Transcript Document

Lecture Notes
ECON 437/837: ECONOMIC COSTBENEFIT ANALYSIS
Lecture Ten
0
MEASUREMENT OF
COSTS AND BENEFITS OF
TRANSPORTATION
INVESTMENTS
1
Economic Benefits of
Transportation Projects
1) Improvement of existing mode
- Example of a road
2) Introducing new modes of transportation
- Example of a Buenos Aires-Colonia
bridge
2
Cost Benefit Analysis of Transportation Projects
-- Road Improvement Benefits --
• Cost Savings for Existing Traffic
- Savings in Vehicle Operation and
Maintenance Costs
- Savings of Time
• Cost Savings for Newly Generated Traffic
3
Cost Savings for Existing and New Traffic
Cost Savings for
Existing Traffic
Di
Cost per vehiclemile for type i
E
cit
c`it
Cost Savings for
Newly Generated
Traffic
F
G
D’ i
Vit
V`it
Traffic Volume of
type i
4
Cost Savings from Road Improvements
• Traffic Volume with Project: the number of vehicles by type
that we expect each year to use the road over its life after
improvement;
• Traffic Volume without Project: the volume of vehicles by
type that would travel on the road without the road
improvement;
• Vehicle Operating Costs Without the Project and With the
Project: the costs incurred by road users in terms of:
- consumption of gasoline and oil
- the wear-and-tear on tires
- the repair expenditures for vehicles
5
Traffic: With Road Improvement
• Diverted Traffic: The traffic that diverted to the
upgraded road from other routes as a result of the
road improvement.
• Generated Traffic: The traffic that will arise from
people who now made the trip more frequently
due to the reduction in the cost of using the road.
6
Savings of Time
• “Normal” traffic: For passengers and trucks, the improved road allows their
vehicles to travel at a higher speed as compared to the existing road, thus
saving them time.
Example: Occupants of a vehicle value time at $20 per hour, vehicle speed is 30 kph
Time cost per km: 20/30= $ 0.66/km
If vehicle speed is 50 kph
Time cost per km is 20/50= $ 0.4/km
Value of Time Savings: 0.66-0.4= $ 0.26 per vehicle - km
• The value of savings is tied to the value placed on occupants’ time and
therefore sensitive to the level of per capita income of the country.
• For Diverted and Generated passenger traffic, the value of time savings is
taken on average as half of the value of time savings for “normal” traffic.
7
Savings of Road Maintenance Expense
• The annual savings in resources used for maintenance is the difference
between the amount of resources spent on maintenance “without” road
improvements minus the maintenance costs during the life of the road
“with” the improvement.
• Road improvements or new roads will affect the pattern of traffic on
other roads that are complements or substitutes to the road being
improved.
– For complementary roads, the maintenance requirements are
expected to rise as the volume of traffic accessing or exiting from
the improved roads increases. The increase in maintenance costs on
the complementary roads should be included as a cost associated
with the road improvement project.
– Substitute road maintenance expenses are expected to decrease due
to the lower traffic levels. The cost savings are a benefit to the road
improvement.
8
Accident Reduction
• A road improvement can be important factor in the reduction of the
number of accidents.
• A road improvement may not automatically imply a substantial
reduction in the rate and severity of accidents as there are other
influencial aspects. Some of these factors are the geometric alignment
of the road, the volume of traffic, effectiveness of law enforcement,
vehicles mechanical conditions and drivers behavior.
• Steps to assess the benefits of accidents reduction:
– the rate of traffic accidents “with” and “without” the proposed
improvements must be estimated. (Number of accidents per million
vehicle-kilometer)
– the monetary value of accident reduction should be estimated
which includes the savings in damages such as property and cargo
damages. It is difficult to put a monetary value on injuries and
fatalities.
9
Calculation of Cost Savings in
Transportation Projects
Step One: Estimate a projection over time of the traffic
volume in the area for different types of traffic:
Vt=Vit
i
where Vt is the expected volume of traffic in year t, V is
traffic, i is a type of traffic, t is time.
10
Step Two: Calculate the Average Speed
Sit=ƒ(Vt),
where Sit is the average speed of the ith vehicle type.
