Concession Length and Investment Timing Flexibility Chiara D’Alpaos, Cesare Dosi and Michele...
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Transcript of Concession Length and Investment Timing Flexibility Chiara D’Alpaos, Cesare Dosi and Michele...
Concession Length and Investment Timing Flexibility
Chiara DrsquoAlpaos Cesare Dosi and Michele Moretto
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 (eg 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
Concession contracts (2)
The goverment objective function is to maximize the concession value ie 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
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 (ie the value of the contract) when the concessionaire has no obligation about the investment timing
The model
We simplified McDonald and Siegelrsquos 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 Tc years
3 the investment exercise time is ( Tc)
Π=ΠdzΠσ+dtΠ)δr(=Πd 0tttt
4 the investment entails a sunk capital cost I
5 the residual value S is
)cT(ξIeS --
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)
)cT)(ξr()cT(δ
)cT(rt
rtcT0
Ie)e1(δΠ
SedtΠeE)Π(V
The value of the opportunity to invest F (ie the Extended Net Present Value) is analogous to a European call option on a dividend paying asset 0I)Π(VmaxeE τ
)t(rtt )t)tΠ(F
where )e1()Π(V )cT(δδΠ )e1(II )cT)(ξr(
is the expiration date and is the projectrsquos cash flow at time
The model (3)
Imposing a non-arbitrage condition F (Vtt) can be obtained by solving the following second order differential equation (Black and Scholes 1973 Merton 1973)
0FrFF)V)(δr(F)V(σ21
tVVV22
subject to the terminal condition (DrsquoAlpaos and Moretto 2004)
and the boundary conditions
1V)tV(Flim0)t0(F ttV
0]0)I)Π(V[(maxlim)Π(FlimcT
τcT
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
I)d(Φe)Π(V)d(Φe)tΠ(F 2)t(r
t1)t(δ
t
tσ
)t)(2σδr()I)Π(Vln()Π(d
2t
t1
tσ)Π(d)Π(d t1t2
The Reform of the Italian Water Service Sector
The Law 3694 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
The case of a water abstraction plant Letrsquos 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 NPV1=0 Therefore we will not consider alternative 1
The case of a water abstraction plant (2) Assuming a profit function linear in X we obtain
where Rt are the revenues per cubic meter Ct the operating costs for cubic meter X is the plantrsquos capacity (m3) i volume losses in the network
We make the following assumptions
XCX)i1(RΠ ttt
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
tttt dzCσdtC)δr(dC
c) the risk free discount rate is constant over time
d) the projectrsquos residual value at the end of its lifetime is zero
The case of a water abstraction plant (3) Therefore
bullX=03 m3s
bullI=3500000 Euros
bullTc=30 years
bullC=013 Eurom3 R=030 Eurom3
bulli=20 =2 r=5 =30
X)e1(
δC
e1r
R)i1(
Xdt]CR)i1[(eEV
)cT(δ)cT(r
ttrtcT
0
I)d(Φe)Π(V)d(Φe)tΠ(F 2)t(r
t1)t(δ
t
and
Summary information for the water abstraction plant
The concession value F is concave in
Figure 1 Concession value for different Tc
The case of an abstraction plant results
Figure 2 Concession value for different and Tc
The case of a water abstraction plant results (2)
In order to maximize the concession value should determine the couple )T( c
that maximizes F
F
F
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
Concluding Remarks (2) In fact there is not a monotone relationship between F and Tc
Investment timing flexibility not always increases the concession value
Under a short-term contract it might become optimal to invest immediately (NPV F)
Tc affects the optimal investment timing Therefore if the concession contact is ldquotoo longrdquo the concessionaire might be forced to defer investments in order to reduce uncertainty over future returns
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
-
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 (eg 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
Concession contracts (2)
The goverment objective function is to maximize the concession value ie 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
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 (ie the value of the contract) when the concessionaire has no obligation about the investment timing
