (sc5,6). This happens, because at these high prices the standalone biofuel production becomes less unprofitable and therefore adding more production facilities does not harm

>=30% [500, 1000]

 medium [1.17, 1.34) high [1.34, 1.50]

Under the financial incentive, we can see a shift of the higher-share biofuel production (sc4–6) into a more profitable range, while the less share biofuel production (sc1–3) remains relatively unchanged (Figure 7), a similar phenomenon to what was seen with the fuzzy pay-off method (Figure 2) is revealed. This happens, because the financial incentive is paid per liter of biofuel produced in the blend and affects more the higher-share operations. Nevertheless, the overall picture has not changed much. The price variation dilutes the effect of the subsidy. Scenarios with high prices (sc3,6) are profitable in both, the no-support situation and with the financial subsidy, which translates into a deterio-Under the financial incentive, we can see a shift of the higher-share biofuel production (sc4–6) into a more profitable range, while the less share biofuel production (sc1–3) remains relatively unchanged (Figure 7), a similar phenomenon to what was seen with the fuzzy pay-off method (Figure 2) is revealed. This happens, because the financial incentive is paid per liter of biofuel produced in the blend and affects more the higher-share operations. Nevertheless, the overall picture has not changed much. The price variation dilutes the effect of the subsidy. Scenarios with high prices (sc3,6) are profitable in both, the no-support situation and with the financial subsidy, which translates into a deteriorated incentive to increase the share of biofuel production, when the future price development is uncertain. *Sustainability* **2022**, *14*, 147 10 of 15 (sc1–3) is an embodiment of the incentive to switch to the production of a high share of biofuel blend.

rated incentive to increase the share of biofuel production, when the future price devel-

Color Scenario Share of Biofuel Price sc1 <30% low sc2 medium sc3 high sc4 low Figure 8 demonstrates how different the profitability of fuel-blend production looks like under the combination of penalties and tax-relief. The lower bounds of low-share biofuel production (sc1–3), which represent the standalone conventional fuel production, are all pushed into the negative profitability zone. of the cases within these scenarios that are closer to the 30% biofuel requirement still stay in the positive profitability zone. The high biofuel share operations are almost entirely found to be in the positive profitability range due to the tax-relief and the absence of penalties. The difference remains sharp even under the vast price uncertainty. This contrast between the green (sc4–6) and the fossil scenarios (sc1–3) is an embodiment of the incentive to switch to the production of a high share of biofuel blend.

**Figure 8.** Simulation decomposition for fuel production net present value (NPV) with different fuel

The above-described differences between the effects the different policies become

blends and price uncertainty under a combination of penalties and tax-relief.

even more evident, if the graphs are presented together, see Table 3.

>=30%

 sc5 medium sc6 high

NPV, M€

0%

1%

2%

PROBABILITY

3%

4%

*Sustainability* **2022**, *14*, 147 11 of 15

*Sustainability* **2022**, *14*, 147 11 of 15

blends and price uncertainty under financial incentive.

**Figure 8.** Simulation decomposition for fuel production net present value (NPV) with different fuel blends and price uncertainty under a combination of penalties and tax-relief. **Figure 8.** Simulation decomposition for fuel production net present value (NPV) with different fuel blends and price uncertainty under a combination of penalties and tax-relief. *Sustainability* **2022**, *14*, 147 11 of 15 *Sustainability* **2022**, *14*, 147 11 of 15

(sc1–3) is an embodiment of the incentive to switch to the production of a high share of

Color

sc1

sc4

**Figure 7.** Simulation decomposition for fuel production net present value (NPV) with different fuel

Scenario

Share of

<30%

>=30%

 sc5 medium sc6 high

 sc2 medium sc3 high

Biofuel

Price

low

low

The above-described differences between the effects the different policies become even more evident, if the graphs are presented together, see Table 3. The above-described differences between the effects the different policies become even more evident, if the graphs are presented together, see Table 3. *Sustainability* **2022**, *14*, 147 11 of 15 *Sustainability* **2022**, *14*, 147 11 of 15 **Table 3.** Summary of the results. **Table 3.** Summary of the results.

**Table 3.** Summary of the results. **Table 3.** Summary of the results. **Table 3.** Summary of the results. **Table 3.** Summary of the results. **Table 3.** Summary of the results.  **Pay-Off Method Simulation Decomposition Pay-Off Method Simulation Decomposition** 

biofuel blend.

