September  2020, 16(5): 2065-2086. doi: 10.3934/jimo.2019043

Optimal expansion timing decisions in multi-stage PPP projects involving dedicated asset and government subsidies

1. 

Department of Mathematics, Tianjin University of Commerce, Tianjin 300134, China

2. 

Coordinated Innovation Center for Computable Modeling in Management Science, Tianjin University of Finance and Economics, Tianjin 300222, China

* Corresponding author: Jinghuan Li

Received  September 2018 Revised  January 2019 Published  September 2020 Early access  May 2019

Fund Project: This project was supported in part by the the Major Research Plan of the National Natural Science Foundation of China (91430108), the National Natural Science Foundation of China (11771322, 71471132, 71573189), and Tianjin Education Commission Scientific Research Plan(2017SK076, 2017KJ236)

The topic of investment timing in multi-stage public-private partnership (PPP) projects has not been received much attention so far. This study investigates optimal expansion timing decisions in multi-stage PPP projects under an uncertain demand and where the first-stage greenfield project involving a dedicated asset is immediately implemented as the PPP contract is closed, whereas the timing of the later expansion is flexibly decided according to the demand. In this setting, the optimal multiple stopping timing theory is adopted to model the expansion framework. Furthermore, we integrate a government subsidy, including an investment subsidy and revenue subsidy, into the expansion timing decisions. Through a hypothetical three-stage investment plan for a sanitary sewerage project, the optimal expansion strategies and the value of the multi-stage project before and after the subsidy are provided using a least squares Monte Carlo simulation. Also, the influences of a dedicated asset on the expansion strategies and project value are illustrated. In addition, we compare the incremental value before and after the subsidy and earlier expansion derived from two types of subsidies. The comparisons show that there is more incremental value for the revenue subsidy, and that the investment subsidy brings an earlier expansion.

Citation: Jinghuan Li, Yu Li, Shuhua Zhang. Optimal expansion timing decisions in multi-stage PPP projects involving dedicated asset and government subsidies. Journal of Industrial and Management Optimization, 2020, 16 (5) : 2065-2086. doi: 10.3934/jimo.2019043
References:
[1]

M. J. R. ArmadaP. J. Pereira and A. Rodrigues, Optimal subsidies and guarantees in public-private partnerships, Eur. J. Financ., 18 (2012), 469-495. 

[2]

L. E. T. Brandao and E. Saraiva, The option value of government guarantees in infrastructure projects, Constr. Manag. Econ., 26 (2008), 1171-1180. 

[3]

G. CortazarM. Gravet and J. Urzua, The valuation of multidimensional American real options using the LSM simulation method, Comput. Oper. Res., 35 (2008), 113-129.  doi: 10.1016/j.cor.2006.02.016.

[4]

E. Dahlgren and T. Leung, An optimal multiple stopping approach to infrastructure investment decisions, J. Econ. Dynam. Contr., 53 (2015), 251-267.  doi: 10.1016/j.jedc.2015.02.001.

[5]

T. Dangl, Investment and capacity choice under uncertain demand, Eur. J. Oper. Res., 117 (1999), 415-428.  doi: 10.1016/S0377-2217(98)00274-4.

[6]

P. Doan and K. Menyah, Impact of irreversibility and uncertainty on the timing of infrastructure projects, J. Constr. Eng. Manage., 139 (2013), 331-338.  doi: 10.1061/(ASCE)CO.1943-7862.0000615.

[7]

U. Dörr, Valuation of Swing Options and Examination of Exercise Strategies by Monte Carlo Techniques, Master thesis, University of Oxford, 2003.

[8]

E. EngelR. Fischer and A. Galetovic, The basic public finance of public-private partnerships, J. Euro. Econ. Assoc., 11 (2013), 83-111.  doi: 10.3386/w13284.

[9]

B. C. Esty, Modern Project Finance: A Casebook, Princeton, Wiley, 2003.

[10]

B. FlyvbjergM. Holm and S. Buhl, How common and how large are cost overruns in transport infrastructure projects?, Transp. Rev., 23 (2003), 71-88.  doi: 10.1080/01441640309904.

