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Using bi-level programming to
analyze the royalty for private–public
partnership projects: the operational
quantity-based model
Chao-Chung Kang a , Cheng-Min Feng b & Chiu-Yen Kuo b a
Department of Business Administration and Graduate Institute of Management , Providence University , 200, Chung-Chi Rd., Shalu, Taichung Hsien, 433, Taiwan
b
Institute of Traffic and Transportation , National Chiao Tung University , 114, 4F, Sec.1, Chung Hsiao W. Rd., Taipei, 100, Taiwan
Published online: 23 Apr 2010.
To cite this article: Chao-Chung Kang , Cheng-Min Feng & Chiu-Yen Kuo (2010) Using
bi-level programming to analyze the royalty for private–public partnership projects: the
operational quantity-based model, Transportation Planning and Technology, 33:3, 315-328, DOI: 10.1080/03081061003732383
To link to this article: http://dx.doi.org/10.1080/03081061003732383
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Using bi-level programming to analyze the royalty for private
public
partnership projects: the operational quantity-based model
Chao-Chung Kanga*, Cheng-Min Fengband Chiu-Yen Kuob
a
Department of Business Administration and Graduate Institute of Management, Providence University, 200, Chung-Chi Rd., Shalu, Taichung Hsien 433, Taiwan;bInstitute of Traffic and Transportation, National Chiao Tung University, 114, 4F, Sec.1, Chung Hsiao W. Rd.,
Taipei 100, Taiwan
(Received 16 September 2008; final version received 9 February 2010) This paper develops a royalty negotiation model based on the operating quantity of Build, Operate, and Transfer (BOT) projects for both government and the private sector using a bi-level programming (BLP) approach. The royalty negotiation is one of many critical negotiation items of a concession contract. This study develops a royalty negotiation model to simulate the negotiation behavior of two parties, and derives the heuristic algorithm for the BLP problem. A number of factors are incorporated into this algorithm including the concession rate, the time value discount rate, the learning rate, and the number of negotiations. The paper includes a case study of the Taipei Port Container Logistic BOT Project. The results show that the two parties involved completed royalty negotiation at the sixth negotiation stage. The findings show that the government can receive a royalty from the concessionaire, calculated at 0.00386% of the operating quantity of this BOT project. Therefore, the royalty negotiation model developed here could be employed to explain negotiation behavior. Keywords: BOT project; royalty; negotiation; bi-level programming
1. Introduction
This paper develops a royalty negotiation model using the bi-level programming (BLP) approach and derives an algorithm for determining the royalty fee for a Build, Operate, and Transfer (BOT) project from a game theory perspective. BOT is an approach the private sector utilizes to obtain a granted concession for completing a specific project independently. However, the ownership of the project must be returned to the public sector once it is completed (Hwang 1995, Kang et al. 2005). This has been widely employed to implement infrastructure projects in many developed and developing countries. For example, the 80 km elevated toll expressway in metropolitan Bangkok in Thailand; the 300 MW coal-fired power station projects in the Philippines; and the 5400 km road-building project in Mexico (Walker and Smith 1996). In addition, in Taiwan, many infrastructure projects, including the High Speed Rail Project (HSRBOT) and Taipei Port Container Logistic BOT Project have also been carried out using the BOT approach.
*Corresponding author. Email: cckang@pu.edu.tw
ISSN 0308-1060 print/ISSN 1029-0354 online
#2010 Taylor & Francis
DOI: 10.1080/03081061003732383 http://www.informaworld.com
Vol. 33, No. 3, April 2010, 315328
The host utility uses the royalty from the concessionaire to cover their investment in the BOT project. It is obvious that the royalty or franchise is a revenue sharing scheme between the host utility and private sector (Tiong and Alum 1997). Tiong and Alum (1997) pointed out that the royalty amount should be included in the BOT agreement through negotiations by both parties. For instance, the franchise fee in the Dulles Greenway BOT Project in Virginia is about US$4.3 million, and the royalty amount for the M2 Motorway BOT Project in Australia for the host utility was about AU$7 million (Walker and Smith 1996). In 1998, the lump sum royalty levied for the 101 Skyscraper BOT Project in Taiwan was NT$ 30 billion which was calculated according to the fixed royalty method. The royalty, which includes 10% of the pre-tax amount of annual operational benefit for the High Speed Rail BOT Project of the concession, is paid to the government (Public Construction Commission 2001).