Step Three: Estimate cit which is the average cost per
vehicle-mile at time t for vehicle type i on the
unimproved road. cit includes vehicle operating
costs, depreciation, maintenance and time cost.
Step Four: Estimate c’it which is the average cost per
vehicle-mile at time t for vehicle type i on the
improved road.
11
Step Five: Estimate the benefits of savings in cost of
travel due to road improvement in year t:
(cit – c’it)*Vit
i
and the present value of these benefits at discount
rate r:
(1+r)-t *(cit – c’it)*Vit
t
i
Step Six: Estimate M’t and Mt , which are the annual road
maintenance costs with and without the road
improvement.
12
Step Seven: Estimate the benefits of savings in road
maintenance cost due to road improvement in year
t, in some cases maintenance costs may rise
(Mt – M’t)
Step Eight: Estimate the present value of total benefits due
to improvement (when volume of traffic remains
constant after improvement):
(1+r)-t* (cit – c’it)*Vit + (1+r)-t*(Mt – M’t)
t
i
t
13
Cost Savings with an Increase in Traffic
Volume after Road Improvement
Step Nine: There is an additional benefit in consumer
surplus of generating new traffic volume due to road
improvement.
EFG = ½(1+r)-t*(cit – c’it)*(V’it -Vit)
Di
i
t
Cost per vehiclemile for type i
E
cit
c`it
Gain in Consumer
Surplus due to
Improvement
F
G
D`i
Vit
V`it
Traffic Volume of
type i
14
Total Cost Savings with an Increase in Traffic
Volume after Road Improvement
Step Ten: The total present value of benefits due to road
improvement with a traffic volume increase:
(1+r)-t*(cit – c’it)*Vit + (1+r)-t*(Mt – M’t)
i
t
t
+
½(1+r)-t*(cit – c’it)*(V’it -Vit)
t
i
15
Externalities Connected with Road Projects
Need to take into account all external benefits and
costs:
Dit*(X’it - X0it)
i
Where:
Dit is the excess of benefits over costs associated with a
unit change in the level of activity, Xi at time t,
X’it is that level in the presence of the project,
X0it is that level in the absence of the project.
16
Externalities Involving Traffic on
Other Roads
Externalities can be:
• Excess of marginal social cost over marginal
social benefit for traffic on roads;
• Excess of marginal social benefit over marginal
social cost for traffic on other modes such as
railroads.
• Congestion impacts, a very important and
pervasive externality.
17
• There is a negative relationship between volume of traffic
(V) to speed of traffic (S).
S = a - b*V
• If H is the value of the occupant’s time per vehicle hour,
cost can be approximated by time per vehicle-mile, or H/S,
which is also the marginal private time-cost as seen by the
typical driver. The total time-cost of all users will be VH/S,
and the marginal social time-cost:
 VH 
S



 S V
S

  H *
V
2
V
 S




a  bV  bV  aH
  H * 
 2
2
S
S





18
• Excess of marginal social cost, MSC, over
marginal private cost, MPC, can be expressed as:
 a*H  H
 2 
MSC  MPC  S  S α  S


H
MPC
S
S
Where: MSC is the marginal social cost; MPC is
the marginal private cost; S is actual speed; H is
time value per vehicle-hour; a is the average
speed at low traffic volumes.
Example: a= 80 kph, s= 50 kph, Thus, (80-50)/50 = 0.60
MSC exceeds MPC by 60 percent.
19
Externalities (Congestion) in Case of
Complementary Road
S’ (social costs)
Cost
per
vehiclemile
I
D
’
D
F
External costs
associated with
traffic increase
C’(private costs)
C1
J
D
’
E
C0
C
D
V0
V1
Traffic Volume on
Complementary Road
D’D’ is an increase in traffic on the complementary road.
EFIJ is the external costs.
20
Externalities in Case of Substitution Road
S’ (social costs)
Cost
per
vehiclemile
D
External benefits
associated with
traffic decrease
F
D*
G
E
C0
C1
C’ (private costs)
H
C
D*
V*
V0
D
Traffic Volume on
Substitute Road
D*D* is a decrease in traffic on the substitute
(competitive) road.
