## 2 Materials and Methods
### Financial Analysis  
Financial analysis has been undertaken individually for all BGPs by applying the discounted cash flow method. The financial analyses focus on the financial viability of the biogas produced for CN BGPs and the electricity and heat for the DE BGPs. The assumptions that were used for the financial analysis include:  
* Project costs are expressed in Euro (\(\xi\)), and the average exchange rate in 2017 (\(\xi\) 1.00 = CNY 7.6293) was used for CN BGPs wherever needed.  
All BGPs were expected to be fully implemented (civil works and equipment supply and installation) in one year following the completion of construction, and the residual value of the investment is zero.
* DE BGPs are assumed to operate for 20 years due to the existing EEG contracts while CN BGPs were operated for 10 years based on the actual operation situation.
* Based on the consultation with operators of DE BGPs, replacement of the CHP unit is required after seven years of operation.
* Operation and maintenance costs have been estimated to cover the costs of fuel and power for the BGPs, salaries and welfare, routine maintenance (including CHP units), and other operating expenses.
* For DE BGPs, the income tax rate is calculated individually for each BGP according to the German Income Tax Act, assuming that the income from the BGP is the total taxable joint income per calendar year 2017 of the operators, and BGPs are sole proprietorships [34].
* The weighted average cost of capital (WACC) used for the financial analysis is estimated based on the actual interest rate that operators paid for loans from commercial bank(s) and the investments that are financed by the operators in DE BGPs, or in CN BGPs, by the village committees and government.
* Revenues are based on prevailing prices in 2017 and are expressed in constant 2017 terms.  
In the present work, the future scenario using an average market price cap for biomass (2018 auction price, 14.37 \(\text{ct}/\text{kWh}\)) [6] is used to explore the financial viability when German renewable energy will face the end of guaranteed pricing. This scenario also applies to newly built BGPs in the future, which are operated similarly as these selected BGPs.  
The financial net present value (NPV) is defined as the sum of the present values of the individual (yearly) cash flows. A project is financially feasible when the NPV is positive, and the financial internal rate of return (IRR) must be greater than WACC, which is used as the discount rate to estimate the NPV of the BGP cash flows [35; 36]. The higher the NPV, the more profitable the BGP [37]. The IRR of a net cash flow is calculated after tax. Equations for calculating the NPV, IRR, and WACC are expressed as [38]:  
\[PV=\sum_{t=0}^{n}a_{t}S_{t} \tag{5}\]  
\[0=\sum\frac{S_{t}}{(1+IRR)^{t}} \tag{6}\]  
\[WACC=\left[r_{debt}*(1-tax\ rate)*\frac{Debt}{Debt+Equity}\right]+\left[r_{ equity}*\frac{Equity}{Debt+Equity}\right] \tag{7}\]  
where \(a_{t}\) is the financial discount factor chosen for discounting at time t, \(S_{t}\) is the balance of cash flow at time t (\(\xi\)), \(r_{debt}\) is the cost of debt (\(\%\)) (actual cost collected from the operators), and \(r_{equity}\) is the cost of equity (8.1\(\%\) was used in the calculation for DE BGPs) [39].