Previously, many researchers have conducted risk evaluation, risk management, and financing viability in BOT projects for allocating risk (Walker and Smith 1996, Chang and Chen 2001, Chen et al. 2002, Kang et al. 2005). In recent years, some studies have adopted game theory or BLP approaches to determine the price, the operating quantity level, or to identify the concession period of a BOT project. For example, Yang and Meng (2000) explored the toll scheme of highway networks using BLP under the BOT mechanism. Xing and Wu (2001) used BLP to construct a Stackelberg game model for determining the price and production quantity of a power utility in a BOT project. Shen et al. (2007) used Bargaining Game Theory to identify the concession period of a BOT project. They proposed a BOT concession model to identify a specific concession period which takes into account the bargaining behavior of the two parties engaged in a BOT contract.
As seen, the price, the determination of operational quantity, or the identification of the concession period should be written into the franchise contract through the negotiations between both parties under the BOT mechanism. However, those factors, including the concession rate, the time value discount rate, and the learning rate, have not been incorporated into their models. Conversely, during the negotiation process, those factors will actually affect the determination of price, production quantity, or the identification of the concession period of a BOT project. As for royalty formulae, some studies have used mathematical programming, simulation, or for the case of BOT projects, financial engineering models. For instance, Chiou and Lan (2006) constructed a royalty model using fuzzy program-ming for analyzing different types of royalty formulae which were pre-tax profit based, total revenue based, and patronage based under uncertain demand. Moreover, Kang et al. (2003, 2004, 2007) constructed royalty models for a BOT project using mathematical programming and financial cash flow from the viewpoint of the government and the private sector, respectively. The contributions of Kang et al. (2003, 2004, 2007) for the determination of royalty amounts for BOT projects are from the perspective of the government and private sectors, respectively. Further-more, their study describes the royalty at the lower boundary and the upper boundary for the two parties. However, those studies lack the exploration of the royalty negotiation issue for private and public sectors. Although Kang et al. (2003, 2004, 2007) as well as Chiou and Lan (2006) have proposed many different royalty models, nevertheless, it is worth analyzing royalty negotiations for both parties because few studies have explored this issue in sufficient depth.
The purpose of this paper is to construct a royalty negotiation model and to investigate royalty negotiation for a BOT project. The remainder of the paper is structured as follows: Section 2 describes the assumptions of the developed model; Section 3 constructs a royalty negotiation model and a solution algorithm; Section 4 presents a numerical example; and finally, a discussion of findings is presented and conclusions are drawn.
2. Assumptions used in model development
Theories, including game theory, bargaining theory, or BLP, have been widely employed to analyze resource allocation, price determination, wage determination, Stackelberg’s Duopoly Model for economic policies or BOT projects, and other problems (Wen and Hsu 1991, Adams et al. 1996, Houba 1997, Lim 1999, Strand 2000, Xing and Wu 2001, Aloysius 2002). According to previous research on bargaining theory or BLP mentioned above, these authors have made some assumptions about their models in terms of number of players, competent information, rational behavior, bargaining cost, and time value. Hence, based on the above mentioned studies, the following assumptions for developing the model were made:
(1) Two parties, the government concerned and the private investor, establish contractual relations with a BOT contract through appropriate negotiations conducted with rational behavior. Assuming rational behavior means that both parties will calculate and adequately compare all the possible outcomes for protecting their own interests and profit-making objectives.
(2) The two parties are both entitled to the same full and frank disclosure of relevant information in regards to the BOT project concerned. Furthermore, parties should endeavor to ensure they communicate to each other clearly and effectively.
3. Methodology
3.1. Concept of financing BOT projects
The concept of financing projects proposed by Kang et al. (2003, 2004) was utilized to describe the annual royalty relationship between government and private investments. The concept is shown in Figure 1.
