# Economic Superiority of PIP Slip Joint Compared to Conventional Tubular Joints
## 2 Methodology
### Economic Analysis  
The economic viability of PIP slip joints is assessed through \(LCCA\) and \(NPV\) analysis to compare long-term costs and benefits. The \(LCCA\) methodology accounts for all costs incurred throughout the lifespan of the offshore wind foundation, including initial investment, installation, maintenance, and decommissioning [53; 54; 55]. The total lifecycle cost (\(C_{t}\)) is calculated using  
\[C_{t}=C_{init}+C_{install}+\sum_{t=1}^{n}\frac{C_{\text{maint}}}{(1+r)^{t}}+ \frac{C_{\text{decom}}}{(1+r)^{n}} \tag{1}\]  
where \(C_{\text{init}}\) is the initial investment cost, \(C_{\text{install}}\) covers installation expenses, \(C_{\text{maint}}\) represents periodic maintenance costs, and \(C_{\text{decom}}\) includes the final decommissioning costs. The discount rate \(r\) accounts for the time value of money, and \(t\) represents each year of the project's lifespan. The initial cost also includes factors such as the turbine cost, foundation cost, and others. This can be detailed as shown in Equation (2). \[C_{\text{init}}=C_{\text{turb}}+C_{\text{found}}+C_{\text{fab}}+C_{\text{dev}} \tag{2}\]  
where  
\(C_{\text{turb}}\): Turbine cost--procurement and transportation of wind turbine components. \(C_{\text{found}}\): Foundation cost--materials and design associated with the selected joint type. \(C_{\text{fab}}\): Fabrication cost--manufacturing costs of structural elements, including joints. \(C_{\text{dev}}\): Development and other costs--includes permitting, engineering, design studies, insurance, and contingencies. In addition to lifecycle cost estimation, the \(NPV\) method is used to assess the present value of future costs and revenues associated with each joint system. The \(NPV\) is calculated using  
\[NPV=\sum_{t=0}^{n}\frac{R_{t}-C_{t}}{(1+r)^{t}} \tag{3}\]  
where \(R_{t}\) is the revenue or cost savings in year \(t\). A higher \(NPV\) signifies better economic feasibility and cost-effectiveness. Another key financial metric, the \(LCOE\), is used to determine the overall cost of generating electricity when considering the different joint types of offshore wind farms. The \(LCOE\) is defined as  
\[LCOE=\frac{\sum C_{t}(1+r)^{-t}}{\sum E_{t}(1+r)^{-t}} \tag{4}\]  
Here, \(E_{t}\) is the energy generated in year \(t\). A lower LCOE implies that the joint system is more cost-efficient in energy production. The \(IRR\) is the discount rate at which the \(NPV\) of all future cash flows equals zero. It shows the expected annual rate of return on the investment. The formula for the \(IRR\) is the same as the \(NPV\) equation--but instead of solving for NPV, you solve for the discount rate \(r\) that makes \(NPV=0\). Therefore,  
\[0=\sum_{t=0}^{n}\frac{NCF_{t}}{(1+r)^{t}} \tag{5}\]  
where \(NCF_{t}\) is the net cash flow in year \(t\). For this condition, \(r=IRR\). Another important parameter is the Benefit-Cost Ratio, which is extensively studied in this paper. It is a financial metric used in cost-benefit analysis to evaluate the economic feasibility or efficiency of a project or investment. The Benefit-Cost Ratio (\(BCR\)) is the ratio of the PV of benefits to the present value of costs over the lifetime of a project. \[BCR_{joint}=\frac{\sum_{t=1}^{n}\frac{Gross\ income}{(1+r)^{t}}}{\sum_{t=1}^{n} \frac{Expenditure}{(1+r)^{t}}} \tag{6}\]  
In case of \(BCR\),  
\(BCR>1\): Project is economically viable (benefits outweighs the costs). \(BCR=1\): Break-even point (benefits equal costs). \(BCR<1\): Project is not economically viable (costs outweigh the benefits). To understand a quick snapshot of profitability and for easy comparison between different projects and joint types, the rate of investment (\(ROI\)) is widely used, which measures the profitability of an investment. This financial metric shows how much return you earn on an investment relative to its cost. It can be expressed as follows:  
\[ROI=\frac{Net\ Profit}{Total\ Investment}\times 100 \tag{7}\]  
where  
Net Profit = Total Revenue--Total Costs. Total Investment = Initial Capital or Total Cost of the Project.