Biomass Power Generation Investment in China: a Real Options Evaluation

This paper proposes a real options model for evaluating the biomass power generation investment in China. The uncertainties in the market price of electricity, CO 2 price and straw price are considered. Meanwhile the dynamic relationship between installed capacity and fuel cost, as well as the long-term reduction of subsidy are described. Two scenarios, i.e., with the carbon emission trading scheme existent and non-existent, respectively, is built to empirically analyze the investment of a 25-MW straw-based power generation project. The results show that investors should undertake the investment in 2030 under two scenarios. The implementation of the carbon emission trading scheme theoretically helps improve investment value and advance the most likely optimal investment time. However, the current CO 2 price is not sufficient to advance the most likely optimal investment time. The impacts of several factors, including subsidy policy, CO 2 price, straw price, installed capacity, correlation structure and the validity period of investment, on the optimal investment strategy are also examined. It is suggested that governments take some measures, including increasing subsidy, setting the growth pattern of subsidy and establishing and perfecting a nationwide carbon trading market, to improve the investment environment and attract more investments.


Introduction
As energy shortage and greenhouse gas emission problems become increasingly serious, the development of renewable energy becomes an inevitable choice for the future energy mix.As one of the renewable energy resources having the most potential, biomass has drawn wide attention across the world.China has made great efforts to promote the development of biomass energy.In its Middle and Long Term Plan for Renewable Energy Development, the Chinese government has proposed the target of increasing the installed capacity of biomass energy to 30 million kW by 2020 [1].
As a large agricultural country, China is abundant in straw resource, and annual output is about 700 million tons [2].Straw-based power generation is the most effective way to utilize straw.There are many advantages to develop straw-based power generation [3].First, since straw-based power generation does not require the type of straw, straw can be utilized more effectively.Second, straw-based power generation is carbon neutral and does not contribute to the greenhouse effect.Third, much straw is burned as waste in situ, which may result in serious environmental pollution Table 1.Summary of the studies on biomass power generation in China.

Purposes of Study Solution Methods Uncertain Factors
Zhao and Yan [19] Assessing the strengths, weaknesses, opportunities and threats (SWOT) of the biomass power generation industry of China.

SWOT analysis -
Wu et al. [20] Analyzing the economic characteristics regarding the associated costs for investment, electricity generation and waste treatment.
Net present value -Liu et al. [21] Analyzing temporal and spatial patterns of crop stalk resources, the potential bio-energy of straw resources and the possible pathways of straw-based energy strategies.
Cost-profit analysis -Zhao and Feng [22] Exploring the characteristics, opportunities and risks of the investment in biomass direct combustion power generation.
Cost-profit analysis -Zhao and Zuo [23] Assessing the competitiveness of China's biomass power industry.Five forces model -Zhang et al. [3] Estimating the straw-fired power generation costs.
Cost-profit analysis -Sun et al. [24] Identifying the appropriate developing areas of biomass energy at the regional level.

Spatial analysis technology, economic model and scenario analysis -
Wang et al. [18] Evaluating China's biomass power production investment based on a policy benefit model.

Real options method (binomial tree)
Straw price and CO 2 price

System Boundary
In reference to the relevant literature (e.g., [25]), we divide the life cycle of straw-based power generation into four stages, i.e., straw acquisition, transportation, power generation and grid connection.At the stage of straw acquisition, straw is bought from farmers and is pre-processed to facilitate transportation.At the stage of transportation, straw is transported to the storage area in the power plant.At the stage of power generation, straw is transformed to electricity by the power generation system.Finally, at the stage of grid connection, the electricity is input to the power grid.Note that the life cycle of straw-based power generation is accompanied by a value flow process (Figure 1).In this study, a 25-MW straw-based power plant will be empirically evaluated.In recent years, most of the straw-based power generation projects built in China have ranged from 20 MW to 50 MW.Thus, 25 MW is the scale representative for the straw-based power plant.At the same time, several earlier studies, e.g., Zhang et al. [3] and Wang et al. [18], also used 25 MW as the scale representative to carry out analyses.Thus, we choose 25 MW as the analysis object.In addition, it should be pointed out that the fuel consumed by this straw-based power plant is mainly crop straw, including corn stalk, cotton stalk and beanstalk, which are collected from the surrounding area.

Study Purposes of Study Solution Methods Uncertain Factors
Zhao and Yan [19] Assessing the strengths, weaknesses, opportunities and threats (SWOT) of the biomass power generation industry of China.
SWOT analysis -Wu et al. [20] Analyzing the economic characteristics regarding the associated costs for investment, electricity generation and waste treatment.
Net present value -Liu et al. [21] Analyzing temporal and spatial patterns of crop stalk resources, the potential bio-energy of straw resources and the possible pathways of straw-based energy strategies.
Cost-profit analysis -Zhao and Feng [22] Exploring the characteristics, opportunities and risks of the investment in biomass direct combustion power generation.
Cost-profit analysis -Zhao and Zuo [23] Assessing the competitiveness of Chinaʹs biomass power industry.Five forces model -Zhang et al. [3] Estimating the straw-fired power generation costs.
Cost-profit analysis -Sun et al. [24] Identifying the appropriate developing areas of biomass energy at the regional level.

Spatial analysis technology, economic model and scenario analysis -
Wang et al. [18] Evaluating China's biomass power production investment based on a policy benefit model.