Figure 1 indicates that the fund resource for both construction and operation in a BOT project comes from the concessionaire and the government (Finnerty 1996). The construction cost of the project comprises Cgt and Cpt; where Cgt and Cpt
Cgt
Cpt Kt Rt Bt + g(1 + φ)t Qt + Dt
Government BOT project
Private sector
Figure 1. Concept of annual royalty of BOT projects, the operational quantity-based case.
represent the government investment cost and the private investment cost at time t during the construction period, respectively; and Ktis the nominal operation cost at time t during the operation period. The concessionaire pays Btg(1f)tQtDtto the government according to the product quantity and affiliated business income, where Btis the land-use rent at time t, Qtis the product quantity at time t, and Dtis the tax at time t. The term Btg(1f)tQtDtin Figure 1 is the sum of the land-use rent, royalty, and tax. Let g be the proportion of the product quantity of BOT project during the operating period, and let f be the annual growth rate of g.
3.2. The model
To develop the royalty negotiation model, this study assumes that the concession period of a BOT project is made up of both the construction period (t 0 n) and the operation period (t n1 N). We also assume that the government has no affiliated business income, no joint development income, no subsidies given to the private sector, and the salvage value of the fixed asset component of the BOT project is not considered. After the concession period expires, the facilities of the BOT project should be returned to the government unconditionally. Further, we assume that the government investment is entirely capitalized by debt and the planning cost of government is not considered. Additionally, we assume that the royalty is not tax deductible. Finally, the capital cost of the BOT project was evaluated using the Weighted Average Cost of Capital (WACC) method.
As shown in Figure 1, a causal relationship exists between royalty, government investment, private-sector investment, and the government finance recovery ratio in cash flow for BOT projects. The government finance recovery ratio for the operating quantity of a BOT project for which the royalty is calculated has been defined by Kang et al. (2004, 2007) as:
Pg;Q(k) 1 Cg [rggu(k) fg] 1 C(1 Pc)[rggu(k) fg] (1) where rg PN t 0 Bt Dt (1 i)t; fg PN t h (1 f)t hQt
(1 i)t is a discount factor of royalty for the project; Pc
Cp C
Cp Cg Cp
; h is the first year for royalty collection; PCis the rate of the concessionaire’s investment cost; C is the sum of the present value of construction costs which is discounted to the first year of the construction period; Cg is the sum of the present value of construction costs financed by government investment, and the cost is discounted to the first year of the construction period; Cp is the sum of the present value of construction costs financed by private investment, and the cost is discounted to the first year of the construction period; and i is the interest rate of government bonds.
Equation (1) represents the government finance recovery ratio Pg,Q(k) at the kth negotiation. There exists a positive relationship between Pg,Q(k) and (rggu(k) fg). That is, the more in royalty, tax, and land-use rent for the host utilities, the higher the value of Pg,Q(k). Thus, Pg,Q(k) goes up when variables of rg, gu(k), and fgincrease.
Conversely, Pg,Q(k) decreases as PC increases or variables of rg, gu(k), and fg decrease.
Furthermore, let Pp,Q(k) be the profit index of the concessionaire. Pp;Q(k) NI gl(k) fp PC C (2) Where NI PN t n1 Rt Ct Bt Dt
(1 d)t ; NI is the total revenue of the BOT project, which includes operational and non-operational revenues; fp P
N
t h
(1 f)t hQt (1 d)t ; dis the risk-adjusted discount ratio after tax of the concessionaire, where d i; it can be estimated using the WACC with corporate tax that:
d dB (1 Tc) B S B dS S S B (3) where dBis the cost of long-term debt of the BOT project for the private firm; dSis the cost of equity of the BOT project for the private firm; B is the market value of the debt of the BOT project for the private firm; Tcis the marginal tax ratio of the BOT project; and S is the market value of the equity of the BOT project for the private firm.
The numerator of Eq. (2) is the net operating income minus its royalty at the kth negotiation, and the denominator is the investment cost of the concessionaire. Equation (2) is the profitability of the private sector at the kth negotiation. It indicates that the concessionaire pursues its maximum financial profit at the kth negotiation if the private sector is a rational decision-maker.