The model
We simplified McDonald and Siegelrsquos 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 Tc years
3 the investment exercise time is ( Tc)
Π=ΠdzΠσ+dtΠ)δr(=Πd 0tttt
4 the investment entails a sunk capital cost I
5 the residual value S is
)cT(ξIeS --
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)
)cT)(ξr()cT(δ
)cT(rt
rtcT0
Ie)e1(δΠ
SedtΠeE)Π(V
The value of the opportunity to invest F (ie the Extended Net Present Value) is analogous to a European call option on a dividend paying asset 0I)Π(VmaxeE τ
)t(rtt )t)tΠ(F
where )e1()Π(V )cT(δδΠ )e1(II )cT)(ξr(
is the expiration date and is the projectrsquos cash flow at time
The model (3)
Imposing a non-arbitrage condition F (Vtt) can be obtained by solving the following second order differential equation (Black and Scholes 1973 Merton 1973)
0FrFF)V)(δr(F)V(σ21
tVVV22
subject to the terminal condition (DrsquoAlpaos and Moretto 2004)
and the boundary conditions
1V)tV(Flim0)t0(F ttV
0]0)I)Π(V[(maxlim)Π(FlimcT
τcT
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
I)d(Φe)Π(V)d(Φe)tΠ(F 2)t(r
t1)t(δ
t
tσ
)t)(2σδr()I)Π(Vln()Π(d
2t
t1
tσ)Π(d)Π(d t1t2
The Reform of the Italian Water Service Sector
The Law 3694 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
The case of a water abstraction plant Letrsquos 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 NPV1=0 Therefore we will not consider alternative 1
The case of a water abstraction plant (2) Assuming a profit function linear in X we obtain
where Rt are the revenues per cubic meter Ct the operating costs for cubic meter X is the plantrsquos capacity (m3) i volume losses in the network
We make the following assumptions
XCX)i1(RΠ ttt
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
tttt dzCσdtC)δr(dC
c) the risk free discount rate is constant over time
d) the projectrsquos residual value at the end of its lifetime is zero
The case of a water abstraction plant (3) Therefore
bullX=03 m3s
bullI=3500000 Euros
bullTc=30 years
bullC=013 Eurom3 R=030 Eurom3
bulli=20 =2 r=5 =30
X)e1(
δC
e1r
R)i1(
Xdt]CR)i1[(eEV
)cT(δ)cT(r
ttrtcT
0
I)d(Φe)Π(V)d(Φe)tΠ(F 2)t(r
t1)t(δ
t
and
Summary information for the water abstraction plant
The concession value F is concave in
Figure 1 Concession value for different Tc
The case of an abstraction plant results
Figure 2 Concession value for different and Tc
The case of a water abstraction plant results (2)
In order to maximize the concession value should determine the couple )T( c
that maximizes F
F
F
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
Concluding Remarks (2) In fact there is not a monotone relationship between F and Tc
Investment timing flexibility not always increases the concession value
Under a short-term contract it might become optimal to invest immediately (NPV F)
Tc affects the optimal investment timing Therefore if the concession contact is ldquotoo longrdquo the concessionaire might be forced to defer investments in order to reduce uncertainty over future returns
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
-
Concession contracts (2)
The goverment objective function is to maximize the concession value ie 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
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 (ie the value of the contract) when the concessionaire has no obligation about the investment timing
The model
We simplified McDonald and Siegelrsquos 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 Tc years
3 the investment exercise time is ( Tc)
Π=ΠdzΠσ+dtΠ)δr(=Πd 0tttt
4 the investment entails a sunk capital cost I
5 the residual value S is
)cT(ξIeS --
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)
)cT)(ξr()cT(δ
)cT(rt
rtcT0
Ie)e1(δΠ
SedtΠeE)Π(V
The value of the opportunity to invest F (ie the Extended Net Present Value) is analogous to a European call option on a dividend paying asset 0I)Π(VmaxeE τ
)t(rtt )t)tΠ(F
where )e1()Π(V )cT(δδΠ )e1(II )cT)(ξr(
is the expiration date and is the projectrsquos cash flow at time
The model (3)
Imposing a non-arbitrage condition F (Vtt) can be obtained by solving the following second order differential equation (Black and Scholes 1973 Merton 1973)
