Research on Single Port Investment Decision ... - Semantic Scholar
Research on Single Port Investment Decision-making Optimization Model Based on Real Options Kuang Haibo,Wang Jian
Research on Single Port Investment Decision-making Optimization Model Based on Real Options Kuang Haibo1,2*,Wang Jian2 1.School of Transportation Management; Dalian Maritime University; Dalian 116026，China 2. Institute of Policy and Management, Chinese Academy of Sciences, Beijing 100190, China doi:10.4156/jdcta.vol4. issue9.28
Abstract Chinese ports investment theory and practice are still in infant, have been unable to adapt to the future port of the actual needs of sustainable development.The managerial flexibility involved in the contingent investment can be described and valued by expansive real options, the port investment in the expansion of the integrated value function model is established. The model is set up to calculate the optimal capacity with numerical techniques when the target investment returns index of the port is mainly concerned. Finally, with the practical example, the results show that the model has the practical application in practical significance.
Keywords: Port Investment, Real Options, Decision-making Model* 1. Introduction Port investment with the features of great scope, long construction and recovery period，is close relation with the base installation such as road, railway and so on. In addition, more benefits for the society, and its recovery period is longer (between 20 and 30 years)1,the research of port investment is complicated.However, comparing with other industry, port industry is very stable. It also has low ebb because of changing marke.With the general global economy developing,the main industry’s development can not leave the development of port.
In recent years, there are some problems,aimless expansion,ambiguous function division and strand line resource utilization are not used reasonably because of the low level reconstruction, which result from the irrational port invest and more obvious with ports’ rapid development[1],[2],[3],[4].The existing literatures rarely refer to port investment optimization research, especially for Chinese current situation. Li Ji-zi[5]attempted to use Genetic Algorithm and Neural Network to build port berth investment decision-making model[5]. Zeng and Yang used dynamic programming to do optimization research for container port size and positioning [6]. Based on the analysis on the main factors influencing port investment, Hilde discussed the cost and profit of port personal investment and government investment, and tentatively discussed the port investment feasibility of the option idea under undefined environment, and compared with NPV[7].Musso and Ferrari analyzed the factors influencing port investment cost and profit(Musso [8]. Ding Yi-zhong[9]combined Imitation with Integer Programming to build a dynamic investment optimization model which can be used to the cargo handling equipments of container terminal that have multi-wharf. Considering some constraint condition such as volume of freight,investment cost,cargo handling productivit,port transaction network and main ship form, Allahviranloo and Afandizadeh[10] used Fuzzy Integer Programming Model to optimize the investment on ship form and berth of a single port in different period. From the existing research method and strategy, we can see that the existing port investment optimization lacks the discussion for the port investment optimization strategy under undefined environment. Although the existing literature of port investment optimization theory and model has made some progress, but current theories and strategies are still shortcomings, the current lack of port investment optimization under uncertainty optimization strategy of port investment. From the * 1
Corresponding author,This work is supported by China National Science Foundation, No. 70873014 Report from the Port Industry,2007.
- 234 -
International Journal of Digital Content Technology and its Applications Volume 4, Number 9, December 2010
perspective of real options[11],[12], this study do research on port investment optimization, to further improve the investment to enrich the port optimization theory, to better guide practice. In this paper, the main framework as follows,First, a summary review of existing research status. Section II, a real options Approach to port optimal investment decision-making research ideas established and analysis. Section III, the port investment optimization model was established, and the investment decisions perform probabilistic, investment profits after the expansion was analyzed exhaustively. Section IV, Case Study. The last part is the summary.
2.The main research principle 2.1. Real option Real option is the concept evolving from the financial options. Financial option is a contract that gives its holder a specified period of time agreed by both parties buy and sell a certain amount of financial assets, including financial assets, known as the latent or underlying assets,underlying assets. Real Options is a solid investment in the field of financial options. The core idea of real options with the uncertainty can increase the value of business investment, the option owner can choose whether to delay further investment to minimize assets depreciation risk and income to maintain the stability of physical assets. Investment to the port, with the use of real options to assess the three prerequisites for investment in port, net income uncertainty, the irreversibility of the investment cost and project management flexibility. Options thinking means that the port management is more uncertainty, and easier to suspend or adjust the uncertain investment.