According to Wen and Hsu (1991), the BLP is a Stackelberg game associated with a leader and follower. This model can illustrate a sequential decision for two players who pursue the objective of maximizing their own aims subject to another decision-making strategy. The host utility can be regarded as the higher-level problem of BLP because the royalty was first announced by the government in the BOT tender document. Then, the private sector will negotiate with the host utility regarding the royalty. Hence, the private sector can be regarded as the lower-level problem of the BLP. The two problem levels are formulated as follows.
Higher-level problem, max fgu(k)g Pg;Q(k) 1 Cg [rggu fg] 1 C(1 PC)[rggu(k) fg] (4) s:t: gu(k) fgC PG0 PC] C PG0 rg (5) gu(k) 5(NI PC C)=fp (6) gu(k) ]Vl(k) (7) gu(k) 5Wu(k) (8) fg X N t h (1 f)t hQt (1 i)t (9)
fp XN t h (1 f)t hQt (1 d)t : (10) Lower-level problem, max fgl(k)g P p;Q(k) NI gl(k) fp PC C (11) s:t: gl(k) fgC PG0 PC] C PG0 rg (12) gl(k) 5(NI PC C)=fp (13) gl(k)] Vl(k) (14) gl(k) 5Wu(k) (15) fg XN t h (1 f)t hQt (1 i)t (16) fp XN t h (1 f)t hQt (1 d)t (17)
where Vl(k) is the lower-bounded value of the feasible solution at the kth negotiation for the lower-level problem; Wu(k) is the upper-bounded value of the feasible solution at the kth negotiation for the higher-level problem; and gl(k) and gu(k) are decision variables of the BLP problem.
Equation (4) is the objective function of the higher-level problem. It illustrates that the host utility maximizes their financial recovery rate by joining a BOT project. Furthermore, Eq. (4) shows that the higher the royalty amount collected by the government, the higher the Pg,Q (k) index. These are the constraints of the higher-level problem from Eqs. (5) to (8). Equation (5) shows that the host utility should collect the above minimum royalty level from the concessionaire in order to meet the minimum financial recovery rate PG0. Moreover, let PG0 be a constant value. Equation (6) describes that the royalty has been delivered by the private sector to the host utility which has upper-bounded values for avoiding a deficit in operation. ((NIPC C)/fp) ]0 is held, because gu(k) is a non-negative value. Equations (7) and (8) are the upper- and lower-bounded solutions for the higher-level problem, respectively.
Equation (11) is the objective function of the lower-level problem, illustrating that the private sector hopes to reduce the royalty to be paid, and to maximize its profit for each negotiation. These are constraints of the lower-level problem from Eqs. (12) to (17); and the meanings of Eqs. (12) and (13) are the same as those of Eqs. (5) and (6); and the illustration of Eqs. (14) and (15) is also the same as those of Eqs. (7) and (8). Equations (16) and (17) are the discount factors of the decision variables for the higher-level and lower-level problems, respectively.
3.3. Algorithm for bi-level programming (BLP)
Many algorithms for the BLP problem including the vertex enumeration or the KuhnTucker transformation approach have been proposed for finding the optimal
solution (Wen and Hsu 1991, Liu and Stephen 1994). The vertex enumeration approach involves the simplex algorithm for finding the feasible solution for the higher-level problem of the BLP problem, whilst the KuhnTucker transformation approach converts the objective function of the lower-level problem into constraints of the higher-level problem. However, to find the comprisal solution for the level of royalty, a heuristic algorithm was developed. The steps of the heuristic algorithm are shown as follows:
Step 0: Let k 0 and k k1.
Step 1: Find the feasible solution for the higher-level problem. Step 2: Find the feasible solution for the lower-level problem.
Step 3: Converge the test for these feasible solutions for the BLP problem. If all of the solutions converge, then it is the comprisal solution; otherwise, go to Step 4.