0FrFF)V)(δr(F)V(σ21
tVVV22
subject to the terminal condition (DrsquoAlpaos and Moretto 2004)
and the boundary conditions
1V)tV(Flim0)t0(F ttV
0]0)I)Π(V[(maxlim)Π(FlimcT
τcT
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
I)d(Φe)Π(V)d(Φe)tΠ(F 2)t(r
t1)t(δ
t
tσ
)t)(2σδr()I)Π(Vln()Π(d
2t
t1
tσ)Π(d)Π(d t1t2
The Reform of the Italian Water Service Sector
The Law 3694 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
The case of a water abstraction plant Letrsquos 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 NPV1=0 Therefore we will not consider alternative 1
The case of a water abstraction plant (2) Assuming a profit function linear in X we obtain
where Rt are the revenues per cubic meter Ct the operating costs for cubic meter X is the plantrsquos capacity (m3) i volume losses in the network
We make the following assumptions
XCX)i1(RΠ ttt
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
tttt dzCσdtC)δr(dC
c) the risk free discount rate is constant over time
d) the projectrsquos residual value at the end of its lifetime is zero
The case of a water abstraction plant (3) Therefore
bullX=03 m3s
bullI=3500000 Euros
bullTc=30 years
bullC=013 Eurom3 R=030 Eurom3
bulli=20 =2 r=5 =30
X)e1(
δC
e1r
R)i1(
Xdt]CR)i1[(eEV
)cT(δ)cT(r
ttrtcT
0
I)d(Φe)Π(V)d(Φe)tΠ(F 2)t(r
t1)t(δ
t
and
Summary information for the water abstraction plant
The concession value F is concave in
Figure 1 Concession value for different Tc
The case of an abstraction plant results
Figure 2 Concession value for different and Tc
The case of a water abstraction plant results (2)
In order to maximize the concession value should determine the couple )T( c
that maximizes F
F
F
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
Concluding Remarks (2) In fact there is not a monotone relationship between F and Tc
Investment timing flexibility not always increases the concession value
Under a short-term contract it might become optimal to invest immediately (NPV F)
Tc affects the optimal investment timing Therefore if the concession contact is ldquotoo longrdquo the concessionaire might be forced to defer investments in order to reduce uncertainty over future returns
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
-
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 (ie the value of the contract) when the concessionaire has no obligation about the investment timing
The model
We simplified McDonald and Siegelrsquos 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 Tc years
3 the investment exercise time is ( Tc)
Π=ΠdzΠσ+dtΠ)δr(=Πd 0tttt
4 the investment entails a sunk capital cost I
5 the residual value S is
)cT(ξIeS --
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)
)cT)(ξr()cT(δ
)cT(rt
rtcT0
Ie)e1(δΠ
SedtΠeE)Π(V
The value of the opportunity to invest F (ie the Extended Net Present Value) is analogous to a European call option on a dividend paying asset 0I)Π(VmaxeE τ
)t(rtt )t)tΠ(F
where )e1()Π(V )cT(δδΠ )e1(II )cT)(ξr(
is the expiration date and is the projectrsquos cash flow at time
The model (3)
Imposing a non-arbitrage condition F (Vtt) can be obtained by solving the following second order differential equation (Black and Scholes 1973 Merton 1973)
0FrFF)V)(δr(F)V(σ21
tVVV22
subject to the terminal condition (DrsquoAlpaos and Moretto 2004)
and the boundary conditions
1V)tV(Flim0)t0(F ttV
0]0)I)Π(V[(maxlim)Π(FlimcT
τcT
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
I)d(Φe)Π(V)d(Φe)tΠ(F 2)t(r
t1)t(δ
t
tσ
)t)(2σδr()I)Π(Vln()Π(d
2t
t1
tσ)Π(d)Π(d t1t2
The Reform of the Italian Water Service Sector
The Law 3694 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
The case of a water abstraction plant Letrsquos 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 NPV1=0 Therefore we will not consider alternative 1
The case of a water abstraction plant (2) Assuming a profit function linear in X we obtain
where Rt are the revenues per cubic meter Ct the operating costs for cubic meter X is the plantrsquos capacity (m3) i volume losses in the network
We make the following assumptions
XCX)i1(RΠ ttt
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