2.2. Research theory Generally, the single port investment optimization based on real options belongs to undefined investment, optimizing port investment under undefined environment, and is more suitable for the real condition that Chinese port is in a status of rapid development and intense competition(Mun 2002). Usually,the defined investment is periodic investment, especially for port expansion investment optimization problem. Under the constraints such as valuing port future development potential and competitive port and so on, port management can search best investment strategy, When t=0, port management analyzed kinds of constraints, and decided to invest a certain berth and wharf (the construction cycle is n), whether the port throughput can satisfy according requirement in the future nth year can be seen in Fig 1.This study uses stochastic progress to describe decision-making touching time and the executive probability, expanding real options to describe the flexibility value of port investment decision-making, building port investment expansion synthetic value function model, and resolving the best investment size which is targeted at port investment profit index. Berth being put into practice
dicision-making t=0
t=n
Figure 1. Port investment decision-making optimal theory
3. Port investment model 3.1. Model supposition At the time t=0, based on the analysis of port market competition and development trend, port management discussed whether to invest to port for its expansion. Suppose the amount of port investment on expansion is I, port expansion period is n years, and the port will be put in use in the nth year. The basic variables of the study are as follows, qt：t time the revenue of per unit throughput, (Principal business income- Principal business cost)/
- 235 -
Research on Single Port Investment Decision-making Optimization Model Based on Real Options Kuang Haibo,Wang Jian
the port's total throughput, mt:at t time the port's total throughput, αq:the expected growth rate of profit per unit throughput, αm:the expected growth rate of total throughput, σq:the volatility of profit per unit throughput, σm:the volatility of total throughput, ρqm:the related coefficient of the profit per unit and total throughput, ζ:a fixed parameter, which can be got according to the related data of port industry, aY: the expected growth rate of profit per unit throughput, σY:the expected growth rate of total throughput, u:the average discount rate of port industry, r: interest rate without risk, λ:opportunity cost rate, similar with the payout ratio of stock option, I0 :the real total port assets at time t=0. Suppose q0，m0 are the initial value of qt，mt, the above parameters can be valued according with port industry standard. Decision variables are as follows, I:The amount investment for port expansion and renovation. Port operation risk is mainly reflected on the fluctuation of the profit per throughput and the total port throughput. Port throughput and profit is closely related to social economy development and trade, and there are many complex factors influencing them, which are related with each other, the existed literatures simulating port throughput are mainly single model such as Vector Regression and Grey System whose independent variable is port throughput[13],[14]. Comparing with the existing literatures, Stochastic Volatility Model can better describe the situation that the influencing factors are complex and various, so this research uses historical data and Stochastic Volatility Model to stimulate port throughput and the profit per throughput. Suppose qt stands for the profit per throughput at time t (Principal business income- Principal business cost)/ the port's total throughput); mt stands for the total throughput at time t. suppose their motion path is geometrical Brownian movement, there is[12]
dqt q qt dt q qt dBq (t )
(1)
dmt m mt dt m mt dBm (t )
(2)
αq,αm are the expected growth rate of profit per throughput and total throughput respectively; σq，σm stand for the volatility of profit per throughput and total throughput respectively. Suppose q0，m0 are the initial value of qt，mt, the above parameters can be valued according with port industry standard. Generally, the profit per throughput will decrease with the increase of port throughput; it can be expressed by Stochastic Process as,
E[dBq (t )dBm (t )] qm dt
(3)
Where: the related coefficient of the profit per throughput and total throughput ρqm< 0. At time t=0, port management need to decide whether to increase port input in order to increase port throughput.