HGFE is the external benefits.
21
Calculation of Externalities for
Complementary or Substitute Road
 a j  s0 jk
E   C0 jk * f jk *V jk * 
 s
j
k
0 jk





Where:
C0 is initial cost per vehicle-mile on the alternative road;
f is a fraction of C represented by time-costs;
V is the change in traffic volume;
j is a type of alternative road;
k is a volume interval on a road.
22
Cost Benefit Analysis of Transportation Projects
-- Introduction of New Roads -• Since there was no traffic to the area before the new
road, the whole triangle DiC’itH represents the total
present value of benefits to road construction in year t.
Di
Cost per vehiclemile for type i
C’it
H
D’ i
V`it
Traffic Volume of
type i
23
Introducing New Modes of Transportation
“Buenos Aires Colonia Bridge Project”
• The BAC Bridge will introduce a new mode of traffic to the
Buenos Aires-Colonia area: transportation for passengers and
cargo crossing the river.
- An alternative mode of crossing the river, a ferry
- A long route for cargo
• Beneficiaries of the BAC bridge consist of passengers
diverted from ferry, newly induced bridge river-crossing
passengers, and cargo.
24
25
ANALYSIS OF THE PROJECT
FROM ALTERNATIVE VIEWPOINTS
THREE POINTS OF VIEW
BRIDGE
CONCESSIONAIRE
URUGUAY
Toll
Transportation
Services
Transportation
Services
Payments for
Goods & Services
Payments for
Goods & Services
Sales of
Goods & Services
Sales of
Goods & Services
Additional
Travel
Services
s
od
Go s
of ice
les rv
Sa Se for .
&
s v
ent Ser
ym &
Pa ods
Go
Debt Service
& Dividends
Brazil
Project
Financing
Toll
To
ll
Tr
an
Se spo
rv rta
ice tio
s n
Additional
Travel
Services
ARGENTINA
Rest of the World
26
Key Factors Affecting the Project
• A BOT Project: project life 30 years
• Construction costs
- about US$831 million in 1997 prices
- construction begins in 1999 and last four years
• Volumes of freight and passenger traffic
• Competitive response by ferry operators
• Bridge tolls
• Project financing
- the initial debt/equity ratio is 65/35
- the long-term debt is denominated in US dollars, and
the interest rate is set at 7% real
- loan payment starts at the first year of the bridge’s
operation
27
•
The gross economic benefits of the diverted and induced passenger
traffic is measured by the total willingness of the passenger to pay to
cross the river using this new mode.
Average Cost, $
BAC Bridge
Vmax I
J
CB
R
VOCB
GC
DB
+
TCB
P
N
tB
Taxes and Other
Distortions on
VOC B and TCB
K
DB
O
qB
River Crossing
per Year
If the toll level is tB, the
quantity of trips demanded on
the bridge should be equal to
qB. At this quantity, the
economic benefits of the
diverted and induced traffic is
equal to the consumer surplus,
(CBIJ), plus the value of the
tolls (OtBKqB), plus the value
of any taxes or other
distortions associated with
vehicle operating and time
costs incurred to use the
bridge (NPKtB).
28
•
Economic benefits or costs could arise because of the reduction in activity
of the alternative modes due to the quantity of traffic diverted to the bridge.
$
Alternative
Mode
CA
A
GC
wob
B
VOCA
+
TCA
tA
E
F
G
H
MC
GC
Dwob
GC
D wb
Taxes and Other Distortions
L
O
qwb
M
q wob
With no bridge, the demand for
the alternative mode (the ferries)
is shown as D . With the
introduction of the bridge,
demand for ferries decreases and
the quantity of ferry users falls
from q wob to q wb. In this case, if
the ferry toll were set at tA, which
is above the relevant marginal
cost of the ferry, there would be a
loss in ferry profits of GEFH.