tttt dzCσdtC)δr(dC
c) the risk free discount rate is constant over time
d) the projectrsquos residual value at the end of its lifetime is zero
The case of a water abstraction plant (3) Therefore
bullX=03 m3s
bullI=3500000 Euros
bullTc=30 years
bullC=013 Eurom3 R=030 Eurom3
bulli=20 =2 r=5 =30
X)e1(
δC
e1r
R)i1(
Xdt]CR)i1[(eEV
)cT(δ)cT(r
ttrtcT
0
I)d(Φe)Π(V)d(Φe)tΠ(F 2)t(r
t1)t(δ
t
and
Summary information for the water abstraction plant
The concession value F is concave in
Figure 1 Concession value for different Tc
The case of an abstraction plant results
Figure 2 Concession value for different and Tc
The case of a water abstraction plant results (2)
In order to maximize the concession value should determine the couple )T( c
that maximizes F
F
F
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
Concluding Remarks (2) In fact there is not a monotone relationship between F and Tc
Investment timing flexibility not always increases the concession value
Under a short-term contract it might become optimal to invest immediately (NPV F)
Tc affects the optimal investment timing Therefore if the concession contact is ldquotoo longrdquo the concessionaire might be forced to defer investments in order to reduce uncertainty over future returns
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
-
The model
We simplified McDonald and Siegelrsquos 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 Tc years
3 the investment exercise time is ( Tc)
Π=ΠdzΠσ+dtΠ)δr(=Πd 0tttt
4 the investment entails a sunk capital cost I
5 the residual value S is
)cT(ξIeS --
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)
)cT)(ξr()cT(δ
)cT(rt
rtcT0
Ie)e1(δΠ
SedtΠeE)Π(V
The value of the opportunity to invest F (ie the Extended Net Present Value) is analogous to a European call option on a dividend paying asset 0I)Π(VmaxeE τ
)t(rtt )t)tΠ(F
where )e1()Π(V )cT(δδΠ )e1(II )cT)(ξr(
is the expiration date and is the projectrsquos cash flow at time
The model (3)
Imposing a non-arbitrage condition F (Vtt) can be obtained by solving the following second order differential equation (Black and Scholes 1973 Merton 1973)
0FrFF)V)(δr(F)V(σ21
tVVV22
subject to the terminal condition (DrsquoAlpaos and Moretto 2004)
and the boundary conditions
1V)tV(Flim0)t0(F ttV
0]0)I)Π(V[(maxlim)Π(FlimcT
τcT
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
I)d(Φe)Π(V)d(Φe)tΠ(F 2)t(r
t1)t(δ
t
tσ
)t)(2σδr()I)Π(Vln()Π(d
2t
t1
tσ)Π(d)Π(d t1t2
The Reform of the Italian Water Service Sector
The Law 3694 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
The case of a water abstraction plant Letrsquos 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 NPV1=0 Therefore we will not consider alternative 1
The case of a water abstraction plant (2) Assuming a profit function linear in X we obtain
where Rt are the revenues per cubic meter Ct the operating costs for cubic meter X is the plantrsquos capacity (m3) i volume losses in the network
We make the following assumptions
XCX)i1(RΠ ttt
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
tttt dzCσdtC)δr(dC
c) the risk free discount rate is constant over time
d) the projectrsquos residual value at the end of its lifetime is zero
The case of a water abstraction plant (3) Therefore
bullX=03 m3s
bullI=3500000 Euros
bullTc=30 years
bullC=013 Eurom3 R=030 Eurom3
bulli=20 =2 r=5 =30
X)e1(
δC
e1r
R)i1(
Xdt]CR)i1[(eEV
)cT(δ)cT(r
ttrtcT
0
I)d(Φe)Π(V)d(Φe)tΠ(F 2)t(r
t1)t(δ
t
and
Summary information for the water abstraction plant
The concession value F is concave in
Figure 1 Concession value for different Tc
The case of an abstraction plant results
Figure 2 Concession value for different and Tc
The case of a water abstraction plant results (2)
In order to maximize the concession value should determine the couple )T( c
that maximizes F
F
F
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
Concluding Remarks (2) In fact there is not a monotone relationship between F and Tc
Investment timing flexibility not always increases the concession value
Under a short-term contract it might become optimal to invest immediately (NPV F)