Real options method (binomial tree)
Straw price and CO2 price

System Boundary
In reference to the relevant literature (e.g., [25]), we divide the life cycle of straw-based power generation into four stages, i.e., straw acquisition, transportation, power generation and grid connection.At the stage of straw acquisition, straw is bought from farmers and is pre-processed to facilitate transportation.At the stage of transportation, straw is transported to the storage area in the power plant.At the stage of power generation, straw is transformed to electricity by the power generation system.Finally, at the stage of grid connection, the electricity is input to the power grid.Note that the life cycle of straw-based power generation is accompanied by a value flow process (Figure 1).In this study, a 25-MW straw-based power plant will be empirically evaluated.In recent years, most of the straw-based power generation projects built in China have ranged from 20MW to 50MW.Thus, 25 MW is the scale representative for the straw-based power plant.At the same time, several earlier studies, e.g., Zhang et al. [3] and Wang et al. [18], also used 25 MW as the scale representative to carry out analyses.Thus, we choose 25 MW as the analysis object.In addition, it should be pointed out that the fuel consumed by this straw-based power plant is mainly crop straw, including corn stalk, cotton stalk and beanstalk, which are collected from the surrounding area.

Revenue from Electricity Sale
Electricity sale is the main source of revenue for a straw-based power generation project.The electricity generated by the straw-based power generation system is input to the power grid and sold with the feed-in tariff.The total revenue of electricity sale based on the annual running time and power generation efficiency can be calculated as follows [18,26,27]: where q S t denotes annual running time, IC is the installed capacity (MW), Eue t represents power generation efficiency, r HSCR stands for the house-service consumption rate (%) and Fit t is the feed-in tariff (Chinese Yuan RMB/kWh).
The feed-in tariff is designed to ensure that the investors of renewable energy power generation project can obtain enough revenue.In China, the feed-in tariff of straw-based power generation is constituted by the market price of electricity and subsidy [14,28].Thus, we can get: where P d t denotes the market price of electricity (RMB/kWh) and EPS t stands for unit subsidy (RMB/kWh).
Once the project is built in year t, the subsidy is determined and would be kept constant for 15 years [28].For the entire industry, the Chinese government has announced that the subsidy should decrease by 2% per year.Thus, we assume that the subsidy follows an index movement with a constant change rate as follows: where α EPS represents the constant change rate of subsidy.Recently, the Chinese government has attached great importance to the reform of the power sector.Nowadays, China's electricity pricing is transited from a government-led mechanism to a market-based one.As the reform of the power sector deepens, the electricity price would be completely determined by the market.Several previous studies (e.g., [5,29,30]) have used geometric Brownian motion to describe the changes of the market price of electricity.This study also assumes that the market price of electricity follows geometric Brownian motion:

Returns from Selling CO 2 Emission Allowance
Currently, coal accounts for 66% of China's energy mix in 2014.Oil and natural gas respectively occupy 17.5% and 5.6%.Then, renewable energy just accounts for 11.9%.In addition, electricity is an indispensable resource for the development of the social economy.China's electricity consumption accounts for a larger and larger proportion in energy end-use year by year.Due to the limitation of resource endowments, China's electricity power generation is mainly based on thermal power.In 2014, thermal power generation accounted for about 67.3% [31].Since fossil fuel combustion is the main source of carbon dioxide, China's electricity production causes large amounts of carbon emissions.Therefore, due to the unique energy and electricity mix, China faces great pressure to reduce greenhouse gas emissions now.
In order to reduce carbon emission, recently, in the U.S.-China Joint Statement on Climate Change, China proposed the target of seeking a carbon emissions peak and increasing the share of non-fossil energy to 20% of the primary energy consumption by 2030 [32].Furthermore, the Climate Conference in Paris put forward another stricter temperature reduction target of 1.5 ˝C [33].Additionally, the huge pressure of emission reduction accelerates the formation of the carbon emission trading market in China.Seven provinces, e.g., Shenzhen, Guangzhou and Shanghai, have started their pilot carbon emission trading scheme.It is reported that a nationwide carbon trading market would be piloted in 2017, which means the carbon emission trading will get into the golden period of development in China [32].The nationwide carbon emission trading market will bring great opportunities for the development of renewable energy.
Since straw-based power generation is carbon-central [18,19,[34][35][36][37], the investors of the straw-based power generation project can get revenue from selling CO 2 emission allowance.This study assumes the carbon emission trading scheme is effective.The carbon emission reduction resulting from straw-based power generation can be calculated with the emission factors of local electric power production.Thus, the return from selling carbon emission allowance can be represented by: where CEF t denotes the emission factor (kg/kWh) and P C t represents the CO 2 price (RMB/kg).Since CO 2 price is completely determined by the market, stochastic processes can better reflect the motion process of the CO 2 price.Previous studies have assumed the CO 2 price follows geometric Brownian motion [29,30,38].This study supports their assumptions and applies the geometric Brownian motion to describe the change of the CO 2 price as follows: where P C t denotes the CO 2 price, α C stands for the drift rate of the CO 2 price and σ C represents the instantaneous volatility rate of the CO 2 price.In addition, dz C t is the increment to a standard Wiener process, dz C t " ε C t ?dt, and ε C t is a normally-distributed random variable with zero mean and unit standard deviation.It is shown that the expected value of the CO 2 price is ErP C t s " P C 0 ¨eα C ¨t.This study considers the correlation between CO 2 price and the market price of electricity.ρ Cd denotes the correlation coefficient between them with dz C t dz d t " ρ Cd dt, which can reflect to what extent both stochastic variables influence each other beyond their development trends [30,39].

Revenue of Ash Sale
The ash produced by straw-based power generation, which contains potassium, calcium, phosphorus and other nutrients, is the high-quality raw materials of organic fertilizer.Thus, the ash has important commercial value.The revenues of selling ash could be represented by: ASR t " q S t ¨IC ¨Eue t ¨pAC t (7) where p AC t stands for the price of ash (RMB/kWh).

