1. Concession Length and Investment Timing Flexibility Chiara D’Alpaos, Cesare Dosi and Michele Moretto

2. Concession contracts  In recent years there has been a significant increase of private sector participation in the provision of public utilities, mainly because of the need for increased capital investments and the lack of public financial resources.  Therefore, concessions play a key role in those sectors where natural monopoly persists and competition for the market is the only viable option to achieve efficiency gains (e.g. water services).  Under concession contracts, the government retains ownership of the infrastructure but transfers all risk for running the utility and financing the investments to the concessionaire.

3. Concession contracts (2)  The goverment objective function is to maximize the concession value i.e. the value of the contract  When assigning a concession contract the regulator faces inter alia the issue of setting the concession length.  Moreover, whether or not allowing the concessionaire to set the timing of new investments is another key issue.

4. Questions addressed in the paper  Does investment timing flexibility always increase the concession value?  How should the regulator set the concession length in order to maximize the concession value (i.e. the value of the contract) when the concessionaire has no obligation about the investment timing?

5. The model  We simplified McDonald and Siegel’s model (1986) by introducing the following assumptions: 1.the investment generates an instantaneous profit flow described by a geometric Brownian motion: where r is the risk-free discount rate and r-  is the cost of carry 2.the concession contract lasts for T c years 3.the investment exercise time is  (   T c ) 4.the investment entails a sunk capital cost I 5.the residual value S is:

6. The model (2)  The market value of the project is the expected present value of discounted cash flows: where E is the expectation operator under the risk neutral probability measure (Cox and Ross, 1976; Harrison and Kreps, 1979).  The value of the opportunity to invest F (i.e. the Extended Net Present Value) is analogous to a European call option on a dividend paying asset: where  is the expiration date and   is the project’s cash flow at time 

7. The model (3)  Imposing a non-arbitrage condition, F (V t,t) can be obtained by solving the following second order differential equation (Black and Scholes, 1973; Merton, 1973): subject to the terminal condition (D’Alpaos and Moretto, 2004): and the boundary conditions:

8. The model (4)  The solution of the second order differential equation is given by (Black and Scholes, 1973): where: and  (·) is the cumulative standard normal distribution function.

9. The Reform of the Italian Water Service Sector  The Law 36/94 opened up the water service sector to competition and established a separation between water resource planning and the construction, operation and management of water utilities.  The resource planning is assigned to the local water authority (ATO), which in turn assigns the operation of water utilities to a concessionaire and fixes the tariff.

10. The case of a water abstraction plant  Let’s suppose that the contract calls for an investment in capacity expansion because of a forseeable increase in water demand.  In order to meet the contract requirements the concessionaire has two alternatives: a)provide the service by buying water via another firm (alternative 1) b)invest in capacity expansion by constructing a new water abstraction plant (alternative 2).  However, the price of traded water is established by ATOs according to solidarity and fairness criteria and we assume that the expected NPV of alternative 1 is NPV 1 =0. Therefore, we will not consider alternative 1.

11. The case of a water abstraction plant (2)  Assuming a profit function linear in X we obtain: where R t are the revenues per cubic meter, C t the operating costs for cubic meter X is the plant’s capacity (m 3 ), i volume losses in the network  We make the following assumptions: a)revenues are non stochastic since the tariffs are set by the ATO b)operating costs follow a geokmetric Brownian motion with growth rate (r-  ) and volatility  : c)the risk free discount rate is constant over time d)the project’s residual value at the end of its lifetime is zero

12. The case of a water abstraction plant (3)  Therefore : X=0.3 m 3 /s I=3,500,000 Euros T c =30 years C=0.13 Euro/m 3 R=0.30 Euro/m 3 i=20%  =2% r=5%  =30% and:  Summary information for the water abstraction plant :

13.  The concession value F is concave in  Figure 1: Concession value for different T c The case of an abstraction plant: results

14. Figure 2: Concession value for different  and T c The case of a water abstraction plant: results (2)  In order to maximize the concession value should determine the couple that maximizes F

15. Concluding Remarks  We investigated the impact of concession length and investment timing flexibility on concession value.  It is generally argued that long-term contracts are privately valuable as they allow the concessionaire to increase the overall discounted returns.  The real option theory suggests that investments timing flexibiltiy has a value, making it possible to avoid costly errors.  Our results suggest that it is not always the case.

16. Concluding Remarks (2)  In fact there is not a monotone relationship between F and T c  Investment timing flexibility not always increases the concession value.  Under a short-term contract it might become optimal to invest immediately (NPV  F).  T c affects the optimal investment timing. Therefore, if the concession contact is “too long”, the concessionaire might be forced to defer investments in order to reduce uncertainty over future returns.