6.1.7 Models for optimizing contract period

While common financial management techniques can help project the pay-back period (PBP) of the scheme, the risks associated with the prospective incomes and expenditures must be duly considered to reflect the possible changes in market condition and external environment. To shortcut the decision process, decision-makers may rely on the PBP and value-for-money tests to determine the concession period for a PPP project. With the ability to predict the consequences under different circumstances, models can be conducted to unveil the effects of risks on the concession period. Based on the expected rate of return, decision-makers can establish the corresponding concession period distribution based on the projected costs and revenues of the project.

Like any other capital investment programs, a PPP project must be financial viable and a scheme would be considered attractive to the concessionaire only if it attains a reasonable return rate. Consequently, a number financial evaluation techniques such as the cost- benefit analysis, net present value (NPV), NPV-at-risk, public sector comparator and so on have been initiated. Using conventional NPV methods the PBP is calculated by discounting the net cash flow of the investment, and an investment is paid back when the NPV is equal to zero. In the absence of any uncertainty in the cash flow estimation, the PBP is an ideal concession period for the scheme, as the concessionaire will gain a desirable financial return (see figure below). Therefore, the government would be inclined to count on the PBP to determine the concession period of PPP projects.

Relationship between concession period and NPV

Source: Adapted from Ng et al. 2007.

It is important to model and optimize contract periods to ensure that variables pertaining to cost, performance and management are met for the duration of the contract. This enables to have a clear timetable of results oriented framework for the entire PPP life cycle.

However, cash flow estimation is overshadowed by risks and uncertainties such as fluctuations in interest rate, inflation, cost and revenue. These issues could have profound effects on PBP prediction. But there are mechanisms in the concession contract that allow the concessionaire to increase the toll/tariff (rather than extending the concession period), if they can provide evidence that their revenue falls short of the anticipated level during the operation stage. Many public clients are trying to develop a better toll/tariff adjustment mechanism for their PPP projects. For instance, the toll/tariff can be automatically adjusted according to some occurrences that would have been stipulated by the both parties. To avoid the financial risks from being transferred to the government or users, an appropriate concession period with due consideration of the effect of risks and uncertainties on the return rate of concessionaire would be indispensable.

Ng et al (2007) developed a theoretical model that could cater for the complex implication of various risks associated with PPP projects. In this model, the concession period is an output rather than an input parameter. Since the attainment of a desirable return is the most important consideration, it is sensible to assume that a reasonable toll/tariff regime and an expected internal return rate (IRR) can be established in advance. By inputting the toll/tariff regime and the IRR into the simulation model, the exact concession period in each simulation cycle can be computed according to the simulated cost and revenue. With sufficient numbers of iteration, a frequency distribution curve related to the concession.

A list of deterministic and uncertain parameters is considered as essential for estimating the concession period. The deterministic parameters include the construction period (Tc), discount rate and toll/tariff regime. In contrast, the cost (Ct), operation income (It) and revenue (Rt) are considered as uncertain parameters in the simulation process. Ng et al (2007) conducted a simulation using the above mentioned model to estimate the concession period which is useful for decision-makers.

The results of simulation showed that by considering the minimum, expected and maximum IRR, a concession period that is less risky to the concessionaire can be identified. Furthermore, the simulation model also allows the decision-makers to establish the sensitivity of some parameters (e.g. toll/tariff regime, IRR, etc.) to the concession period and thereby providing them with a basis for negotiation. These and other models illustrate the importance of recognizing deterministic parameters when designing a contract so that the basic principles of benefits and risk allocation are clearly outlined. This helps to standardize certain commercial principles, and reduce risks and conflicts that emerge during the life-cycle of the PPP.

Transparency of the term of the contract duration

[Brazil: Lei 11.079, Art. 5]

The clauses of public-private partnership contracts shall be in accordance with the provisions of art. 23 of Act 8987, dated February 13th, 1995, as applicable, and shall also state:

I - the term of the contract, which shall be in line with the amortization of the investments to be made by the private partner, not shorter than 5 (five), and not longer than 35 (thirty-five) years, including possible extensions;

[Mexico: Acuerdo Secretaria de Hacienda Diario Oficial 9 Abril 2004]

20. Las dependencias y entidades deberán presentar las solicitudes de autorización de proyectos para prestación de servicios ante la Secretaría, a través de las Direcciones Generales de Programación y Presupuesto sectoriales. En el caso de entidades sectorizadas, la solicitud deberá ser presentada por la dependencia coordinadora de sector y, en el caso de las entidades no sectorizadas, la solicitud deberá presentarse por la entidad, directamente a las citadas Direcciones Generales.