In this step, we set the convergence test based on the differences in the royalty amount the government and that the private sector are willing to pay being smaller than the level of error tolerated. The condition is defined as:
j
gu(k) fg gl(k) fpgl(k) fp
j
5 d andj
gu(k) fg gl(k) fp
gu(k) fg
j
5 d (18) where d is the error tolerated; and d 0.01. If the solutions of BLP satisfy the convergence test condition, then the royalty negotiation was ceased.Step 4: Set initial concession rates for the two parties, and let k "0. Substitute concession rates into Eqs. (17)(20), and find Vl(k1) and Wu(k1).
Step 5: Find the concession rates at the next negotiation, ru(k1), rl(k1), and find gl(k1) and gu(k1).
Step 6: Repeat Steps 05. The solution of the BLP problem will be obtained if the solution from convergence testing holds, if not, there is no solution, and thus stop the algorithm.
The learning effect, concession rate and time value discount of players are very important impact factors for the bargaining process (Cross 1965). These factors have been introduced into studies of the BOT bargaining model (Lin and Chiang 2005, Shen et al. 2007). Following the concept of Cross (1965), we defined the concession rate of the government and the private firm, respectively. The concession rates for both parties are shown in Eqs. (19) and (20), respectively.
ru(k) (buvrl(k 1) (ab(1 v 2) (1 u 2) uv)ru(k 1)) (ab (1 u 2) (1 v 2) uv) (19)
rl(k) (auvru(k 1) (ab(1 u 2) (1 v 2) uv) rl(k 1)) (ab (1 u 2) (1 v 2) uv) (20)
Where ru(k) and rl(k) are concession rates at the kth negotiation for higher-level and lower-level programming problems, respectively; similarly, ru(k1) and rl(k1) are the concession rates at the (k1)th negotiation. Variables of a and b are the time value discounts of the higher-level and lower-level programming problems, respectively. Let a and b be constant values. Let m and n to be the learning rates for higher-level and lower-level programming problems, respectively. Assume m and n are constant. Equation (19) demonstrates that the concession rate at the kth negotiation for the higher-level programming problems were affected by rl(k1), ru(k1), u, v, a, and b. Similarly, rl(k) in Eq. (20) it was affected by rl(k1), ru(k1), u, v, a, and b. This implies that the royalty negotiation between the host utility and concessionaire was reflected by the concession rate of both parties. Then, Eqs. (19) and (20) were substituted into Eqs. (21)(24) and Wu(k1) and Vl(k1) of higher-level and the lower-level programming were modified, respectively.
Wu(k1) Wu(k) Wu(k) ru(k) (21) Vl(k1) Vl(k)Vl(k) ru(k) (22) Wu(k1) Wu(k) Wu(k) rl(k) (23) Vl(k1) Vl(k)Vl(k) rl(k) (24) Where Wu(k) and Vl(k) are the upper- and lower-bounded value at the kth negotiation for higher-level and the lower-level programming, respectively. Wu(k1) and Vl(k1) are the upper- and lower-bounded value at the (k1)th negotiation, respectively. 4. Case study
4.1. Background of Taipei Port Container Logistic BOT Project
A case study using financial data from the Container Terminal in Taipei Port BOT Project was conducted to illustrate the application of the proposed model. According to the Terms of Reference (TOR) of Concessions of the Container Terminal in Taipei Port issued by the Keelung Harbor Bureau in 2000, some of the key points of this project are described as follows:
(a) The scope of this BOT project includes seven wharves in the container terminal.
(b) The duration of the concession period of this project is 50 years. The construction period would be from 2001 to 2010. According to the TOR of this BOT project, the concessionaire will construct seven wharves, among which wharves 6 and 7 (W6 and W7) would be completed first at the end of 2004 and commence operation in the beginning of 2005. W6W9 and the container yard would be completed at the end of 2007. All the other wharves, W10W12, would be completed by the end of 2010 and commence operation in 2011.
(c) The annual container handling volume of W6 and W7 from 2005 to 2006 is assumed to be 500,000 twenty-foot equivalent units (TEUs) containers. By 2008, the assumed annual container handling volume for four wharves would be 1,000,000 TEUs. From 2011 to 2050, the end of the concession period, the seven wharves would maintain 1,750,000 TEUs.
(d) The basic corporate income tax rate is 25%; however, according to the AFPPIP, the concessionaire could have corporate income tax exemption for up to 5 years. Therefore, it was assumed that the tax exemption period would be between 2005 and 2009.