[11]

C. C. Gkochari, Optimal investment timing in the dry bulk shipping sector, Transp. Res. Part E, 79 (2015), 102-109.  doi: 10.1016/j.tre.2015.02.018.

[12]

H. B. Herath and C. Park, Mult-stage capital unvestment opportunities as compound real options, Eng. Econ., 47 (2002), 1-27. 

[13]

Y. Huang, Project and Policy Analysis of Build-Operate-Transfer Infrastructure Developments, Ph.D thesis, University of California at Berkeley, 1995.

[14]

Y. L. Huang and S. P. Chou, Valuation of the minimum revenue guarantee and the option to abandon in BOT infrastructure projects, Constr. Manag. Econ., 24 (2006), 379-389.  doi: 10.1080/01446190500434997.

[15]

Y. Huang and C. Pi, Valuation of multi-stage BOT projects involving dedicated asset investments: a sequential compound option approach, Constr. Manag. Econ., 27 (2009), 653-666.  doi: 10.1080/01446190903002789.

[16]

B. Klein and K. B. Leffler, The role of market forces in assuring contractual performance, J. Polit. Econ., 89 (1981), 615-641.  doi: 10.1086/260996.

[17]

Y. KwakY. Chih and C. I. William, Towards a comprehensive understanding of public-private partnerships for infrastructure development, California Manag. Rev., 51 (2009), 51-78.  doi: 10.2307/41166480.

[18]

S. Li and H. B. Cai, Government incentive impacts on private investment behaviors under demand uncertainty, Transp. Res. Part E, 101 (2017), 115-129.  doi: 10.1016/j.tre.2017.03.007.

[19]

W. Li and S. Wang, Pricing American options under proportional transaction costs using a penalty approach and a finite difference scheme, J. Ind. Manag. Optim., 9 (2013), 365-389.  doi: 10.3934/jimo.2013.9.365.

[20]

F. A. Longstaff and E. S. Schwartz, Valuing American options by simulation: A simple least squares approach, Rev. Financ. Stud., 14 (2001), 113-147.  doi: 10.1093/rfs/14.1.113.

[21]

L. J. Maseda, Real Options Analysis of Flexibility in a Hospital Emergency Department Expansion Project: A Systems Approach, Master thesis, MIT, 2008.

[22]

N. Meinshausen and B. M. Hambly, Monte Carlo methods for the valuation of multiple exercise options, Math. Financ., 14 (2004), 557-583.  doi: 10.1111/j.0960-1627.2004.00205.x.

[23]

S. NadarajahF. Margot and N. Secomandi, Comparison of least squares Monte Carlo methods with applications to energy real options, Eur. J. Oper. Res., 256 (2017), 196-204.  doi: 10.1016/j.ejor.2016.06.020.

[24]

R. Neufville, Y. S. Lee and S. Scholtes, Flexibility in hospital infrastructure design, Working Paper, MIT, 2008.

[25]

E. Pennings, Optimal pricing and quality choice when investment in quality is irreverible, J. Ind. Econ., 52 (2004), 569-589. 

[26]

M. Skamris and B. Flyvbjerg, Inaccuracy of traffic forecasts and cost estimates on large transport projects, Transp. Policy, 4 (1997), 141-146.  doi: 10.1016/S0967-070X(97)00007-3.

[27]

S. Szymanski, The optimal timing of infrastructure investment, J. Transp. Econ. Policy, 25 (1991), 247-258. 

[28]

Z. Tan and H. Yang, Flexible build-operate-transfer contracts for road franchising under demand uncertainty, Transp. Res. Part B, 46 (2012), 1419-1439.  doi: 10.1016/j.trb.2012.07.001.

[29] O. E. Williamson, The Economic Institutions of Capitalism, The Free Press, New York, 1985. 
[30]

Y. Xenidis and D. Angelides, The financial risks in build-operate-transfer projects, Constr. Manag. Econ., 23 (2005), 431-441.  doi: 10.1080/01446190500041552.

[31]

X. Zhang, Financial viability analysis and capital structure optimization in privatised public infrastructure projects, J. Constr. Eng. Manag., 131 (2005), 656-668. 

show all references

References:
[1]

M. J. R. ArmadaP. J. Pereira and A. Rodrigues, Optimal subsidies and guarantees in public-private partnerships, Eur. J. Financ., 18 (2012), 469-495. 