3.2. Model (1) Profit analysis after deciding to increase investment If port management decides to invest, the amount of port wharfs and berths, operation efficiency will increase, which means that port throughput will increase dramatically. Supposing the throughput obeys to geometrical Brownian movement shown in formula (2), m0’ is related with the amount of investment, we get,
- 236 -
International Journal of Digital Content Technology and its Applications Volume 4, Number 9, December 2010
m0' m0 emn ( I/ 0I)，0 1
(4)
So after t=n（t>n）, the expected profit discounted present value after increasing investment is, Yt E
' 0
q0 m
Y
t
qs ms e us ds | Ft
e Y t
2 exp Y BY (t ) Y t 2
(5)
and, BY (t ) [ q Bq (t ) m Bm (t )] / Y
(6)
Y u q m qm q m
(7)
Y ( q2 m2 2qm q m )1/ 2
(8)
From formula (5), we can see the motion path of
Yt obeys to geometrical Brownian movement,
then, dYt Y Yt dt Y Yt dBY (t )
t n
(9)
(2) The investment decision-making executive probability Supposing p is the probability of increase construction investment, that is, (10)
p Prob(Yt I )
We calculate that,
p Prob(Yt I ) N (d )
(11)
and, d
ln(q0 m0' ) ln(Y I ) (Y Y2 / 2)n
Y
(12)
n
N(.) is the cumulative distribution function of standard normal distribution. The probability that port management gives up increasing construction investment and operates original size is, 1-p=Prob( Yt
I)
(13)
(3) The port investment value In fact,the chance of increasing construction investment is equivalent to a European call whose executive price is I and due date is τ ,we can use B-S model to get the value of the option, n C E ( Max(Y | I , 0)e rn ) n e
q0 m0'
Y
n
e N (d1 ) Ie
rn
(14)
N (d 2 )
Where, d1
ln(q0 m0' ) ln(Y I ) (r Y2 / 2)n
Y
n
- 237 -
(15)
Research on Single Port Investment Decision-making Optimization Model Based on Real Options Kuang Haibo,Wang Jian
d2
ln(q0 m0' ) ln(Y I ) (r Y2 / 2)n
d1 Y
Y n
(16)
n
u Y
(17)
(4) Objective function No matter which decision will be made, even if port decides not to invest, port will remain current
situation, and will gain the expected profit discounted present value R0 , that is,
R0 E ( qs ms e us ds ) 0
q0 m0
Y
(18)
If port decides to invest, the value after port increases construction investment is, VT R0 pC I
q0 m0 pC I a
(19)
We define the optimization target as maximizing port investment profit index (the future value that investment produces and investment cost), that is, gain
VT R0 I 0 pI
(20)
gain
pC I I 0 pI
(21)
The simplified form is,
Using numerical solution to resolve formula (14), we can get the best investment amount I. The port investment Optimization Model (14) shows three characteristics: First, the investment reflects the high degree of uncertainty port characteristics, more in line with the current rapid development of China's port in the highly competitive situation, solve current theory and practice the lack of uncertain investment environment to optimize the port of the state. Second, it embodies the port or the pursuit of maximizing the return on investment principles. Long-term perspective, the direct control of the port investment cost, to solve the practice of blind pursuit of short-term investment returns, the size of defects, which effectively reflects the investment and operation of port rules. Third, reflect the actual characteristics of the port phased investment, expansion of the port investment optimization problem, in assessing the potential for future development and competitiveness of the port and other ports in the constraints, the port management for finding the optimal investment strategy.
4. Case study Port management decided whether to increase construction investment at t=0. Suppose n=3 years; the expected increase rate of profit per throughput and total throughput αq，αm are -10% and 10% respectively. The volatility rate σq and σm are 20% and 40% respectively, the value of q0 and m0 are 2 yuan/ton and 9 million tons, the related coefficient of profit per throughput and total throughput is ρqm=-0.6, parameter ζ=0.05.The risk free rate per year is r=5%.The average discount rate of port industry is u=10%.The real total port assets I0=2 billion yuan. The investment profit index that stimulating investment amount I is shown in Fig 2. The investment profit index gain was gotten according to the different value of I. When increase investment amount I=2.5 million, gain is the max and is 10.64%. From Fig 2, we can see, on the left of
- 238 -
International Journal of Digital Content Technology and its Applications Volume 4, Number 9, December 2010
the highest point, the return on investment increases slowly; on the right, the return on investment decreases rapidly, the main reason is the rapid increase of investment size.
Figure 2. Port investment gin index curve
5. Sensitivity analysis of the main variables 5.1. Revenue per unit of throughput and the initial value of total throughput Suppose the initial value of profit per unit of throughput and total throughput q0 and m0 change, other parameters and variables remain unchanged. When q0= 1.5 and m0= 1200, we can get the expansion investment I = 7.48 million and maximum gain=33.86 %. When q0=2.5 and m0= 1000, we can get the expansion investment I = 10.1 million and maximum gain=47.38 %. See Figure 3 and Figure 4.
Figure 3. Port investment optimaization sensitivity analysis( )
Figure 4. Port investment optimaization sensitivity sensitivity analysis( )
From the investment point of view, the port the initial value of profit per unit of throughput and total throughput q0 and m0 is relatively small impact investment decisions.