(e) The interest rate of government bonds is assumed to be 8%. The annual inflation rate is assumed to be 3.5%.
(f) Some of the items and assumptions of this BOT project are summarized in Table 1.
According to Table 1, the construction period is from 2001 to 2004 (n 3), and the operating period is from 2005 to 2050 during which royalty collection begins in 2011; hence h 0. According to the TOR of this BOT project, the private-sector investment rate of the total investment is 94% and the government investment rate of the total investment is 6%. On the other hand, the government investment items such as construction of access roads, land acquisition, and basic utility infrastructures are assumed to account for 10% of the total cost of this project, which is approximately NT$653 million, L 653; where L is the sum of the present value of the part of construction cost which the government agrees to pay. Moreover, it was assumed
Table 1. Summary of TOR of Container Terminal in Taipei Port BOT Project.
Items Summary
Concession period 50 years
Implementation schedule Contract negotiation phase: 2001, construction
period: 20012007, operating period: 20052050
Wharves 7 wharves
Total project installation cost (including government-related costs)
$US332.14 million (2001 currency)
Project volume a. 20052006, for 2 wharves: 0.5 million TEU/year
b. 2007, for 3 wharves: 0.8 million TEU/year c. 2008, for 4 wharves: 1.0 million TEU/year d. 20112050, for 7 wharves: 1.75 million TEU/year
Concession scope a. Seven wharves and storage yard with exclusive
operation rights and land superficies b. Operation scope: vessel berthing, container
loading/unloading, trans-shipping, transporta-tion, warehouse and storage, and container repair business
Interest rate of government bonds 8%
Corporate income tax exemption Maximum of 5 years, exemption period 20052009 corporate income tax rate is 25%
Subsidy No subsidy
Sources: Terms of Reference (TOR) of ‘Concessions of Container Terminal in Taipei Port.’
that the discount rate is 10%, d 10%, and the annual cash flow occurs at the end of each year.
As for the concession rate, when Cross (1965) proposed the Concession Rate Formula, he assumed that the concession rate of players I and II is given in an application of the bargaining model. Following the concept of Cross (1965) and Lin and Chiang (2005), it was also assumed that the concession-rate values of both government and private sectors are constant. Hence, it was assumed that the initial concession rate of the government and the private firm are 20% and 17%, respectively. Furthermore, it was assumed that the time value discount rate and the learning rate are the same for both parties that is, a b 0.2 and m n 0.1 (Cross 1965, Lin and Chiang 2005).
4.2. Results of model application
The financial data of this BOT project were substituted into the BLP problem and the algorithm was implemented; both LINGO and MATLAB programming were used, which involved the heuristic algorithm, to simulate the bargaining process for royalty negotiation for both parties.
The initial solution of the higher-level programming is gu(k 0) 0.0001 whilst that of the lower-level programming is gl(k 0) 0.0019%. The gu(k 0) 0.0001 value illustrates that the government first wants to receive the royalty from 0.01% of the operation quantity during the period from the concessionaire according to the announced TOR of this project. However, gl(k 0) 0.0019%, which shows that the private firm pays only 0.0019% of the operating quantity to the government. The convergence test is not held because
j
0:01% fg 0:0019% fp0:0019% fp
j
0:01 andj
0:01% fg 0:0019% fp0:01% fg
j
0:01: Then, substitute the assumed concession rates of ru(k 0) 20% and rl(k 0) 17%, time value discount rates of a 0.2 and b 0.2, and learning rates of m 0.1 and n 0.1 into Eqs. (17)(22) to modify the concession rate the next negotiation for two parties. Steps 05 of the algorithm were repeated. Results are shown in Table 2.As reported in Table 2, the solutions are gu(k 5) 0.0000386 and gl(k 5) 0.0000386 for the higher-level and lower-level programming, respectively. As shown, the convergence test solution for the BLP problem was held. Therefore, the