Investment Cost
Investment cost is an important factor that affects the rapid development of straw-based power generation.Nowadays, realizing the maturity of technology is a long and gradual process.In this study, given that investment cost may decrease with technological advance in the long run, we assume investment cost follows a constantly reduction trend.Thus, we can get: where TI t represents the total investment cost (RMB), I t denotes unit investment cost (RMB/kW) and α IDR stands for the reduction rate.

Fuel Cost
Fuel cost refers to the costs in the process that straw is transported from the producing area to the storage area in the power plant.Thus, fuel cost mainly comprises straw-purchased cost, transportation cost and storage cost.Thus, we can get: where where P SP t denotes straw price (RMB/kWh).Straw price is determined by the market.Wang et al. [18] thought that the straw price is full of uncertainty in the future because it may fluctuate with the prospect of the biomass power generation industry.They used geometric Brownian motion to describe straw price.In this study, we also use geometric Brownian motion to describe straw price: dP SP t " α SP P SP t dt `σSP P SP t dz SP t (12) where P SP t denotes the straw price, α SP stands for the drift rate of straw price and σ SP represents the instantaneous volatility rate of straw price.In addition, dz SP t is the increment to a standard Wiener process, dz SP t " ε SP t ?dt, and ε SP t is a normally-distributed random variable with zero mean and unit standard deviation.It is shown that the expected value of straw price is ErP SP t s " P SP 0 ¨eα SP ¨t.In generally, transportation cost contains transportation fuel cost, as well as loading and unloading cost.Transportation cost is directly related to the distance of collection.More straw consumption must lead to a bigger collection radius and a higher transportation cost.In order to reflect the process of determining transportation cost, we propose three assumptions: (1) The distribution of straw has the characteristics of universality and uniformity.Universality means that crop yield is able to meet the demand.Uniformity implies that the yield difference caused by crop varieties and differences in plant conditions do not exist and crops are distributed evenly.(2) There are enough transport vehicles and labor to complete the task of straw collection and transportation.(3) Some risk factors, e.g., weather factors, are not considered.On the basis of the above assumptions, the details of determining transportation cost could be described as follows.
First, it is necessary to determine the unit collection volume of straw (per ha).The unit straw yield in a certain area is represented bySuq 0 .The collection coefficient that reflects the possibility and reliability of collecting straw is k 1 .The planting coefficient isk 2 , and the coefficient that reflects that straw is used as fuel is k 3 .The unit collection volume of straw is calculated by: Second, it is essential to determine the collection radius.Based on the distance, we split the collection area into M areas, and the distance between two adjacent areas is 1 km (Figure 2).It is assumed that R i represents the distance between area i and the power plant (considering that the roads in the countryside are usually winding, we use external diameter R i to represent the distance between straw collection area i and power plant).For example, R 1 means the distance is 1 km, and R 20 means the distance is 20 km.Thus, the acreage of area i is: On this basis, the collection radius is determined as follows: where Rts is the unit straw consumption (t/kWh).Third, the total transportation cost can be obtained: where C LUC represents the unit loading and unloading cost (RMB/t), n stands for the frequency of loading and unloading and UC SPC denotes unit transportation fuel cost (RMB/t).
First, it is necessary to determine the unit collection volume of straw (per ha).The unit straw yield in a certain area is represented by 0 Suq .The collection coefficient that reflects the possibility and reliability of collecting straw is 1 k .The planting coefficient is 2 k , and the coefficient that reflects that straw is used as fuel is 3 k .The unit collection volume of straw is calculated by: Second, it is essential to determine the collection radius.Based on the distance, we split the collection area into M areas, and the distance between two adjacent areas is 1 km (Figure 2).It is assumed that Ri represents the distance between area i and the power plant (considering that the roads in the countryside are usually winding, we use external diameter Ri to represent the distance between straw collection area i and power plant).For example, R1 means the distance is 1 km, and R20 means the distance is 20 km.Thus, the acreage of area i is: On this basis, the collection radius is determined as follows: where Rts is the unit straw consumption (t/kWh).
Third, the total transportation cost can be obtained: ( ) where LUC C represents the unit loading and unloading cost (RMB/t), n stands for the frequency of loading and unloading and SPC UC denotes unit transportation fuel cost (RMB/t).After straw is transported to the power plant, it is stored in stack up yard.This process would create the storage cost, including storage venue rental fees, office equipment, personnel salary and insurance premiums.Mathematically, we can get: After straw is transported to the power plant, it is stored in stack up yard.This process would create the storage cost, including storage venue rental fees, office equipment, personnel salary and insurance premiums.Mathematically, we can get: where UC SSC t is unit storage cost (RMB/kWh).

Operation and Maintenance Cost
Operation and maintenance cost, which is used to ensure the normal operation of the power generation plant, mainly is comprised of repair cost, management fee, finance charge and material cost.Thus, we can get: where SRC t represents unit repair cost (RMB/kWh), SMC t stands for unit management cost (RMB/kWh), SFC t denotes unit finance cost (RMB/kWh) and SMAC t represents unit material cost (RMB/kWh).

Tax Expenditure
The tax expenditure mainly comprises value-added tax and corporate income tax.At present, the straw-based power generation project can enjoy two years of corporate income tax relief and three years half pay.Mathematically, the value-added tax and corporate income tax can be respectively represented by: Vatax t " pESR t `CSR t `ASR t q ¨rVa (21 CITax t " rpESR t `CSR t `ASR t q ¨p1 ´rVa q ´FTC SP t ´SOMC S t s ¨rCI where r Va and r CI respectively denote the rate of value-added tax and corporate income tax (%).