5.2. The expected growth rate of total throughput and per unit revenue of throughput Suppose the expected growth rate of profit per throughput and total throughput αq and αm change, other parameters and variables remain unchanged. When the αq and αm vary from -5% and 10% into a -4% and 12%, we can get the expansion investment I = 17.52 million and maximum gain=80.91%. However, when the αq and αm vary from -5% and 10% into a -6% and 8%, we can get the expansion investment I = 4.35 million and maximum gain=20.17% .See Figure5 and Figure 6.
- 239 -
Research on Single Port Investment Decision-making Optimization Model Based on Real Options Kuang Haibo,Wang Jian
Figure 5. Port investment optimaization sensitivity analysis ( )
Figure 6. Port investment optimaization sensitivity sensitivity analysis( )
From the investment point of view, the port expected growth rate of throughput per unit of revenue and the total throughput has great influence investment decisions, investment decision-making largely depends on the port profit per throughput and overall throughput growth level.
5.3. The expected volatility of per unit throughput revenue and the total throughput Suppose the expected volatility of profit per throughput and total throughput σq and σm change, other parameters and variables remain unchanged. When the σq and σm vary from 10% and 20% into a 20% and 40%, we can get the expansion investment I = 5.5 million and maximum gain =24.72%. However, when the σq and σm vary from 10% and 20% into a 5% and 10%, we can get the expansion investment I = 9.9 million and maximum gain=30.76% .See Figure7 and Figure 8.
Figure 7. Port investment optimaization sensitivity analysis ( )
Figure 8. Port investment optimaization sensitivity sensitivity analysis ( )
From the investment point of view, profit per throughput and total throughput is expected to increase volatility uncertainty of port operations, which reduces the port investment amount.
6. Conclusion Using expanding real option to describe the contingent value of port investment decision-making, building the synthetical value function model for port construction investment was set up, and numerically resolving the best investment size targeted at port investment profit index. Finally, using real example to analyze the above model, the degree of main influence factors were analyzed, and the result shows that the described model can get the best resolution quickly and conveniently, which can verify the practicability of the model.
- 240 -
International Journal of Digital Content Technology and its Applications Volume 4, Number 9, December 2010
7. Reference [1] Emirates International Credit Rating Co., Ltd,”2007 Annual Industry Risk Study(the port industry)”,2007 [2] Shu H F,"China’s current port investment potential risk analysis",China Ports, 2006, (2): 23-24 [3] Wu Guofu,"Early Warning Management Study to Investment Risk of Regional Port Construction Project ",Doctorial dissertation, Wuhan University of Technology, 2006 [4] Kuang H B, Li H Z,"Chinese port X–efficiency measurement ",Systems Engineering Theory & Practice, 2009,29(2): 1-9 [5] Li J Z, NiW F, Fang C X,"Artificial neural network model of harbor investment aided decision–making by genetic algorithm",Chinese Journal of Management Science, 2000,8(1):56-60 [6] Zeng Z, Yang Z,"Dynamic programming of port position and scale in the hierarchized container ports network ",Maritime Policy & Management, 2002, 29 (2):163-177 [7] Ilde M.A.,Meersman,"Port Investments in an Uncertain Environment ",Research in Transportation Economics,2005(13): 279-298 [8] Musso E.,Ferrari C.,Benacchio M.,"Port Investment:Profitability, Economic Impact and Financing ",Research in Transportation Economics. 2006(16):171-218 [9] Ding Y Z,"Simulation based methods and integer programming of multiterminal container port handling equipment investment optimization model and its application in Shanghai Port",Journal of Shanghai Maritime University, 2006, S1(27): 21-26. [10] Allahviranloo M.,Afandizadeh S,"Investment optimization on port’s development by fuzzy integer programming ",European Journal of Operational Research,2008(186): 423-434 [11] Tom, C., Vladimir. A.,"Real Option: a Practitioner’s Guide",New York, 2001 [12] Mun, J.,"Real Options Analysis: Tools and Techniques for Valuing Strategic Investments and Decisions",Hoboken, New Jersey, USA: John Wiley & Sons Inc, 2002 [13] Liu Y, Chen Y M,"Application of grey system model in throughput forecasting of inland river port",Port &Waterway Engineering, 2006, (4):31-34 [14] Gao S, Mei L,"Port throughput forecasting based on Support Vector Machine",Port & Waterway Engineering, 2007, (5): 50-53
- 241 -
Research on Single Port Investment Decision-making Optimization Model Based on Real Options Kuang Haibo1,2*,Wang Jian2 1.School of Transportation Management; Dalian Maritime University; Dalian 116026，China 2. Institute of Policy and Management, Chinese Academy of Sciences, Beijing 100190, China doi:10.4156/jdcta.vol4. issue9.28
Abstract Chinese ports investment theory and practice are still in infant, have been unable to adapt to the future port of the actual needs of sustainable development.The managerial flexibility involved in the contingent investment can be described and valued by expansive real options, the port investment in the expansion of the integrated value function model is established. The model is set up to calculate the optimal capacity with numerical techniques when the target investment returns index of the port is mainly concerned. Finally, with the practical example, the results show that the model has the practical application in practical significance.