Table 2. Result of simulated royalty negotiation. Number of negotiation ru(k) rl(k) gu(k) gl(k) PG,Q(k) PP,Q(k) k 0 0.2000 0.1700 0.001 0.000019 12.7976 1.0843 k 1 0.1853 0.1608 0.00008 0.0000222 12.4258 1.0815 k 2 0.1719 0.1520 0.0000652 0.0000258 12.1503 1.0784 k 3 0.1596 0.1432 0.000054 0.0000297 11.9420 1.0750 k 4 0.1484 0.1350 0.0000454 0.000340 11.7878 1.0714 k 5 0.1380 0.1270 0.0000386 0.0000386 11.6567 1.0675
royalty negotiation for the two parties finished at k 5. The results obtained imply that the government and the private firm make a compromise royalty solution. As a consequence, the government can collect the royalty which is computed by 0.00386% of the operating quantity of this BOT project from the concessionaire. At the same time, the objective function values, PG,Q(k 5) 11.6567 and PP,Q(k 5) 1.0675, for the two parties were found, respectively. Results show that the government can get the government finance recovery ratio 11.6567 times of its investment cost and the concessionaire has an operational benefit of 1.0675 based on the royalty negotiation process for BOT projects. In addition, the concession rates of ru(k 5) 0.1380 and rl(k 5) 0.1270 for the government and the private firm were also obtained, respectively. It reveals that the decrease in the concession rates of the two parties contributes to successful royalty negotiations.
In addition, Table 2 indicates the relationship between the royalty and the number of negotiations. PG,Q(k) decreased from 12.7976 to 11.6567 when the number of negotiations increases. Similarly, PP,Q(k) decreased from 1.0843 to 1.0675 as k increased. It shows that the royalty for the host utility decreases as the number of negotiations increases. In contrast, the royalty the concessionaire is willing to pay increases when the number of negotiations increases. Clearly, we are able to conclude that changes in the concession rates of two parties affect the number of negotiations necessary. At the same time, those concession rates of the two parties affect change in PG,Q(k) and PP,Q(k). Furthermore, it can be shown that the royalty of concern to the host utility decreases when the number of negotiations increases. Conversely, the royalty the concessionaire is willing to pay increases when the number of negotiations increases. In addition, Table 2 shows that changes in concession rates of both parties affect the number of negotiations. At the same time, the concession rates of both parties affect changes in PG,Q(k) and PP,Q(k).
4.3. Sensitivity analysis
As reported in Table 2, changes in the concession rate of both parties will lead to variations in PG,Q(k), PP,Q(k), gu(k), and gl(k). Therefore, in this section, a sensitivity analysis among ru(k), rl(k), PG,Q(k), PP,Q(k), gu(k), and gl(k) was conducted. Two cases are considered: firstly, where ru(k) is fixed but rl(k) varies; and secondly where ru(k) varies whilst rl(k) remains fixed.
4.3.1. Case 1: ru(k) is fixed whilst rl(k) varies
As Table 3 indicates, a change in rl(k) can be classified into two conditions: a decrease and a subsequent increase in rl(k) whilst ru(k) remains constant. A decrease in rl(k) with ru(k) kept constant will increase the number of negotiations k for the royalty game. Conversely, increasing rl(k) whilst ru(k) is kept constant will decrease the number of negotiations k. If the concession rate of the private firm decreases rapidly, PG,Q(k) will increase. However, both gu(k) and gl(k) will decrease, when rl(k) changes with ru(k) kept constant. PP,Q(k) decreased from 1.0760 to 1.0576 whilst rl(k) increased from 0.04 to 0.42 as the PG,Q(k) increased from 11.4910 to 11.8933.
4.3.2. Case 2: ru(k) varies whilst rl(k) is fixed
Similarly, sensitivity analysis was conducted as ru(k) varies whilst rl(k) is kept constant. This case can also be classified into two conditions, manipulating ru(k) by increasing and decreasing it as rl(k) remains constant. Results of this analysis are summarized in Table 4. Table 4 shows that a decrease in ru(k) with rl(k) kept constant will increase the number of negotiations k. However, an increase in ru(k) with rl(k) kept constant will decrease the number of negotiation k decreases. At the same time, PG,Q(k) decreased when the ru(k) increased rapidly; but PP,Q(k) increased when the ru(k) increased. Results of Table 4 show that PP,Q(k) increased from 1.0515 to 1.0745 whilst PG,Q(k) decreased from 12.0209 to 11.5040 as ru(k) increased from 0.04 to 0.36.