Net Present Value of the Straw-Based Power Generation Project
It is necessary to express the assumptions before describing the project value function.First, we assume the project can be constructed instantaneously.Second, after the completion of the project construction, the operating state of the power generation project is just the full load operation.Third, the investors may undertake the investment decision only once within the validity period.
The returns from selling electricity (ESR t ), gains through selling CO 2 emission allowances (CSR t ), gains through selling ash content (ASR t ), operation and maintenance cost (SOMC S t ), fuel cost (FTC SP t ) and tax expenditure (Tax t ) constitute the yearly cash flow.Thus, the yearly cash flow could be represented by: Consider that a straw-based power generation project with lifetime L SL could be built in year t (1 ď t ď t v ).Due to the impacts of several uncertain factors, the project value of a straw-based power generation project should be expressed with its expectation Er¨s.Thus, the project value of a straw-based power generation project is: where r is the discount rate.

Optimal Investment Rules
In the deterministic setting, i.e., without the consideration of uncertainty and managerial flexibility, investors have limited investment decision options, i.e., undertaking investment or abandoning investment.Nevertheless, in the stochastic setting, uncertainty and managerial flexibility endow investors with more decision options.They can delay investment and wait for the arrival of a better investment environment.That is, investors can choose the optimal time to undertake investment and get the highest value.Mathematically, we can get:

Model Solution
Given the introduction of three stochastic variables and the complexity of the project value function, we use the least squares Monte Carlo (LSM) method to solve the model [40].The method and process resemble some previous studies [41][42][43][44][45][46].The details of the solution process are as follows: Step 1: Take W and N as the number of simulation paths and decision points per path, respectively, where N " t v ∆t , and ∆t is the step size.The stochastic variables are simulated by following the discrete versions of their stochastic motions.For each decision point per path, we should calculate the expected project value.
Step 2: For any path j, the model solution process starts from the last decision point and goes back to the beginning decision point.At the last decision point (t " t v ), conditional on not having invested before, we can get: where Π t,j " 1 means immediate investment and Π t,j " 0 means delaying investment.
In each decision point 1 ď t ă t v , the investors may evaluate whether it is better to invest immediately rather than delay the investment by comparing the expected project value from immediate investment and the expected investment opportunity value by delaying investment.F t,j " max V t,j , e ´r E t rF t`1,j s ( Π t,j " # 1, V t,j ą e ´r E t rF t`1,j s 0, Otherwise It should be pointed out that the expected investment opportunity value, i.e., the continuation value, is estimated by least squares regression.The dependent variable is the investment value from year t + 1 to the end of the validity period under the optimal investment behavior.The independent variables are the uncertain factors in year t.The regression function is e ´r E t rF t`1,j s " a 0 `a1 P C t à2 pP C t q 2 `a3 P d t `a4 pP d t q 2 `a5 P SP t `a6 pP SP t q 2 , which is the same as some previous studies [42,45].
Longstaff and Schwartz [40] have proved that the results are remarkably robust to the choice of basis functions, and the value of regression is unaffected by the correlation among the independent variables.However, we still test various polynomials to ensure the rationality of the results, which shows that the results may not be affected significantly in this study [43].
Step 3.The recursion is rolled back in time and repeated unit the optimal decision in each paths are determined.t j is the optimal investment time in path j.The final most likely optimal investment time is the one with the highest frequency.Additionally, the final investment value is the average value over all of the paths.
In addition, it should be noted that this studies applies the antithetic variable variance reduction technique to improve the accuracy of simulation and reduce the complexity [47].

Data
In this study, a 25-MW straw-based power plant will be evaluated with the model explained in Section 2. Table 2 shows the parameters used in this study.The base year is 2015 and the validity period is 15 years (2016-2030).The step size is one year.The desulfurization electricity price is used to represent the market price of electricity.Now the average desulfurization electricity price is 0.43 RMB/kWh.The data are collected from the Notice of National Development and Reform Commission (NDRC) on Reducing the Price of Coal-fired Electricity and Electricity Prices for Industrial and Commercial Use in 2015 [48].Under the free market mechanism, the market price of electricity varies with the power generation cost.The drift rate and volatility rate are taken from Zhou et al. [40].In addition, we use the CO 2 prices from October 2014-June 2016 in the Shenzhen carbon trading market.The drift rate and volatility rate of the CO 2 price are estimated with the maximum-likelihood method [49].The straw price is taken from the history data in the collection area.Additionally, its drift rate and volatility rate are estimated with the maximum-likelihood method [49].The value-added tax rate and corporate-income tax rate are respectively collected from The Provisional Regulations on Value Added Tax of China [50] and Corporate Income Tax Law of the People's Republic of China [51].

Variables Descriptions Values r Va
The rate of value-added tax 0.17 r CI The rate of corporate income tax 0.25 The validity period of investment 15 year (2016-2030)