Keywords: Port Investment, Real Options, Decision-making Model* 1. Introduction Port investment with the features of great scope, long construction and recovery period，is close relation with the base installation such as road, railway and so on. In addition, more benefits for the society, and its recovery period is longer (between 20 and 30 years)1,the research of port investment is complicated.However, comparing with other industry, port industry is very stable. It also has low ebb because of changing marke.With the general global economy developing,the main industry’s development can not leave the development of port.
In recent years, there are some problems,aimless expansion,ambiguous function division and strand line resource utilization are not used reasonably because of the low level reconstruction, which result from the irrational port invest and more obvious with ports’ rapid development[1],[2],[3],[4].The existing literatures rarely refer to port investment optimization research, especially for Chinese current situation. Li Ji-zi[5]attempted to use Genetic Algorithm and Neural Network to build port berth investment decision-making model[5]. Zeng and Yang used dynamic programming to do optimization research for container port size and positioning [6]. Based on the analysis on the main factors influencing port investment, Hilde discussed the cost and profit of port personal investment and government investment, and tentatively discussed the port investment feasibility of the option idea under undefined environment, and compared with NPV[7].Musso and Ferrari analyzed the factors influencing port investment cost and profit(Musso [8]. Ding Yi-zhong[9]combined Imitation with Integer Programming to build a dynamic investment optimization model which can be used to the cargo handling equipments of container terminal that have multi-wharf. Considering some constraint condition such as volume of freight,investment cost,cargo handling productivit,port transaction network and main ship form, Allahviranloo and Afandizadeh[10] used Fuzzy Integer Programming Model to optimize the investment on ship form and berth of a single port in different period. From the existing research method and strategy, we can see that the existing port investment optimization lacks the discussion for the port investment optimization strategy under undefined environment. Although the existing literature of port investment optimization theory and model has made some progress, but current theories and strategies are still shortcomings, the current lack of port investment optimization under uncertainty optimization strategy of port investment. From the * 1
Corresponding author,This work is supported by China National Science Foundation, No. 70873014 Report from the Port Industry,2007.
- 234 -
International Journal of Digital Content Technology and its Applications Volume 4, Number 9, December 2010
perspective of real options[11],[12], this study do research on port investment optimization, to further improve the investment to enrich the port optimization theory, to better guide practice. In this paper, the main framework as follows,First, a summary review of existing research status. Section II, a real options Approach to port optimal investment decision-making research ideas established and analysis. Section III, the port investment optimization model was established, and the investment decisions perform probabilistic, investment profits after the expansion was analyzed exhaustively. Section IV, Case Study. The last part is the summary.
2.The main research principle 2.1. Real option Real option is the concept evolving from the financial options. Financial option is a contract that gives its holder a specified period of time agreed by both parties buy and sell a certain amount of financial assets, including financial assets, known as the latent or underlying assets,underlying assets. Real Options is a solid investment in the field of financial options. The core idea of real options with the uncertainty can increase the value of business investment, the option owner can choose whether to delay further investment to minimize assets depreciation risk and income to maintain the stability of physical assets. Investment to the port, with the use of real options to assess the three prerequisites for investment in port, net income uncertainty, the irreversibility of the investment cost and project management flexibility. Options thinking means that the port management is more uncertainty, and easier to suspend or adjust the uncertain investment.