If there were taxes (or subsidies)
associated with vehicle operating
and time costs incurred when
using the ferry, then the reduction
in this activity would create a
further economic loss (or gain).
on VOC A , TC A
, and MC
A
River Crossing
per Year
29
Cargo: International Traded Goods
Impact of Transportation Cost Reduction on International Traded Goods
P
P
SB
S A  tc
S A  tc'
Exporting Country A
COUNTRY
cif B  PBw
fob A1  PA1
fob A 0  PA 0
t c'
A
B
D
Importing
IMPORTING
Country B
SA
S A B
'
S A B
tc
C
DB
DA
d
Q Ad1 Q A 0
Q As 0 Q As 1
Q
Q
Q Bm0  Q Ax 0
Q Ax 0
Q
s
s
d
Q AB
0 Q AB 1 Q B
QBs
QBm1  Q Ax1
x
A1
Net Gains in Exporting Country: ABCD
Net Gains in Importing Country: Nil
30
Cargo: Regionally Traded Goods
Impact of Transportation Cost Reduction on Regionally Traded Goods
P
P
S A  tc'
S A  tc
Exporting Country A
SB
S A B
SA
Importing
Country B
cif B 0  PB 0
cif B1  PB1
fobA1  PA1
fob A0  PA0
S A'  B
E
F
H
A
tc
B
D
G
t c'
C
m
x
QB 0  Q A 0
Q Ax 0
DB
DA
Q As 0 Q As 1
Q Ad1 Q Ad 0
Q
Q Ax1
QBs 1
QBs 0
QBd 0
QBd1
Q
QB1  Q A1
m
x
Net Gains in Exporting Country: ABCD
Net Gains in Importing Country: EFGH
31
Benefits from Cost Reduction in
Cargo Transportation
• When the goods are internationally traded,
producers of the exporting country within the
region would benefit from the savings in
transportation or logistics cost between the two
neighboring countries.
• In the case of regionally traded goods, producers
in the exporting country and consumers in the
importing country will share the benefit from
savings in transportation and logistics cost.
32
Case Study Conclusions
• The project is financially viable as the real rate of return on
equity is in excess of 16%.
• ADSCR is larger than 1.9 for the option with financing that
requires debt be repaid over 15 years.
• After paying the foreign concessionaire for the investment,
the project will make a substantial contribution to the
economies of Argentina and Uruguay.
• Producers in Brazil will also benefit for international traded
goods due to increased shipments of these goods from
Brazil to Argentina via the bridge.
• The big winners are bridge passengers in Argentina and
Uruguay.
• Airline and ferry operators are losers because of diversion
of travelers to the bridge.
33
Externalities Involving
Railroad Traffic
34
Externalities Involving Railroad Traffic
•
The problems involved in the relationships between road and rail
transport can be complex, given the difficulty of isolating the
relevant costs of rail transport.
•
Measuring Marginal Cost for Railroads:
-
The marginal costs of carrying additional passengers or freight on
trains that are in any event running are very low.
-
The marginal costs of running additional trains where the track and
station facilities will in any event be kept in working condition are at an
intermediate level.
-
The marginal costs of providing rail service on a stretch of track as
against the alternative of abandoning that stretch are higher still.