Base Case Analysis
This study uses MATLAB software to solve the model [41,42].The investment value and the most likely optimal investment time are employed to reflect the optimal investment strategy.Additionally, we differentiate two cases, i.e., with the carbon emission trading scheme non-existent (Case 1) and existent (Case 2), respectively, to carry out analyses and examine the effects of the carbon emission trading scheme.At first, it is essential to check the stability of the results and then to determine an appropriate number of simulations.The robustness of the result is determined by calculating the investment value for a great number of simulated paths [44].Figure 3a,b illustrate the statistical convergence of the investment value in both cases.It can be observed that the solutions are robust for a number of simulations greater than 7000 and 4000 in both cases.Thus, we perform 10,000 simulations.Table 3 shows the optimal investment strategy.As shown, it is not wise for investors to undertake an investment decision in 2016 under two cases.Investors should delay the investment decision.Figure 4 shows the probability distribution of the most likely optimal investment time.It can be seen that the investors should undertake the investment in 2030, i.e., the last year of the validity period.Comparing two cases, the probability that the investment should be undertaken in 2030 in Case 2 is lower than that in Case 1.In other words, the implementation of the carbon emission trading   Table 3 shows the optimal investment strategy.As shown, it is not wise for investors to undertake an investment decision in 2016 under two cases.Investors should delay the investment decision.Figure 4 shows the probability distribution of the most likely optimal investment time.It can be seen that the investors should undertake the investment in 2030, i.e., the last year of the validity period.Comparing two cases, the probability that the investment should be undertaken in 2030 in Case 2 is lower than that in Case 1.In other words, the implementation of the carbon emission trading scheme theoretically can advance the most likely optimal investment time.In Case 1, investors can obtain investment a value of 14,869,254.8RMB.It is estimated that the payback period is 19 years.When the carbon emission trading scheme is considered, i.e., in Case 2, the investment value reaches 37,608,727.6 RMB.It is estimated that the payback period is 17 years.Therefore, the implementation of the carbon emission trading scheme could improve the investment value.In short, although the current CO 2 price is not able to advance the most likely optimal investment time, the implementation of the carbon emission trading scheme is conductive to promote straw-based power generation investment.

Discussions
The optimal investment strategy could be affected by many factors.It is meaningful to examine the extent of the optimal investment strategy's exposure to some key factors.In this section, we analyze the dynamics of the optimal investment strategy under different subsidy policies, CO2 prices, straw prices, installed capacity, correlation structures and the validity period of investment.

Implications of Subsidy Policy
Under current conditions, it is essential to provide subsidy for investors to attract investment.The subsidy policy can affect the optimal investment strategy by two means, i.e., subsidy level and change pattern.Figure 5a,b display the changes of the optimal investment strategy under different subsidy levels.The positive relationship between subsidy level and investment value can be clearly identified.At the same level of subsidy, the investment value in Case 2 is higher than the one in Case 1, which indicates the extra value brought by the carbon emission trading scheme.As a whole, the most likely optimal investment time is advanced by the increase of the subsidy level.The most likely optimal investment time could be advanced to the year 2016 when the unit subsidy is raised to 0.5 RMB/kWh under two cases.Furthermore, at the same level of subsidy, the most likely optimal investment time in Case 2 is equal to or earlier than the one in Case 1, which indicates the most likely

Discussions
The optimal investment strategy could be affected by many factors.It is meaningful to examine the extent of the optimal investment strategy's exposure to some key factors.In this section, we analyze the dynamics of the optimal investment strategy under different subsidy policies, CO 2 prices, straw prices, installed capacity, correlation structures and the validity period of investment.

Implications of Subsidy Policy
Under current conditions, it is essential to provide subsidy for investors to attract investment.The subsidy policy can affect the optimal investment strategy by two means, i.e., subsidy level and change pattern.Figure 5a,b display the changes of the optimal investment strategy under different subsidy levels.The positive relationship between subsidy level and investment value can be clearly identified.At the same level of subsidy, the investment value in Case 2 is higher than the one in Case 1, which indicates the extra value brought by the carbon emission trading scheme.As a whole, the most likely optimal investment time is advanced by the increase of the subsidy level.The most likely optimal investment time could be advanced to the year 2016 when the unit subsidy is raised to 0.5 RMB/kWh under two cases.Furthermore, at the same level of subsidy, the most likely optimal investment time in Case 2 is equal to or earlier than the one in Case 1, which indicates the most likely optimal investment time is more easily advanced when the carbon emission trading scheme is implemented.The National Development and Reform Commission (NDRC) has proposed that the subsidy should be reduced by 2% per year [52].However, in the Notice of Improving the Price Policy of Biomass Power Generation, the NDRC further increased the feed-in tariff to 0.75 RMB/kWh, i.e., the subsidy is raised to 0.32 RMB/kWh [53].At the same time, many professionals also proposed that the subsidy should be further raised due to the increase of fuel cost.Therefore, the change pattern of subsidy has some effect on the investment of the straw-based power generation project.
In order to reveal the impact of different change patterns of subsidy, we set three values of EPS  = {−0.02, 0, 0.02} to examine the corresponding changes of the optimal investment strategy.EPS  = −0.02 is the base case.EPS  =0 represents a constant-pattern, and EPS  =0.02 indicates a growth pattern.Figure 6a and 6b display the results.It can be seen that the growth pattern of subsidy may lead to a higher investment value and the earliest investment time.These indicate that the government should continue raising the subsidy.In addition, the most likely optimal investment time in the constant pattern and the growth pattern is the same because the impact of the change pattern of the subsidy on the most likely optimal investment time is not even [14,18,39,41].The National Development and Reform Commission (NDRC) has proposed that the subsidy should be reduced by 2% per year [52].However, in the Notice of Improving the Price Policy of Biomass Power Generation, the NDRC further increased the feed-in tariff to 0.75 RMB/kWh, i.e., the subsidy is raised to 0.32 RMB/kWh [53].At the same time, many professionals also proposed that the subsidy should be further raised due to the increase of fuel cost.Therefore, the change pattern of subsidy has some effect on the investment of the straw-based power generation project.
In order to reveal the impact of different change patterns of subsidy, we set three values of α EPS = {´0.02,0, 0.02} to examine the corresponding changes of the optimal investment strategy.α EPS = ´0.02 is the base case.α EPS =0 represents a constant-pattern, and α EPS =0.02 indicates a growth pattern.Figure 6a,b display the results.It can be seen that the growth pattern of subsidy may lead to a higher investment value and the earliest investment time.These indicate that the government should continue raising the subsidy.In addition, the most likely optimal investment time in the constant pattern and the growth pattern is the same because the impact of the change pattern of the subsidy on the most likely optimal investment time is not even [14,18,39,41].