2.2. Research theory Generally, the single port investment optimization based on real options belongs to undefined investment, optimizing port investment under undefined environment, and is more suitable for the real condition that Chinese port is in a status of rapid development and intense competition(Mun 2002). Usually,the defined investment is periodic investment, especially for port expansion investment optimization problem. Under the constraints such as valuing port future development potential and competitive port and so on, port management can search best investment strategy, When t=0, port management analyzed kinds of constraints, and decided to invest a certain berth and wharf (the construction cycle is n), whether the port throughput can satisfy according requirement in the future nth year can be seen in Fig 1.This study uses stochastic progress to describe decision-making touching time and the executive probability, expanding real options to describe the flexibility value of port investment decision-making, building port investment expansion synthetic value function model, and resolving the best investment size which is targeted at port investment profit index. Berth being put into practice
dicision-making t=0
t=n
Figure 1. Port investment decision-making optimal theory
3. Port investment model 3.1. Model supposition At the time t=0, based on the analysis of port market competition and development trend, port management discussed whether to invest to port for its expansion. Suppose the amount of port investment on expansion is I, port expansion period is n years, and the port will be put in use in the nth year. The basic variables of the study are as follows, qt：t time the revenue of per unit throughput, (Principal business income- Principal business cost)/
- 235 -
Research on Single Port Investment Decision-making Optimization Model Based on Real Options Kuang Haibo,Wang Jian
the port's total throughput, mt:at t time the port's total throughput, αq:the expected growth rate of profit per unit throughput, αm:the expected growth rate of total throughput, σq:the volatility of profit per unit throughput, σm:the volatility of total throughput, ρqm:the related coefficient of the profit per unit and total throughput, ζ:a fixed parameter, which can be got according to the related data of port industry, aY: the expected growth rate of profit per unit throughput, σY:the expected growth rate of total throughput, u:the average discount rate of port industry, r: interest rate without risk, λ:opportunity cost rate, similar with the payout ratio of stock option, I0 :the real total port assets at time t=0. Suppose q0，m0 are the initial value of qt，mt, the above parameters can be valued according with port industry standard. Decision variables are as follows, I:The amount investment for port expansion and renovation. Port operation risk is mainly reflected on the fluctuation of the profit per throughput and the total port throughput. Port throughput and profit is closely related to social economy development and trade, and there are many complex factors influencing them, which are related with each other, the existed literatures simulating port throughput are mainly single model such as Vector Regression and Grey System whose independent variable is port throughput[13],[14]. Comparing with the existing literatures, Stochastic Volatility Model can better describe the situation that the influencing factors are complex and various, so this research uses historical data and Stochastic Volatility Model to stimulate port throughput and the profit per throughput. Suppose qt stands for the profit per throughput at time t (Principal business income- Principal business cost)/ the port's total throughput); mt stands for the total throughput at time t. suppose their motion path is geometrical Brownian movement, there is[12]
dqt q qt dt q qt dBq (t )
(1)
dmt m mt dt m mt dBm (t )
(2)
αq,αm are the expected growth rate of profit per throughput and total throughput respectively; σq，σm stand for the volatility of profit per throughput and total throughput respectively. Suppose q0，m0 are the initial value of qt，mt, the above parameters can be valued according with port industry standard. Generally, the profit per throughput will decrease with the increase of port throughput; it can be expressed by Stochastic Process as,
E[dBq (t )dBm (t )] qm dt
(3)
Where: the related coefficient of the profit per throughput and total throughput ρqm< 0. At time t=0, port management need to decide whether to increase port input in order to increase port throughput.