21. Las solicitudes a que se refiere el numeral anterior deberán acompañarse de la siguiente información:

VI. Los elementos principales que contendrá el contrato de servicios de largo plazo que se celebraría entre la dependencia o entidad contratante y el inversionista proveedor, incluyendo:

b) La duración del contrato;

27. LA solicitud de autorización, las dependencias y entidades deberán anexar los siguientes documentos:

I. El proyecto de contrato de servicios de largo plazo, que deberá contener, entre otros términos y condiciones, los establecidos en la fracción VI del numeral 21, así como los siguientes:

a) El plazo para dar inicio a la prestación de los servicios;

f) Las condiciones para la modificación y prórroga del contrato;

Model for estimating Optimal Concession Period under risky contracts of PPPs

Source: Adapted from Ng et al 2007.

Application to the Optimal Concession Period Simulation in Hong Kong

The simulation is useful to categorize different contract period scenarios. This simulation, consisting in different phases of data entry, used inormation from annual traffic flow of crossing harbor tunnel in Hong Kong. Having established the deterministic and uncertain parameters, the simulation can proceed by inputting these parameters. With the simulation results, the public partner can determine a concession period that would guarantee the concessionaire to gain the anticipated IRR under the proposed toll/tariff regime with a particular confidence level. For instance, the government might wish to fix the concession period to 17 years, as there is a 80% confidence that the concessionaire can attain the desired return rate.

However, in order to ensure a probability of not less than 90% to realize the designated IRR, the concession period must be set at 18 years.

Cumulative probability of concession period

Year

13

14

15

16

17

18

19

20

21

IRR

0.001

0.020

0.152

0.497

0.804

0.944

0.988

0.999

1.000

In order to conduct the second phase of the simulation, the following aspects must be defined:

• The construction period (5 years)

• The construction cost ($100,000,000 [which are apportioned in accordance with a 5-year construction period at 10%, 20%, 30%, 20% and 20% respectively])

• The annum operation and maintenance cost (15% of the annum operation revenue)

• The estimated traffic volume and proposed toll regime

• The discount rate (14%)

• The concession period (15 years)

Estimated traffic volume and proposed toll regime

Vehicle type

Estimated number of vehicles (million)

Estimated annual growth rate (%)

Basic toll rate per trip ($)

Cars/vans

0.47

5

10

Buses

0.51

4

20

Trucks

0.26

5

20

Motorbikes

3.71

5

2

Other assumptions for the model:

• Inflation rate - the rate of change follows a normal distribution with mean and standard deviation equivalent to 2.5% and 2% respectively

• Traffic flow - the estimated average annual traffic volume follows a normal distribution with standard deviation equal to 20% of the first year's traffic volume.

• Operation cost - the annum operation and maintenance costs follow a uniform distribution in an interval [0.13, 0.17]

It is apparent that the cumulative probabilities of the IRR min, IRR expected and IRR max in the 15th year are 0.551, 0.149 and 0.012 respectively. The results illustrate that the initial decision of fixing the concession period to 15 years is indeed rather risky to the concessionaire, as such a period can only just ensure the expected IRR (IRR expected = 14%) be realized at a probability of 14.9%. In other words, there is 85.1% possibility that the IRR will not reach the expected level.

Cumulative probability of concession period to realize different IRR

IRR

Year

13

14

15

16

17

18

19

20

21

22

23

24

25

26

IRRmin

0.004

0.129

0.551

0.878

0.982

0.998

1

1

1

1

1

1

1

1

IRRexpected

0

0.013

0.149

0.480

0.798

0.941

0.986

0.996

1

1

1

1

1

1

IRRmax

0

0

0.012

0.094

0.338

0.605

0.804

0.914

0.964

0.984

0.994

0.998

0.999

1

Source: Ng et al. 2007.