Implications of the Carbon Emission Trading Scheme
The implementation of the carbon emission trading scheme has unavoidable effects on the straw-based power generation investment.In this subsection, we analyze the changes of the optimal investment strategy caused by the CO2 price and its volatility.Figure 7 displays how the changes of the CO2price influence the optimal investment strategy.It can be observed that the increase of the CO2 price corresponds to a growth of investment value.At the same time, the most likely optimal investment time is shifted to an earlier year.If CO2 price is increased to 0.28 RMB/kWh, investors can undertake the investment in 2016.Thus, it can be concluded that the increase of the CO2 price is completely conducive to attract straw-based power generation investment.

Implications of the Carbon Emission Trading Scheme
The implementation of the carbon emission trading scheme has unavoidable effects on the straw-based power generation investment.In this subsection, we analyze the changes of the optimal investment strategy caused by the CO 2 price and its volatility.Figure 7 displays how the changes of the CO 2 price influence the optimal investment strategy.It can be observed that the increase of the CO 2 price corresponds to a growth of investment value.At the same time, the most likely optimal investment time is shifted to an earlier year.If CO 2 price is increased to 0.28 RMB/kWh, investors can undertake the investment in 2016.Thus, it can be concluded that the increase of the CO 2 price is completely conducive to attract straw-based power generation investment.

Implications of the Carbon Emission Trading Scheme
The implementation of the carbon emission trading scheme has unavoidable effects on the straw-based power generation investment.In this subsection, we analyze the changes of the optimal investment strategy caused by the CO2 price and its volatility.Figure 7 displays how the changes of the CO2price influence the optimal investment strategy.It can be observed that the increase of the CO2 price corresponds to a growth of investment value.At the same time, the most likely optimal investment time is shifted to an earlier year.If CO2 price is increased to 0.28 RMB/kWh, investors can undertake the investment in 2016.Thus, it can be concluded that the increase of the CO2 price is completely conducive to attract straw-based power generation investment.Figure 8 shows the dynamics of the optimal investment strategy under different CO 2 price volatilities.As shown, the increase of the CO 2 price volatility raises the investment value.Although the CO 2 price volatility can delay the most likely optimal investment time by following the real options theory, the most likely optimal investment time in this study is kept to the year 2030, i.e., the last year within the validity period of investment, which indicates that we cannot advance the most likely optimal investment time just by reducing the volatility of CO 2 price.The volatility of the CO 2 price is caused by the carbon market fluctuation.Thus, maintaining the stability of the CO is an important measure to improve the investment environment and attract more recent investment.
Figure 8 shows the dynamics of the optimal investment strategy under different CO2 price volatilities.As shown, the increase of the CO2 price volatility raises the investment value.Although the CO2 price volatility can delay the most likely optimal investment time by following the real options theory, the most likely optimal investment time in this study is kept to the year 2030, i.e., the last year within the validity period of investment, which indicates that we cannot advance the most likely optimal investment time just by reducing the volatility of CO2 price.The volatility of the CO2 price is caused by the carbon market fluctuation.Thus, maintaining the stability of the CO2 price is an important measure to improve the investment environment and attract more recent investment.

Influence of Straw Price
Straw price is an important factor influencing straw-based power generation investment.This subsection examines the impact of straw price and its volatility on the optimal investment strategy.Figure 9a and 9b show the impact of the straw price.It can be observed that the increase of the straw price may reduce investment value.Under the same straw price, the investment value in Case 1 is lower than that in Case 2, which indicates the extra revenue brought by the carbon emission trading scheme.Additionally, the most likely optimal investment time is delayed by the increase of the straw price.Under the same straw price, the most likely optimal investment time in Case 2 is equal to or earlier than the one in Case 1, which indicates that the most likely optimal investment time is more difficult to delay when the carbon emission trading scheme is implemented.The implementation of the carbon emission trading scheme mitigates the negative impact of straw price.

Influence of Straw Price
Straw price is an important factor influencing straw-based power generation investment.This subsection examines the impact of straw price and its volatility on the optimal investment strategy.Figure 9a,b show the impact of the straw price.It can be observed that the increase of the straw price may reduce investment value.Under the same straw price, the investment value in Case 1 is lower than that in Case 2, which indicates the extra revenue brought by the carbon emission trading scheme.Additionally, the most likely optimal investment time is delayed by the increase of the straw price.Under the same straw price, the most likely optimal investment time in Case 2 is equal to or earlier than the one in Case 1, which indicates that the most likely optimal investment time is more difficult to delay when the carbon emission trading scheme is implemented.The implementation of the carbon emission trading scheme mitigates the negative impact of straw price.
Figure 8 shows the dynamics of the optimal investment strategy under different CO2 price volatilities.As shown, the increase of the CO2 price volatility raises the investment value.Although the CO2 price volatility can delay the most likely optimal investment time by following the real options theory, the most likely optimal investment time in this study is kept to the year 2030, i.e., the last year within the validity period of investment, which indicates that we cannot advance the most likely optimal investment time just by reducing the volatility of CO2 price.The volatility of the CO2 price is caused by the carbon market fluctuation.Thus, maintaining the stability of the CO2 price is an important measure to improve the investment environment and attract more recent investment.