[2]

L. E. T. Brandao and E. Saraiva, The option value of government guarantees in infrastructure projects, Constr. Manag. Econ., 26 (2008), 1171-1180. 

[3]

G. CortazarM. Gravet and J. Urzua, The valuation of multidimensional American real options using the LSM simulation method, Comput. Oper. Res., 35 (2008), 113-129.  doi: 10.1016/j.cor.2006.02.016.

[4]

E. Dahlgren and T. Leung, An optimal multiple stopping approach to infrastructure investment decisions, J. Econ. Dynam. Contr., 53 (2015), 251-267.  doi: 10.1016/j.jedc.2015.02.001.

[5]

T. Dangl, Investment and capacity choice under uncertain demand, Eur. J. Oper. Res., 117 (1999), 415-428.  doi: 10.1016/S0377-2217(98)00274-4.

[6]

P. Doan and K. Menyah, Impact of irreversibility and uncertainty on the timing of infrastructure projects, J. Constr. Eng. Manage., 139 (2013), 331-338.  doi: 10.1061/(ASCE)CO.1943-7862.0000615.

[7]

U. Dörr, Valuation of Swing Options and Examination of Exercise Strategies by Monte Carlo Techniques, Master thesis, University of Oxford, 2003.

[8]

E. EngelR. Fischer and A. Galetovic, The basic public finance of public-private partnerships, J. Euro. Econ. Assoc., 11 (2013), 83-111.  doi: 10.3386/w13284.

[9]

B. C. Esty, Modern Project Finance: A Casebook, Princeton, Wiley, 2003.

[10]

B. FlyvbjergM. Holm and S. Buhl, How common and how large are cost overruns in transport infrastructure projects?, Transp. Rev., 23 (2003), 71-88.  doi: 10.1080/01441640309904.

[11]

C. C. Gkochari, Optimal investment timing in the dry bulk shipping sector, Transp. Res. Part E, 79 (2015), 102-109.  doi: 10.1016/j.tre.2015.02.018.

[12]

H. B. Herath and C. Park, Mult-stage capital unvestment opportunities as compound real options, Eng. Econ., 47 (2002), 1-27. 

[13]

Y. Huang, Project and Policy Analysis of Build-Operate-Transfer Infrastructure Developments, Ph.D thesis, University of California at Berkeley, 1995.

[14]

Y. L. Huang and S. P. Chou, Valuation of the minimum revenue guarantee and the option to abandon in BOT infrastructure projects, Constr. Manag. Econ., 24 (2006), 379-389.  doi: 10.1080/01446190500434997.

[15]

Y. Huang and C. Pi, Valuation of multi-stage BOT projects involving dedicated asset investments: a sequential compound option approach, Constr. Manag. Econ., 27 (2009), 653-666.  doi: 10.1080/01446190903002789.

[16]

B. Klein and K. B. Leffler, The role of market forces in assuring contractual performance, J. Polit. Econ., 89 (1981), 615-641.  doi: 10.1086/260996.

[17]

Y. KwakY. Chih and C. I. William, Towards a comprehensive understanding of public-private partnerships for infrastructure development, California Manag. Rev., 51 (2009), 51-78.  doi: 10.2307/41166480.

[18]

S. Li and H. B. Cai, Government incentive impacts on private investment behaviors under demand uncertainty, Transp. Res. Part E, 101 (2017), 115-129.  doi: 10.1016/j.tre.2017.03.007.

[19]

W. Li and S. Wang, Pricing American options under proportional transaction costs using a penalty approach and a finite difference scheme, J. Ind. Manag. Optim., 9 (2013), 365-389.  doi: 10.3934/jimo.2013.9.365.

[20]

F. A. Longstaff and E. S. Schwartz, Valuing American options by simulation: A simple least squares approach, Rev. Financ. Stud., 14 (2001), 113-147.  doi: 10.1093/rfs/14.1.113.

[21]

L. J. Maseda, Real Options Analysis of Flexibility in a Hospital Emergency Department Expansion Project: A Systems Approach, Master thesis, MIT, 2008.