As shown above, changes in the concession rate for both parties affect the number of negotiations. In other words, if either party keeps the concession-rate constant, the negotiation for royalty will not be easily settled, and the number of negotiations required will increase.
5. Conclusions
Whilst few studies have explored royalty negotiations for BOT projects, some research has proposed a variety of royalty formulae to evaluate royalty amounts or franchise fees for a BOT project. Despite this, the royalty negotiation process is one of the many critical negotiation items of a concession contract. This paper has not only developed a royalty negotiation model for BOT projects, but also developed the heuristic algorithm for the BLP problem for the government and the private sector. In addition, the factors incorporated into the heuristic algorithm for the BLP problem include the concession rate, learning rate, and the time value discount rate
Table 4. Result of sensitivity analysis for the case of varying ru(k) and fixing rl(k).
Items k gu(k) gl(k) PG,Q(k) PP,Q(k) ru(k) 0.04, rl(k) 0.17 12 0.0000582 0.0000572 12.0209 1.0515 ru(k) 0.09, rl(k) 0.17 9 0.0000502 0.0000493 11.8748 1.0584 ru(k) 0.12, rl(k) 0.17 8 0.0000460 0.0000459 11.7939 1.0611 ru(k) 0.2, rl(k) 0.17 6 0.0000386 0.0000386 11.6567 1.0675 ru(k) 0.26, rl(k) 0.17 5 0.0000352 0.0000346 11.5938 1.0709 ru(k) 0.36, rl(k) 0.17 4 0.0000304 0.0000304 11.5040 1.0745
Table 3. Result of sensitivity analysis for the case of fixed ru(k) and changed rl(k).
Items k gu(k) gl(k) PG,Q(k) PP,Q(k) ru(k) 0.2, rl(k) 0.04 9 0.0000293 0.0000289 11.4910 1.0760 ru(k) 0.2, rl(k) 0.07 8 0.0000319 0.0000314 11.5319 1.0738 ru(k) 0.2, rl(k) 0.11 7 0.0000348 0.0000342 11.5858 1.0711 ru(k) 0.2, rl(k) 0.17 6 0.0000386 0.0000386 11.6567 1.0675 ru(k) 0.2, rl(k) 0.25 5 0.0000436 0.0000429 11.7579 1.0641 ru(k) 0.2, rl(k) 0.42 4 0.0000510 0.0000501 11.8933 1.0576
for both parties. This paper also presented a case study with data from the Taipei Port Container Logistic BOT Project.
The results of this study showed that the two parties involved finish the concession negotiation at the sixth negotiation, that is k 5, the profit index of the concessionaire is 1.0675, PP,Q(k 5) 1.0675 and the government finance recovery rate is 11.6567, PG,Q(k 5) 11.6567. The government can receive the royalty which is calculated as 0.00386% of the operating quantity of this BOT project from the concessionaire. It reveals that the government can receive the government finance recovery ratio at 11.6567 times of its investment cost and the concessionaire has operation benefit based on the royalty negotiation process for the BOT project. In addition, variations in the concession rate, learning rate, and time value discount rate of the two parties also affect the algorithm of the BLP problem. It shows that the royalty negotiation model developed here could be employed to explain behavior during negotiations.
There are three issues found in this study which need to be further explored in future studies: (1) some assumptions of this model can be substituted to modify the proposed model, in addition, the concession rate, learning rate, and time value discount rate of this model can be re-examined; (2) the royalty negotiation issue for the two parties, the multiple issues of the bargain model and multi-level program-ming problem can be developed in order to explore multiple parties and multiple negotiation issues for BOT projects; and (3) the mixed royalty negotiation model, including both fixed and flexible royalty model, is also worthy of investigation.
Acknowledgements
The authors would like to thank the National Science Council of the Republic of China for financially supporting this research under Contract No. NSC 92-2416-H-126-005.
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