Influence of Straw Price
Straw price is an important factor influencing straw-based power generation investment.This subsection examines the impact of straw price and its volatility on the optimal investment strategy.Figure 9a and 9b show the impact of the straw price.It can be observed that the increase of the straw price may reduce investment value.Under the same straw price, the investment value in Case 1 is lower than that in Case 2, which indicates the extra revenue brought by the carbon emission trading scheme.Additionally, the most likely optimal investment time is delayed by the increase of the straw price.Under the same straw price, the most likely optimal investment time in Case 2 is equal to or earlier than the one in Case 1, which indicates that the most likely optimal investment time is more difficult to delay when the carbon emission trading scheme is implemented.The implementation of the carbon emission trading scheme mitigates the negative impact of straw price.Figure 10a and 10b display how straw price volatility affects the optimal investment strategy.Overall, the straw price volatility can lead to the reduction of the investment value.Under the same straw price volatility, the investment value in Case 2 is higher than that in Case 1.The most likely optimal investment time is kept in the year 2030 under two cases no matter how the straw price volatility changes.These indicate the small impact of straw price volatility on the most likely optimal investment time.

Influence of Installed Capacity
Figure 11a,b show the changes of the optimal investment strategy under different installed capacity.Larger installed capacity is accompanied by more straw consumption, which may result in higher fuel cost.Thus, the changes of installed capacity may affect the optimal investment strategy.Recently, most of the straw-based power generation projects built in China range from 20MW- Figure 10a,b display how straw price volatility affects the optimal investment strategy.Overall, the straw price volatility can lead to the reduction of the investment value.Under the same straw price volatility, the investment value in Case 2 is higher than that in Case 1.The most likely optimal investment time is kept in the year 2030 under two cases no matter how the straw price volatility changes.These indicate the small impact of straw price volatility on the most likely optimal investment time.Figure 10a and 10b display how straw price volatility affects the optimal investment strategy.Overall, the straw price volatility can lead to the reduction of the investment value.Under the same straw price volatility, the investment value in Case 2 is higher than that in Case 1.The most likely optimal investment time is kept in the year 2030 under two cases no matter how the straw price volatility changes.These indicate the small impact of straw price volatility on the most likely optimal investment time.

Influence of Installed Capacity
Figure 11a,b show the changes of the optimal investment strategy under different installed capacity.Larger installed capacity is accompanied by more straw consumption, which may result in higher fuel cost.Thus, the changes of installed capacity may affect the optimal investment strategy.Recently, most of the straw-based power generation projects built in China range from 20MW-

Influence of Installed Capacity
Figure 11a,b show the changes of the optimal investment strategy under different installed capacity.Larger installed capacity is accompanied by more straw consumption, which may result in higher fuel cost.Thus, the changes of installed capacity may affect the optimal investment strategy.Recently, most of the straw-based power generation projects built in China range from 20MW-50MW.As shown, the investment value shows a growth trend with the increase of installed capacity.Under the same installed capacity, the investment value in Case 2 is higher than that in Case 1, which indicates the extra revenue brought by the carbon emission trading scheme.Additionally, the most likely optimal investment time in Case 1 remains at the year 2030.In Case 2, the most likely optimal investment time is shifted to the year 2029 when installed capacity is raised to at least 35 MW.

Impact of Correlation Structure
There may some interactive relationships among stochastic variables in the long run.This study considers the correlation between CO2 price and the market price of electricity.This subsection examines the changes of the optimal investment strategy under different correlation coefficients between the CO2 price and the market price of electricity.Figure 12 shows the results.This subsection only considers Case 2, because the carbon emission trading scheme is non-existent in Case 1.As shown, the investment value shows a growth trend.However, the most likely optimal investment time remains at the year 2030, i.e., the last year of the validity period of investment.

Impact of Correlation Structure
There may some interactive relationships among stochastic variables in the long run.This study considers the correlation between CO 2 price and the market price of electricity.This subsection examines the changes of the optimal investment strategy under different correlation coefficients between the CO 2 price and the market price of electricity.Figure 12 shows the results.This subsection only considers Case 2, because the carbon emission trading scheme is non-existent in Case 1.As shown, the investment value shows a growth trend.However, the most likely optimal investment time remains at the year 2030, i.e., the last year of the validity period of investment.

Impact of the Validity Period of Investment
As shown in the base case analysis, the most likely optimal investment time remains at the last year of the validity period, which indicates the choice of the validity period of investment may influence the optimal investment strategy.Figure 13a,b presents the optimal investment strategy under different validity periods of investment.It can be found that the extension of the validity period of investment may increase the investment value.However, the most likely optimal investment time is kept at the last year of the validity period, which further indicates the drawbacks of the current investment environment.In other words, the current investment environment may delay the strawbased power generation investment.Thus, the government should take great efforts to improve the investment environment.

Impact of the Validity Period of Investment
As shown in the base case analysis, the most likely optimal investment time remains at the last year of the validity period, which indicates the choice of the validity period of investment may influence the optimal investment strategy.Figure 13a,b presents the optimal investment strategy under different validity periods of investment.It can be found that the extension of the validity period of investment may increase the investment value.However, the most likely optimal investment time is kept at the last year of the validity period, which further indicates the drawbacks of the current investment environment.In other words, the current investment environment may delay the straw-based power generation investment.Thus, the government should take great efforts to improve the investment environment.

Impact of the Validity Period of Investment
As shown in the base case analysis, the most likely optimal investment time remains at the last year of the validity period, which indicates the choice of the validity period of investment may influence the optimal investment strategy.Figure 13a,b presents the optimal investment strategy under different validity periods of investment.It can be found that the extension of the validity period of investment may increase the investment value.However, the most likely optimal investment time is kept at the last year of the validity period, which further indicates the drawbacks of the current investment environment.In other words, the current investment environment may delay the strawbased power generation investment.Thus, the government should take great efforts to improve the investment environment.

