# Optimal Investment Timing and Scale Choice of Overseas Oil Projects: A Real Option Approach
## 4 Model Application: Case Project Results and Discussion
### Empirical Analysis of the Impact of Investment Scale on Investment Timing  
It is clear that changes in the market environment influences the optimal investment decisions of oil projects. The critical oil price, which is affected by many factors, indicates the investment threshold. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Model Symbol** & **Value** & **Unit** \\ \hline Investment phase termination & \(T_{0}\) & 1 & year \\ Build-up phase termination & \(T_{1}\) & 2 & year \\ Plateau production termination & \(T_{2}\) & 6 & year \\ Length of contract period & \(T_{3}\) & 20 & year \\ Volume of oilfield & _OIP_ & 300 & million barrels \\ Regional calibration factor & \(A\) & 610 & \\ Recovery factor cost elasticity & \(\zeta\) & 3 & \\ Extraction rate cost elasticity & \(\lambda\) & 1.68 & \\ Oil production decline rate & \(\omega\) & 10 & \%/year \\ Extraction rate & \(a\) & 7 & \%/year \\ After-tax return rate & \(\eta\) & 55 & \% \\ Unit revenue drift rate & \(u\) & 2.130 & \%/year \\ Unit revenue volatility rate & \(\sigma\) & 28.268 & \%/year \\ Discount rate & \(r\) & 10 & \%/year \\ Unit production cost & \(c_{1}\) & 12.67 & US$/bbl \\ Unit environment cost & \(c_{2}\) & 1.5 & US \$/bbl \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters in the case project. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable** & **Value** & **Unit** \\ \hline Profit discount coefficient \(\xi\) & 0.143 & \(\times 10^{9}\) \\ Operation cost discount coefficient \(\kappa\) & 0.124 & \(\times 10^{9}\) \\ \(\beta_{1}\) & 1.833 & \\ Critical unit revenue \(\theta^{*}\) & 45.27 & US$/bbl \\ Critical recovery factor \(s^{*}\) & 27.47 & \% \\ Critical oil price \(P^{*}\) & 82.32 & US$/bbl \\ Investment cost (\(P=82.32\) US$/bbl) & 0.323 & \(\times 10^{9}\) US$ \\ Oil project value (\(P=82.32\) US$/bbl) & 0.969 & \(\times 10^{9}\) US$ \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results for the case project. When the drift or volatility of unit revenue is changed, comparing the difference between the critical oil price with and without the possibility of choosing the investment scale freely focuses on demonstrating the impact of investment scale on investment timing. Section 3.4 demonstrates the limitation of fixed investment scale of oil projects by theoretical analysis. In this part, the effect of variable investment scale is explained by empirical analysis. The drift of unit revenue, which reflects the market environment, affects the expected return and option value of oil projects. The unit revenue is one of the most important profitability factors for oil projects. As the drift rises, the critical oil price and the expected return of the oil project rise. Therefore, it is better to postpone the investment in order to wait for the proper investment threshold. Because the decision of postponing investment is relatively cheaper, investment in the future is more attractive. This also implies that the levels of oil price in the future will be not very low and that investors should choose a relatively larger investment scale. Furthermore, increasing drift leads to a higher value of the option to delay. The variation in the critical oil price with a fixed investment scale is relatively small when the drift of unit revenue is changing. Due to the value of management flexibility, the sensitivity of investment threshold when investment scale can be selected optimally is comparatively high. The volatility implies the uncertainty of a project's profit. When volatility of unit revenue changes, the investment threshold will be much more flexible with variable investment scale than with fixed investment scale. Increasing volatility of unit revenue leads to a higher critical oil price for investors because the market is more volatile and chances of loss are greater. The fixed investment scale makes investors unable to adjust investment decisions effectively and limits the flexibility of investment timing, as already shown in Section 3.4.