3.2. Model (1) Profit analysis after deciding to increase investment If port management decides to invest, the amount of port wharfs and berths, operation efficiency will increase, which means that port throughput will increase dramatically. Supposing the throughput obeys to geometrical Brownian movement shown in formula (2), m0’ is related with the amount of investment, we get,
- 236 -
International Journal of Digital Content Technology and its Applications Volume 4, Number 9, December 2010
m0' m0 emn ( I/ 0I)，0 1
(4)
So after t=n（t>n）, the expected profit discounted present value after increasing investment is, Yt E
' 0
q0 m
Y
t
qs ms e us ds | Ft
e Y t
2 exp Y BY (t ) Y t 2
(5)
and, BY (t ) [ q Bq (t ) m Bm (t )] / Y
(6)
Y u q m qm q m
(7)
Y ( q2 m2 2qm q m )1/ 2
(8)
From formula (5), we can see the motion path of
Yt obeys to geometrical Brownian movement,
then, dYt Y Yt dt Y Yt dBY (t )
t n
(9)
(2) The investment decision-making executive probability Supposing p is the probability of increase construction investment, that is, (10)
p Prob(Yt I )
We calculate that,
p Prob(Yt I ) N (d )
(11)
and, d
ln(q0 m0' ) ln(Y I ) (Y Y2 / 2)n
Y
(12)
n
N(.) is the cumulative distribution function of standard normal distribution. The probability that port management gives up increasing construction investment and operates original size is, 1-p=Prob( Yt
I)
(13)
(3) The port investment value In fact,the chance of increasing construction investment is equivalent to a European call whose executive price is I and due date is τ ,we can use B-S model to get the value of the option, n C E ( Max(Y | I , 0)e rn ) n e
q0 m0'
Y
n
e N (d1 ) Ie
rn
(14)
N (d 2 )
Where, d1
ln(q0 m0' ) ln(Y I ) (r Y2 / 2)n
Y
n
- 237 -
(15)
Research on Single Port Investment Decision-making Optimization Model Based on Real Options Kuang Haibo,Wang Jian
d2
ln(q0 m0' ) ln(Y I ) (r Y2 / 2)n
d1 Y
Y n
(16)
n
u Y
(17)
(4) Objective function No matter which decision will be made, even if port decides not to invest, port will remain current
situation, and will gain the expected profit discounted present value R0 , that is,
R0 E ( qs ms e us ds ) 0
q0 m0
Y
(18)
If port decides to invest, the value after port increases construction investment is, VT R0 pC I
q0 m0 pC I a
(19)
We define the optimization target as maximizing port investment profit index (the future value that investment produces and investment cost), that is, gain
VT R0 I 0 pI
(20)
gain
pC I I 0 pI
(21)
The simplified form is,
Using numerical solution to resolve formula (14), we can get the best investment amount I. The port investment Optimization Model (14) shows three characteristics: First, the investment reflects the high degree of uncertainty port characteristics, more in line with the current rapid development of China's port in the highly competitive situation, solve current theory and practice the lack of uncertain investment environment to optimize the port of the state. Second, it embodies the port or the pursuit of maximizing the return on investment principles. Long-term perspective, the direct control of the port investment cost, to solve the practice of blind pursuit of short-term investment returns, the size of defects, which effectively reflects the investment and operation of port rules. Third, reflect the actual characteristics of the port phased investment, expansion of the port investment optimization problem, in assessing the potential for future development and competitiveness of the port and other ports in the constraints, the port management for finding the optimal investment strategy.
4. Case study Port management decided whether to increase construction investment at t=0. Suppose n=3 years; the expected increase rate of profit per throughput and total throughput αq，αm are -10% and 10% respectively. The volatility rate σq and σm are 20% and 40% respectively, the value of q0 and m0 are 2 yuan/ton and 9 million tons, the related coefficient of profit per throughput and total throughput is ρqm=-0.6, parameter ζ=0.05.The risk free rate per year is r=5%.The average discount rate of port industry is u=10%.The real total port assets I0=2 billion yuan. The investment profit index that stimulating investment amount I is shown in Fig 2. The investment profit index gain was gotten according to the different value of I. When increase investment amount I=2.5 million, gain is the max and is 10.64%. From Fig 2, we can see, on the left of
- 238 -
International Journal of Digital Content Technology and its Applications Volume 4, Number 9, December 2010
the highest point, the return on investment increases slowly; on the right, the return on investment decreases rapidly, the main reason is the rapid increase of investment size.
Figure 2. Port investment gin index curve
5. Sensitivity analysis of the main variables 5.1. Revenue per unit of throughput and the initial value of total throughput Suppose the initial value of profit per unit of throughput and total throughput q0 and m0 change, other parameters and variables remain unchanged. When q0= 1.5 and m0= 1200, we can get the expansion investment I = 7.48 million and maximum gain=33.86 %. When q0=2.5 and m0= 1000, we can get the expansion investment I = 10.1 million and maximum gain=47.38 %. See Figure 3 and Figure 4.
Figure 3. Port investment optimaization sensitivity analysis( )
Figure 4. Port investment optimaization sensitivity sensitivity analysis( )
From the investment point of view, the port the initial value of profit per unit of throughput and total throughput q0 and m0 is relatively small impact investment decisions.