Conclusions
As the energy shortage and greenhouse gas emissions problems become increasingly serious, biomass as an important renewable energy resource has drawn wide attention across the world.China is abundant with straw resource.Straw-based power generation is the most effective way to utilize straw.Given the uncertainty and complexity in the investment environment, it is hard to determine whether and when to invest (concerns of investors), as well as how to determine a reasonable and effective incentive policies system (concern of governments).This paper proposes a real options model for evaluating the straw-based power generation project investment in China.The uncertainties in the market price of electricity, CO 2 price and straw price are considered.Meanwhile the dynamic relationship between installed capacity and fuel cost, as well as the gradual reduction of subsidy are described.Two scenarios, i.e., the carbon emission trading scheme is non-existent (Case 1) and existent (Case 2), is built to empirically evaluate the investment of a 25-MW straw-based power generation project.The results present not only the optimal investment strategy, i.e., the investment value and the most likely optimal investment time, but also the impact of multiple key factors on the optimal investment strategy.
Several conclusions are derived from this study.First, the results suggest that investors should not undertake an investment decision in 2016 in both cases.Investors should undertake investment in 2030 based on which investors can obtain investment values of 14,869,254.8RMB and 37,608,727.6 RMB, respectively.Second, the implementation of the carbon emission trading scheme theoretically could improve the investment value and the most likely optimal investment time.However, the current CO 2 price is not sufficient to advance the most likely optimal investment time.Third, the subsidy level and CO 2 price have a positive relationship with the investment value and may advance the most likely optimal investment time.The volatility of the CO 2 price could increase the investment value and does not change the most likely optimal investment time.The volatility of the straw price could reduce the investment value and does not change the most likely optimal investment time.Fourth, the growth pattern of subsidy helps attract investment, because it could increase the investment value and advance the most likely optimal investment time.Although the growth of installed capacity and the correlation coefficient can increase the investment value, it has less impact on the most likely optimal investment time.Due to the drawbacks of the current investment environment, the most likely optimal investment time remains at the last year of the validity period no matter how the validity period of investment is extended.Sixth, under the carbon emission trading scheme, the most likely optimal investment time is more easily advanced and difficult to delay by the relevant factors.Additionally, the project value is more difficult to change by the relevant factors.
Given the above, the investment environment that has the features of higher subsidy, higher CO 2 price, a growth pattern of subsidy and lower volatility of CO 2 price is conducive to attracting more investments of straw-based power generation projects.Thus, the government should take some measures, such as increasing the subsidy, setting the growth pattern of subsidy, establishing and perfecting a nationwide carbon trading market, as soon as possible.It should be stressed that the effectiveness of the incentive policies would be improved if the volatility of the CO 2 price were reduced to the lowest extent.In addition, strengthening technological progress and improving generating efficiency are also important.
In contrast to the existing literature, this paper successfully addresses the following points: (1) considering more uncertain factors and the long-term reduction of subsidy; (2) explaining the dynamic relationship between installed capacity and fuel cost; (3) applying a simulation method to solve the model; and (4) providing not only the optimal investment strategy, but also the impacts of several key factors on the optimal investment strategy.However, considering the complexity in evaluating the straw-based power generation investment, there are some limitations in this paper.First, the stability of straw supply is not considered.Second, the improvement of power generation efficiency resulting from technological progress is not considered.Future studies that can handle these issues would be of greater practical value.

Figure 1 .
Figure 1.Life cycle and value flow process.

Figure 1 .
Figure 1.Life cycle and value flow process.

Figure 3 .
Figure 3. Investment value in Chinese Yuan (RMB) according to the simulation paths in Case 1 (a) and in Case 2 (b).

Figure 3 .
Figure 3. Investment value in Chinese Yuan (RMB) according to the simulation paths in Case 1 (a) and in Case 2 (b).

Figure 4 .
Figure 4.The probability distribution of investment time.

Figure 4 .
Figure 4.The probability distribution of investment time.

Figure 5 .
Figure 5.The impact of subsidy levels on investment value (a) and investment time (b).

Figure 5 .
Figure 5.The impact of subsidy levels on investment value (a) and investment time (b).

Figure 6 .
Figure 6.The impact of the subsidy's change pattern on investment value (a) and investment time (b).

Figure 7 .
Figure 7.The impact of CO2 price.

Figure 6 .
Figure 6.The impact of the subsidy's change pattern on investment value (a) and investment time (b).

Figure 6 .
Figure 6.The impact of the subsidy's change pattern on investment value (a) and investment time (b).

Figure 7 .
Figure 7.The impact of CO2 price.

Figure 7 .
Figure 7.The impact of CO 2 price.

Figure 8 .
Figure 8.The impact of the CO2 price volatility.

Figure 8 .
Figure 8.The impact of the CO 2 price volatility.

Figure 8 .
Figure 8.The impact of the CO2 price volatility.

Figure 10 .
Figure 10.The impact of straw price volatility on investment value (a) and investment time (b).

Figure 9 .
Figure 9.The impact of the straw price on investment value (a) and investment time (b).

Figure 9 .
Figure 9.The impact of the straw price on investment value (a) and investment time (b).

Figure 10 .
Figure 10.The impact of straw price volatility on investment value (a) and investment time (b).

Figure 10 .
Figure 10.The impact of straw price volatility on investment value (a) and investment time (b).

Figure 11 .
Figure 11.The impact of installed capacity on investment value (a) and investment time (b).

Figure 11 .
Figure 11.The impact of installed capacity on investment value (a) and investment time (b).

Figure 12 .
Figure 12.The impact of the correlation structure.

Figure 13 .
Figure 13.The impact of the validity period on investment value (a) and investment time (b).

Figure 12 .
Figure 12.The impact of the correlation structure.

Figure 13 .
Figure 13.The impact of the validity period on investment value (a) and investment time (b).

Figure 13 .
Figure 13.The impact of the validity period on investment value (a) and investment time (b).

Table 1 .
Summary of the studies on biomass power generation in China.