Tc affects the optimal investment timing Therefore if the concession contact is ldquotoo longrdquo the concessionaire might be forced to defer investments in order to reduce uncertainty over future returns
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
-
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)
)cT)(ξr()cT(δ
)cT(rt
rtcT0
Ie)e1(δΠ
SedtΠeE)Π(V
The value of the opportunity to invest F (ie the Extended Net Present Value) is analogous to a European call option on a dividend paying asset 0I)Π(VmaxeE τ
)t(rtt )t)tΠ(F
where )e1()Π(V )cT(δδΠ )e1(II )cT)(ξr(
is the expiration date and is the projectrsquos cash flow at time
The model (3)
Imposing a non-arbitrage condition F (Vtt) can be obtained by solving the following second order differential equation (Black and Scholes 1973 Merton 1973)
0FrFF)V)(δr(F)V(σ21
tVVV22
subject to the terminal condition (DrsquoAlpaos and Moretto 2004)
and the boundary conditions
1V)tV(Flim0)t0(F ttV
0]0)I)Π(V[(maxlim)Π(FlimcT
τcT
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
I)d(Φe)Π(V)d(Φe)tΠ(F 2)t(r
t1)t(δ
t
tσ
)t)(2σδr()I)Π(Vln()Π(d
2t
t1
tσ)Π(d)Π(d t1t2
The Reform of the Italian Water Service Sector
The Law 3694 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
The case of a water abstraction plant Letrsquos 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 NPV1=0 Therefore we will not consider alternative 1
The case of a water abstraction plant (2) Assuming a profit function linear in X we obtain
where Rt are the revenues per cubic meter Ct the operating costs for cubic meter X is the plantrsquos capacity (m3) i volume losses in the network
We make the following assumptions
XCX)i1(RΠ ttt
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
tttt dzCσdtC)δr(dC
c) the risk free discount rate is constant over time
d) the projectrsquos residual value at the end of its lifetime is zero
The case of a water abstraction plant (3) Therefore
bullX=03 m3s
bullI=3500000 Euros
bullTc=30 years
bullC=013 Eurom3 R=030 Eurom3
bulli=20 =2 r=5 =30
X)e1(
δC
e1r
R)i1(
Xdt]CR)i1[(eEV
)cT(δ)cT(r
ttrtcT
0
I)d(Φe)Π(V)d(Φe)tΠ(F 2)t(r
t1)t(δ
t
and
Summary information for the water abstraction plant
The concession value F is concave in
Figure 1 Concession value for different Tc
The case of an abstraction plant results
Figure 2 Concession value for different and Tc
The case of a water abstraction plant results (2)
In order to maximize the concession value should determine the couple )T( c
that maximizes F
F
F
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
Concluding Remarks (2) In fact there is not a monotone relationship between F and Tc
Investment timing flexibility not always increases the concession value
Under a short-term contract it might become optimal to invest immediately (NPV F)
Tc affects the optimal investment timing Therefore if the concession contact is ldquotoo longrdquo the concessionaire might be forced to defer investments in order to reduce uncertainty over future returns
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
-
The model (3)
Imposing a non-arbitrage condition F (Vtt) can be obtained by solving the following second order differential equation (Black and Scholes 1973 Merton 1973)
0FrFF)V)(δr(F)V(σ21
tVVV22
subject to the terminal condition (DrsquoAlpaos and Moretto 2004)
and the boundary conditions
1V)tV(Flim0)t0(F ttV
0]0)I)Π(V[(maxlim)Π(FlimcT
τcT
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
I)d(Φe)Π(V)d(Φe)tΠ(F 2)t(r
t1)t(δ
t
tσ
)t)(2σδr()I)Π(Vln()Π(d
2t
t1
tσ)Π(d)Π(d t1t2
The Reform of the Italian Water Service Sector
The Law 3694 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
The case of a water abstraction plant Letrsquos 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 NPV1=0 Therefore we will not consider alternative 1
The case of a water abstraction plant (2) Assuming a profit function linear in X we obtain
where Rt are the revenues per cubic meter Ct the operating costs for cubic meter X is the plantrsquos capacity (m3) i volume losses in the network
We make the following assumptions
XCX)i1(RΠ ttt
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
tttt dzCσdtC)δr(dC
c) the risk free discount rate is constant over time