5.2. The expected growth rate of total throughput and per unit revenue of throughput Suppose the expected growth rate of profit per throughput and total throughput αq and αm change, other parameters and variables remain unchanged. When the αq and αm vary from -5% and 10% into a -4% and 12%, we can get the expansion investment I = 17.52 million and maximum gain=80.91%. However, when the αq and αm vary from -5% and 10% into a -6% and 8%, we can get the expansion investment I = 4.35 million and maximum gain=20.17% .See Figure5 and Figure 6.
- 239 -
Research on Single Port Investment Decision-making Optimization Model Based on Real Options Kuang Haibo,Wang Jian
Figure 5. Port investment optimaization sensitivity analysis ( )
Figure 6. Port investment optimaization sensitivity sensitivity analysis( )
From the investment point of view, the port expected growth rate of throughput per unit of revenue and the total throughput has great influence investment decisions, investment decision-making largely depends on the port profit per throughput and overall throughput growth level.
5.3. The expected volatility of per unit throughput revenue and the total throughput Suppose the expected volatility of profit per throughput and total throughput σq and σm change, other parameters and variables remain unchanged. When the σq and σm vary from 10% and 20% into a 20% and 40%, we can get the expansion investment I = 5.5 million and maximum gain =24.72%. However, when the σq and σm vary from 10% and 20% into a 5% and 10%, we can get the expansion investment I = 9.9 million and maximum gain=30.76% .See Figure7 and Figure 8.
Figure 7. Port investment optimaization sensitivity analysis ( )
Figure 8. Port investment optimaization sensitivity sensitivity analysis ( )
From the investment point of view, profit per throughput and total throughput is expected to increase volatility uncertainty of port operations, which reduces the port investment amount.
6. Conclusion Using expanding real option to describe the contingent value of port investment decision-making, building the synthetical value function model for port construction investment was set up, and numerically resolving the best investment size targeted at port investment profit index. Finally, using real example to analyze the above model, the degree of main influence factors were analyzed, and the result shows that the described model can get the best resolution quickly and conveniently, which can verify the practicability of the model.
- 240 -
International Journal of Digital Content Technology and its Applications Volume 4, Number 9, December 2010
7. Reference [1] Emirates International Credit Rating Co., Ltd,”2007 Annual Industry Risk Study(the port industry)”,2007 [2] Shu H F,"China’s current port investment potential risk analysis",China Ports, 2006, (2): 23-24 [3] Wu Guofu,"Early Warning Management Study to Investment Risk of Regional Port Construction Project ",Doctorial dissertation, Wuhan University of Technology, 2006 [4] Kuang H B, Li H Z,"Chinese port X–efficiency measurement ",Systems Engineering Theory & Practice, 2009,29(2): 1-9 [5] Li J Z, NiW F, Fang C X,"Artificial neural network model of harbor investment aided decision–making by genetic algorithm",Chinese Journal of Management Science, 2000,8(1):56-60 [6] Zeng Z, Yang Z,"Dynamic programming of port position and scale in the hierarchized container ports network ",Maritime Policy & Management, 2002, 29 (2):163-177 [7] Ilde M.A.,Meersman,"Port Investments in an Uncertain Environment ",Research in Transportation Economics,2005(13): 279-298 [8] Musso E.,Ferrari C.,Benacchio M.,"Port Investment:Profitability, Economic Impact and Financing ",Research in Transportation Economics. 2006(16):171-218 [9] Ding Y Z,"Simulation based methods and integer programming of multiterminal container port handling equipment investment optimization model and its application in Shanghai Port",Journal of Shanghai Maritime University, 2006, S1(27): 21-26. [10] Allahviranloo M.,Afandizadeh S,"Investment optimization on port’s development by fuzzy integer programming ",European Journal of Operational Research,2008(186): 423-434 [11] Tom, C., Vladimir. A.,"Real Option: a Practitioner’s Guide",New York, 2001 [12] Mun, J.,"Real Options Analysis: Tools and Techniques for Valuing Strategic Investments and Decisions",Hoboken, New Jersey, USA: John Wiley & Sons Inc, 2002 [13] Liu Y, Chen Y M,"Application of grey system model in throughput forecasting of inland river port",Port &Waterway Engineering, 2006, (4):31-34 [14] Gao S, Mei L,"Port throughput forecasting based on Support Vector Machine",Port & Waterway Engineering, 2007, (5): 50-53
- 241 -