NPV, M€

**4. Discussion** 

**4. Discussion** 

**4. Discussion** 

**4. Discussion** 

**4. Discussion** 

**4. Discussion** 



C



Color

Color

F

Color

Scenario

Scenario

Scenario

sc1

sc1

sc1

sc4

sc4

sc4

sc1

sc1

sc1

Color

Color

Color

F

sc4

sc4

sc4

Share of

Share of

Share of

Scenario

Scenario

Scenario

Biofuel

Biofuel

Share of

Share of

Biofuel

Share of

Biofuel

Biofuel

Biofuel

<30%

>=30%

sc5 medium

>=30%

sc5 medium

>=30%

sc5 medium

sc6 high

sc6 high

sc6 high

All obtained graphical results are demonstrated side by side in Table 3. The pay-off method (column 2) shows the distributions with only fuel mix variations between the extremes of standalone fossil fuel and pure biofuel production scenarios. The simulation decomposition technique (column 3) is applied to a case with fixed fossil fuel production size, variable biofuel addition, and price uncertainty. The important difference is that the pay-off distribution is constructed out of discreet scenarios, whereas probability

All obtained graphical results are demonstrated side by side in Table 3. The pay-off method (column 2) shows the distributions with only fuel mix variations between the extremes of standalone fossil fuel and pure biofuel production scenarios. The simulation decomposition technique (column 3) is applied to a case with fixed fossil fuel production size, variable biofuel addition, and price uncertainty. The important difference is that the pay-off distribution is constructed out of discreet scenarios, whereas probability

All obtained graphical results are demonstrated side by side in Table 3. The pay-off method (column 2) shows the distributions with only fuel mix variations between the extremes of standalone fossil fuel and pure biofuel production scenarios. The simulation decomposition technique (column 3) is applied to a case with fixed fossil fuel production size, variable biofuel addition, and price uncertainty. The important difference is that the pay-off distribution is constructed out of discreet scenarios, whereas probability

sc2 medium

<30%

sc2 medium

<30%

sc2 medium

sc3 high

sc3 high

sc3 high

<30%

<30%

sc2 medium

<30%

>=30%

>=30%

sc5 medium

>=30%

sc5 medium

sc6 high

sc5 medium

sc6 high

sc6 high

All obtained graphical results are demonstrated side by side in Table 3. The pay-off method (column 2) shows the distributions with only fuel mix variations between the extremes of standalone fossil fuel and pure biofuel production scenarios. The simulation decomposition technique (column 3) is applied to a case with fixed fossil fuel production size, variable biofuel addition, and price uncertainty. The important difference is that the pay-off distribution is constructed out of discreet scenarios, whereas probability

All obtained graphical results are demonstrated side by side in Table 3. The pay-off method (column 2) shows the distributions with only fuel mix variations between the extremes of standalone fossil fuel and pure biofuel production scenarios. The simulation decomposition technique (column 3) is applied to a case with fixed fossil fuel production size, variable biofuel addition, and price uncertainty. The important difference is that the pay-off distribution is constructed out of discreet scenarios, whereas probability

All obtained graphical results are demonstrated side by side in Table 3. The pay-off method (column 2) shows the distributions with only fuel mix variations between the extremes of standalone fossil fuel and pure biofuel production scenarios. The simulation decomposition technique (column 3) is applied to a case with fixed fossil fuel production size, variable biofuel addition, and price uncertainty. The important difference is that the pay-off distribution is constructed out of discreet scenarios, whereas probability

sc2 medium

sc3 high

sc2 medium

sc3 high

sc3 high

Price

Price

Price

Price

Price

Price

low

low

low

low

low

low

low

low

low

low

low

low

A

A

B

B

C

*Sustainability* **2022**, *14*, 147 11 of 15

*Sustainability* **2022**, *14*, 147 11 of 15

D

D

E

E

F

*Fuel mix variation only Fixed fossil fuel production + variable size of biofuel production* 

*Fuel mix variation only Fixed fossil fuel production + variable size of biofuel production* 