d) the projectrsquos residual value at the end of its lifetime is zero
The case of a water abstraction plant (3) Therefore
bullX=03 m3s
bullI=3500000 Euros
bullTc=30 years
bullC=013 Eurom3 R=030 Eurom3
bulli=20 =2 r=5 =30
X)e1(
δC
e1r
R)i1(
Xdt]CR)i1[(eEV
)cT(δ)cT(r
ttrtcT
0
I)d(Φe)Π(V)d(Φe)tΠ(F 2)t(r
t1)t(δ
t
and
Summary information for the water abstraction plant
The concession value F is concave in
Figure 1 Concession value for different Tc
The case of an abstraction plant results
Figure 2 Concession value for different and Tc
The case of a water abstraction plant results (2)
In order to maximize the concession value should determine the couple )T( c
that maximizes F
F
F
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
Concluding Remarks (2) In fact there is not a monotone relationship between F and Tc
Investment timing flexibility not always increases the concession value
Under a short-term contract it might become optimal to invest immediately (NPV F)
Tc affects the optimal investment timing Therefore if the concession contact is ldquotoo longrdquo the concessionaire might be forced to defer investments in order to reduce uncertainty over future returns
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
-
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
I)d(Φe)Π(V)d(Φe)tΠ(F 2)t(r
t1)t(δ
t
tσ
)t)(2σδr()I)Π(Vln()Π(d
2t
t1
tσ)Π(d)Π(d t1t2
The Reform of the Italian Water Service Sector
The Law 3694 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
The case of a water abstraction plant Letrsquos 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 NPV1=0 Therefore we will not consider alternative 1
The case of a water abstraction plant (2) Assuming a profit function linear in X we obtain
where Rt are the revenues per cubic meter Ct the operating costs for cubic meter X is the plantrsquos capacity (m3) i volume losses in the network
We make the following assumptions
XCX)i1(RΠ ttt
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
tttt dzCσdtC)δr(dC
c) the risk free discount rate is constant over time
d) the projectrsquos residual value at the end of its lifetime is zero
The case of a water abstraction plant (3) Therefore
bullX=03 m3s
bullI=3500000 Euros
bullTc=30 years
bullC=013 Eurom3 R=030 Eurom3
bulli=20 =2 r=5 =30
X)e1(
δC
e1r
R)i1(
Xdt]CR)i1[(eEV
)cT(δ)cT(r
ttrtcT
0
I)d(Φe)Π(V)d(Φe)tΠ(F 2)t(r
t1)t(δ
t
and
Summary information for the water abstraction plant
The concession value F is concave in
Figure 1 Concession value for different Tc
The case of an abstraction plant results
Figure 2 Concession value for different and Tc
The case of a water abstraction plant results (2)
In order to maximize the concession value should determine the couple )T( c
that maximizes F
F
F
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
Concluding Remarks (2) In fact there is not a monotone relationship between F and Tc
Investment timing flexibility not always increases the concession value
Under a short-term contract it might become optimal to invest immediately (NPV F)
Tc affects the optimal investment timing Therefore if the concession contact is ldquotoo longrdquo the concessionaire might be forced to defer investments in order to reduce uncertainty over future returns
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
-
The Reform of the Italian Water Service Sector
The Law 3694 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
The case of a water abstraction plant Letrsquos 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 NPV1=0 Therefore we will not consider alternative 1
The case of a water abstraction plant (2) Assuming a profit function linear in X we obtain
where Rt are the revenues per cubic meter Ct the operating costs for cubic meter X is the plantrsquos capacity (m3) i volume losses in the network
We make the following assumptions
XCX)i1(RΠ ttt
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
tttt dzCσdtC)δr(dC
c) the risk free discount rate is constant over time
d) the projectrsquos residual value at the end of its lifetime is zero
The case of a water abstraction plant (3) Therefore
bullX=03 m3s
bullI=3500000 Euros
bullTc=30 years
bullC=013 Eurom3 R=030 Eurom3
