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Determine the optimal capital structure of BOT projects using interval numbers with Tianjin Binhai New District Metro Z4 line in China as an example

Yuning Wang (School of Geographic and Environmental Sciences, Tianjin Normal University, Tianjin, China)
Xiaohua Jin (School of Computing, Engineering and Mathematics, Western Sydney University, Penrith, Australia)

Engineering, Construction and Architectural Management

ISSN: 0969-9988

Article publication date: 21 June 2019

Issue publication date: 2 August 2019



Various factors may influence project finance when a multi-sourced debt financing strategy is used for financing capital investments, in general, and public infrastructure investments, in particular. Traditional indicators lack comprehensive consideration of the influences of many internal and external factors, such as investment structure, financing mode and credit guarantee structure, which exist in the financing decision making of BOT projects. An effective approach is, thus, desired. The paper aims to discuss these issues.


This paper develops a financial model that uses an interval number to represent the uncertain factors and, subsequently, conducts a standardization of the interval number. Decision makers determine the weight of each objective through the analytic hierarchy process. Through the optimization procedure, project investors and sponsors are provided with a strategy regarding the optimal amount of debt to be raised and the insight on the risk level based on the net present value, as well as the probability of bankruptcy for each different period of debt service.


By using an example infrastructure project in China and based on the comprehensive evaluation, comparison and ranking of the capital structures of urban public infrastructure projects using the interval number method, the final ranking can help investors to choose the optimal capital structure for investment. The calculation using the interval number method shows that X2 is the optimal capital structure plan for the BOT project of the first stage of Tianjin Binhai Rail Transit Z4 line. Therefore, investors should give priority to selecting a capital contribution ratio of 45 per cent for this investment.

Research limitations/implications

In this paper, some parameters, such as depreciation life, construction period and concession period, are assumed to be deterministic parameters, although the interval number model has been introduced to analyze the uncertainty indicators, such as total investment and passenger flow, of BOT rail transport projects. Therefore, more of the above deterministic parameters can be taken as uncertainty parameters in future research so that calculation results fit actual projects more closely.


This model can be used to make the optimal investment decision for a project by determining the impact of uncertainty factors on the profitability of the project in its lifecycle during the project financial feasibility analysis. Project sponsors can determine the optimal capital structure of a project through an analysis of the irregular fluctuation of the unpredictable factors in project construction such as construction investment, operating cost and passenger flow. The model can also be used to examine the effects of different capital investment ratios on indicators so that appropriate measures can be taken to reduce risks and maximize profit.



The authors wish to thank the National Natural Science Foundation of China (Grant No. 51608363), Tianjin normal university’s high research and high visit to young teachers and the Natural Science Foundation of Tianjin Education Commission (043-135202-JW1717).


Wang, Y. and Jin, X. (2019), "Determine the optimal capital structure of BOT projects using interval numbers with Tianjin Binhai New District Metro Z4 line in China as an example", Engineering, Construction and Architectural Management, Vol. 26 No. 7, pp. 1348-1366.



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