*+ price uncertainty* 

*+ price uncertainty* 

 **Pay-Off Method Simulation Decomposition** 

 **Pay-Off Method Simulation Decomposition** 

**Table 3.** Summary of the results.

**Table 3.** Summary of the results.

#### **Table 3.** *Cont.* -3000 -2000 -1000 0 1000





#### method (column 2) shows the distributions with only fuel mix variations between the ex-**4. Discussion 4. Discussion**

tremes of standalone fossil fuel and pure biofuel production scenarios. The simulation decomposition technique (column 3) is applied to a case with fixed fossil fuel production size, variable biofuel addition, and price uncertainty. The important difference is that the pay-off distribution is constructed out of discreet scenarios, whereas probability All obtained graphical results are demonstrated side by side in Table 3. The pay-off method (column 2) shows the distributions with only fuel mix variations between the extremes of standalone fossil fuel and pure biofuel production scenarios. The simulation decomposition technique (column 3) is applied to a case with fixed fossil fuel production size, variable biofuel addition, and price uncertainty. The important difference is that the pay-off distribution is constructed out of discreet scenarios, whereas probability All obtained graphical results are demonstrated side by side in Table 3. The pay-off method (column 2) shows the distributions with only fuel mix variations between the extremes of standalone fossil fuel and pure biofuel production scenarios. The simulation decomposition technique (column 3) is applied to a case with fixed fossil fuel production size, variable biofuel addition, and price uncertainty. The important difference is that the pay-off distribution is constructed out of discreet scenarios, whereas probability distributions display the continuous change of the size of the biofuel production. For the simplicity of representation, the graphs are stripped from axes and titles, however, the scale is kept consistent within the columns and the zero profitability is marked with the red dashed line and aligned within each column. Different policy types are shown in rows, and the final row presents the legends for the graphs for convenience.

All obtained graphical results are demonstrated side by side in Table 3. The pay-off

The general pattern that can be observed is that no matter which analysis technique we are using, the first two rows in Table 3 look similar. Financial incentive (B) improves the profitability of the biofuel blends production, but does not change the entire picture especially, when considering different price levels (E). It can be concluded that this policy-type introduces more flexibility for investors by enabling other profitable options in addition to the conventional ones. Tax-relief alone would have the same effect as the financial incentive. One can observe that biofuel only and 30% biofuel blend scenarios have the same NPV with the pay-off method under the financial incentive (B) and the combination of penalties and tax-relief (C). The price-variation accounted for in the simulation decomposition method, pushes the profitability of high-share of biofuel scenarios (sc4–6) upwards in the "penalties & tax-relief" policy (F) in comparison to the financial incentive only policy (E). In addition, the penalties change the profitability outlook for fossil fuel as well. Both methods show that fossil fuel production becomes deeply unprofitable when penalized (C, F). Such an effect translates into shrinking flexibility for investors. Under this policy type the only profitable choice is the biofuel blend.

Biofuel production is more costly than conventional fuel production, and therefore, requires subsidies. Production of biofuel alone seems to be too expensive under any policy. However, co-production becomes profitable in the case of the combined penalties and tax-relief policy and the financial incentive. Financial incentives alone do not discourage offering 100% fossil fuel, whereas the combined policy does by means of penalties. A policy that is a mix of penalties and incentives may help the industry navigate efficiently towards a desired outcome. These conclusions are shown to be "obtainable" with the pay-off method and the simulation decomposition method. This is in line with the previous use of the pay-off method in comparing different projects [40,55] or scenarios of the same

project [56]. Here the use of the method was not exactly what has been seen before as the variation was in terms of policies, which makes this research novel in that respect also from the methodological point of view.

To complement the analysis with the pay-off method, we have used the simulation decomposition method. As a standalone technique, simulation decomposition has often been used for policy analysis [25,57]. In this research we have combined market, fuel price, and investment factors. Such a combination has allowed us to observe possible preferences of investors that depend on market development. The results allow us to see the effect of both uncertainty and the joint effect of these factors simultaneously.

While the pay-off method exposes the policy effects on a key decision of how much biofuel to introduce to the blend, simulation decomposition complements the analysis by incorporating market uncertainty into the investment profitability profile.

Previous academic literature has pointed out the possibility of adopting complex and sophisticated methods for the ex-ante study of policy effects and a quasi-unanimous conclusion found in the literature is that ex-ante policy decision-making support is crucial also in the shift towards more renewable fuels. Araujo Enciso et al. [58] arrive at this conclusion by using a sophisticated stochastic recursive-dynamic multi-commodity model. Moncada et al. [59] employ a complex multi-agent model to show that a combination of penalties for fossil fuel with incentives for biofuel provides the best biofuel adoption results. In this paper, we demonstrate that novel, but simple-to-implement and understand methods are able to keep up with more complex techniques in terms of analytical richness both in the inclusion of multiple variables and especially in the provision of visual and in-depth insights for decision-making.

Based on what has been seen here we are ready to recommend the combined use of the fuzzy pay-off method and the simulation decomposition for ex-ante policy analysis and more generally for gaining better understanding of profitability analysis problems with several key factors the interplay of which have an effect on the end result.