bulli=20 =2 r=5 =30
X)e1(
δC
e1r
R)i1(
Xdt]CR)i1[(eEV
)cT(δ)cT(r
ttrtcT
0
I)d(Φe)Π(V)d(Φe)tΠ(F 2)t(r
t1)t(δ
t
and
Summary information for the water abstraction plant
The concession value F is concave in
Figure 1 Concession value for different Tc
The case of an abstraction plant results
Figure 2 Concession value for different and Tc
The case of a water abstraction plant results (2)
In order to maximize the concession value should determine the couple )T( c
that maximizes F
F
F
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
Concluding Remarks (2) In fact there is not a monotone relationship between F and Tc
Investment timing flexibility not always increases the concession value
Under a short-term contract it might become optimal to invest immediately (NPV F)
Tc affects the optimal investment timing Therefore if the concession contact is ldquotoo longrdquo the concessionaire might be forced to defer investments in order to reduce uncertainty over future returns
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
-
The case of a water abstraction plant Letrsquos 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 NPV1=0 Therefore we will not consider alternative 1
The case of a water abstraction plant (2) Assuming a profit function linear in X we obtain
where Rt are the revenues per cubic meter Ct the operating costs for cubic meter X is the plantrsquos capacity (m3) i volume losses in the network
We make the following assumptions
XCX)i1(RΠ ttt
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
tttt dzCσdtC)δr(dC
c) the risk free discount rate is constant over time
d) the projectrsquos residual value at the end of its lifetime is zero
The case of a water abstraction plant (3) Therefore
bullX=03 m3s
bullI=3500000 Euros
bullTc=30 years
bullC=013 Eurom3 R=030 Eurom3
bulli=20 =2 r=5 =30
X)e1(
δC
e1r
R)i1(
Xdt]CR)i1[(eEV
)cT(δ)cT(r
ttrtcT
0
I)d(Φe)Π(V)d(Φe)tΠ(F 2)t(r
t1)t(δ
t
and
Summary information for the water abstraction plant
The concession value F is concave in
Figure 1 Concession value for different Tc
The case of an abstraction plant results
Figure 2 Concession value for different and Tc
The case of a water abstraction plant results (2)
In order to maximize the concession value should determine the couple )T( c
that maximizes F
F
F
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
Concluding Remarks (2) In fact there is not a monotone relationship between F and Tc
Investment timing flexibility not always increases the concession value
Under a short-term contract it might become optimal to invest immediately (NPV F)
Tc affects the optimal investment timing Therefore if the concession contact is ldquotoo longrdquo the concessionaire might be forced to defer investments in order to reduce uncertainty over future returns
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
-
The case of a water abstraction plant (2) Assuming a profit function linear in X we obtain
where Rt are the revenues per cubic meter Ct the operating costs for cubic meter X is the plantrsquos capacity (m3) i volume losses in the network
We make the following assumptions
XCX)i1(RΠ ttt
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
tttt dzCσdtC)δr(dC
c) the risk free discount rate is constant over time
d) the projectrsquos residual value at the end of its lifetime is zero
The case of a water abstraction plant (3) Therefore
bullX=03 m3s
bullI=3500000 Euros
bullTc=30 years
bullC=013 Eurom3 R=030 Eurom3
bulli=20 =2 r=5 =30
X)e1(
δC
e1r
R)i1(
Xdt]CR)i1[(eEV
)cT(δ)cT(r
ttrtcT
0
I)d(Φe)Π(V)d(Φe)tΠ(F 2)t(r
t1)t(δ
t
and
Summary information for the water abstraction plant
The concession value F is concave in
Figure 1 Concession value for different Tc
The case of an abstraction plant results
Figure 2 Concession value for different and Tc
The case of a water abstraction plant results (2)
In order to maximize the concession value should determine the couple )T( c
that maximizes F
F
F
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
Concluding Remarks (2) In fact there is not a monotone relationship between F and Tc
Investment timing flexibility not always increases the concession value