[22]

N. Meinshausen and B. M. Hambly, Monte Carlo methods for the valuation of multiple exercise options, Math. Financ., 14 (2004), 557-583.  doi: 10.1111/j.0960-1627.2004.00205.x.

[23]

S. NadarajahF. Margot and N. Secomandi, Comparison of least squares Monte Carlo methods with applications to energy real options, Eur. J. Oper. Res., 256 (2017), 196-204.  doi: 10.1016/j.ejor.2016.06.020.

[24]

R. Neufville, Y. S. Lee and S. Scholtes, Flexibility in hospital infrastructure design, Working Paper, MIT, 2008.

[25]

E. Pennings, Optimal pricing and quality choice when investment in quality is irreverible, J. Ind. Econ., 52 (2004), 569-589. 

[26]

M. Skamris and B. Flyvbjerg, Inaccuracy of traffic forecasts and cost estimates on large transport projects, Transp. Policy, 4 (1997), 141-146.  doi: 10.1016/S0967-070X(97)00007-3.

[27]

S. Szymanski, The optimal timing of infrastructure investment, J. Transp. Econ. Policy, 25 (1991), 247-258. 

[28]

Z. Tan and H. Yang, Flexible build-operate-transfer contracts for road franchising under demand uncertainty, Transp. Res. Part B, 46 (2012), 1419-1439.  doi: 10.1016/j.trb.2012.07.001.

[29] O. E. Williamson, The Economic Institutions of Capitalism, The Free Press, New York, 1985. 
[30]

Y. Xenidis and D. Angelides, The financial risks in build-operate-transfer projects, Constr. Manag. Econ., 23 (2005), 431-441.  doi: 10.1080/01446190500041552.

[31]

X. Zhang, Financial viability analysis and capital structure optimization in privatised public infrastructure projects, J. Constr. Eng. Manag., 131 (2005), 656-668. 

Figure 1.  The schematic diagram of a three-stage PPP project
Figure 2.  The project value for different demand levels
Figure 3.  The optimal exercise boundaries for the i-th (i = 1, 2) expansions
Figure 4.  The influences of the dedicated asset ratio
Figure 5.  The project value and subsidy amount under different demands
Figure 6.  The influences of the investment subsidy proportion
Figure 7.  Revenue subsidy at different demand levels
Figure 8.  The influences of the revenue subsidy price
Figure 9.  The comparison of the subsidy amount
Figure 10.  The comparison of the incremental value
Figure 11.  The comparison of the exercise boundary under the same subsidy amount
Table 1.  Default parameters used in the calculations
Constant Symbol Value Unit
Concession Period $ T_{c} $ 30 Year
Investment period $ T $ 10 Year
Planned investment times $ N $ 3 time
Construction period $ \nu $ 1 Year
Refraction time $ \delta $ 2 Year
Capacity of i-th stage $ m_{i} $ 40,000 $ m^3 $/day
Unit price $ p $ 1.8 CNY/$ m^3 $
Unit operational cost $ c $ 0.8 CNY/$ m^3 $
Construction cost parameter $ b $ 2917.8
Construction cost parameter $ \gamma $ 0.9427
Drift $ \alpha $ 6%
Volatility rate $ \sigma $ 15%
Discount rate $ \rho $ 8%
Dedicated asset ratio $ \eta $ 10%
Constant Symbol Value Unit
Concession Period $ T_{c} $ 30 Year
Investment period $ T $ 10 Year
Planned investment times $ N $ 3 time
Construction period $ \nu $ 1 Year
Refraction time $ \delta $ 2 Year
Capacity of i-th stage $ m_{i} $ 40,000 $ m^3 $/day
Unit price $ p $ 1.8 CNY/$ m^3 $
Unit operational cost $ c $ 0.8 CNY/$ m^3 $
Construction cost parameter $ b $ 2917.8
Construction cost parameter $ \gamma $ 0.9427
Drift $ \alpha $ 6%
Volatility rate $ \sigma $ 15%
Discount rate $ \rho $ 8%
Dedicated asset ratio $ \eta $ 10%
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