Under a short-term contract it might become optimal to invest immediately (NPV F)
Tc affects the optimal investment timing Therefore if the concession contact is ldquotoo longrdquo the concessionaire might be forced to defer investments in order to reduce uncertainty over future returns
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
-
The case of a water abstraction plant (3) Therefore
bullX=03 m3s
bullI=3500000 Euros
bullTc=30 years
bullC=013 Eurom3 R=030 Eurom3
bulli=20 =2 r=5 =30
X)e1(
δC
e1r
R)i1(
Xdt]CR)i1[(eEV
)cT(δ)cT(r
ttrtcT
0
I)d(Φe)Π(V)d(Φe)tΠ(F 2)t(r
t1)t(δ
t
and
Summary information for the water abstraction plant
The concession value F is concave in
Figure 1 Concession value for different Tc
The case of an abstraction plant results
Figure 2 Concession value for different and Tc
The case of a water abstraction plant results (2)
In order to maximize the concession value should determine the couple )T( c
that maximizes F
F
F
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
Concluding Remarks (2) In fact there is not a monotone relationship between F and Tc
Investment timing flexibility not always increases the concession value
Under a short-term contract it might become optimal to invest immediately (NPV F)
Tc affects the optimal investment timing Therefore if the concession contact is ldquotoo longrdquo the concessionaire might be forced to defer investments in order to reduce uncertainty over future returns
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
-
The concession value F is concave in
Figure 1 Concession value for different Tc
The case of an abstraction plant results
Figure 2 Concession value for different and Tc
The case of a water abstraction plant results (2)
In order to maximize the concession value should determine the couple )T( c
that maximizes F
F
F
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
Concluding Remarks (2) In fact there is not a monotone relationship between F and Tc
Investment timing flexibility not always increases the concession value
Under a short-term contract it might become optimal to invest immediately (NPV F)
Tc affects the optimal investment timing Therefore if the concession contact is ldquotoo longrdquo the concessionaire might be forced to defer investments in order to reduce uncertainty over future returns
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
-
Figure 2 Concession value for different and Tc
The case of a water abstraction plant results (2)
In order to maximize the concession value should determine the couple )T( c
that maximizes F
F
F
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
Concluding Remarks (2) In fact there is not a monotone relationship between F and Tc
Investment timing flexibility not always increases the concession value
Under a short-term contract it might become optimal to invest immediately (NPV F)
Tc affects the optimal investment timing Therefore if the concession contact is ldquotoo longrdquo the concessionaire might be forced to defer investments in order to reduce uncertainty over future returns
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
-
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
Concluding Remarks (2) In fact there is not a monotone relationship between F and Tc
Investment timing flexibility not always increases the concession value
Under a short-term contract it might become optimal to invest immediately (NPV F)
Tc affects the optimal investment timing Therefore if the concession contact is ldquotoo longrdquo the concessionaire might be forced to defer investments in order to reduce uncertainty over future returns
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
-
Concluding Remarks (2) In fact there is not a monotone relationship between F and Tc
Investment timing flexibility not always increases the concession value
Under a short-term contract it might become optimal to invest immediately (NPV F)
Tc affects the optimal investment timing Therefore if the concession contact is ldquotoo longrdquo the concessionaire might be forced to defer investments in order to reduce uncertainty over future returns
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
-