35
Project of Road Improvement
Road
Railroad
c0
DR(C1)
DR(C0)
c1
MC3
DROAD MC2
MC1
V0
V1
Q1R
Q0R
Consequences: 1) traffic is diverted from rail to road
2) the railroad no longer has to bear the marginal cost
of carrying diverted traffic
The net external effect will therefore almost certainly be negative, and will
be measured by:
 ( F  R )X
i
i
i
i
Fi
Ri
- is the fare or freight rate for the type of rail traffic
- is the marginal cost associated with carrying that traffic
X i - is the change in the volume, induced by the road improvement
i th
- type of traffic on the railroad
36
Figure 1
Unit
Cost of
Travel on
road
D2
D1
C1'
C1 C1'
C2'
M
*
1
*
2
c
c
P
N
D1 D1'
R
D2'
C1
D1'
C2
v1 v2' v2
Volume of traffic on road
D3
Fare
G
c1* v1
-the initial levels of unit costs and traffic
volume on the road
- the equilibrium levels after the road has
been improved but before railway abandoned
-the equilibrium levels after the road
has been improved and the railroad abandoned
J
D3'
D4'
H
-the demand curve for services of the road
on the assumption that the railroad is operating
and charging the fare level OF (from Figure 2)
-the demand curve for the services of the road
assuming the railroad has been abandoned
c2* v2
D4
- after the improvement
D 2 D '2
c*2 v '2
Figure 2
F
O
C2 C2'
- the private unit costs of travel on the road
before the improvement
D3 D3'
-the demand curve for services of the railroad
on the assumption that there is no improvement
on the road
D4 D4'
- the demand curve for services of the railroad
after improvement on the road
I
Traffic level on railroad
37
Unit
Cost of
Travel on
road
D2
D1
C1'
C2'
M
*
1
*
2
c
c
N
P
R
D2'
C1
D1'
C2
v1 v2' v 2
Volume of traffic on road
c1* MN c2* - the measure of direct benefits
c1* MR c2* - the benefit perceived by traffic that would
have used the unimproved road in any event
MNR
- represents the net benefit perceived by those who would not have used
NPV2V’2
- represents cost incurred in the road by traffic because of the abandoned
the road at unit cost of C1, but who would have it at unit cost of C2.
railroad.
38
Figure 1
D2
Unit
Cost of
Travel on
road
D1
C1'
SUMMARY
C2'
M
*
1
*
2
c
c
a) The present values of cost savings to the users
of the road (represented by area c* MN c*)
1
2
P
N
R
D2'
C1
D1'
C2
less
b) The present value of those private net costs
associated with abandonment of the railroad
(represented by FD4G)
less
c) The present value of the excess of rail fares over
the direct marginal costs of operation
plus
d) The present value of the savings stemming
lower equipment, maintenance, station operation
costs, and so forth, for the railroad
v1 v2' v2
Volume of traffic on road
Figure 2
D3
D4
Fare
G
J
F
plus e) The current market value in alternative uses
of the properties to be abandoned
'
3
D
MC
D4'
O
H
I
Traffic level on railroad
39
COSTS AND BENEFITS OF
ELECTRICITY INVESTMENTS
40
Economic Valuation of
Additional Electricity Supply
• Willingness to pay for new connections
• Willingness to pay for more reliable service
• Resource cost savings from replacement of
more expensive generation plants
• Marginal cost pricing
41
Economic Value of Electricity
For New Connections or For Reduction of
with Rotating Power Shortages
$
P
S0
=P’ D
MAX
Shaded area = economic
value of shortage power
B
P0
m
0
(Q’-Q0) = Power
shortage, evenly rotated
to all customers
C
F
Q0
D0
Q’
Quantity
Assuming willingness to pay (WTP) of all customers are also evenly distributed
from highest 0P’ to lowest P0m:
Economic Value of Additional Power Supply = ((PMAX+ P0m)/2) * (Q’-Q0)
42
Economic Value of Electricity
Computation Formula
P’
D
S0
B
Pt
0
C
F
D0
Q0
Q’
Quantity
P’ = Maximum willingness to pay per unit of shortage power
= 2 (capital costs of own generation/KWh) + Fuel Costs/KWh
Need one generation to produce electricity and the second generation to
provide reliability
43
Estimated Cost of Power Failure
1. Based on willingness to pay
- Based on customers survey
2. Based on actual costs to users
3. Based on linear relationship between GDP and
electricity consumption of industrial/commercial
users
44
Estimated Cost of Power Failure*
1. Based on Willingness to Pay
- Based on customers survey (Contingent valuation)
Ontario Hydro Estimates of Outage Costs (1981 US$/kwh)
Duration
Large
Small
Commercial
Residential
Manufacturers
Manufacturers
1 min
58.76
83.25
1.96
0.17
20 min
8.81
13.56
1.66
0.15
1 hr
4.35
7.16
1.68
0.05
2 hr
3.75
7.35
2.52
0.03
4 hr
1.87
8.13
2.10
0.03
8 hr
1.80
6.42
1.89
0.02
16 hr
1.45
4.96
1.75
0.02
Average**
2.15
6.38
1.98
0.12
All groups average***:
1.96
Average power price:
0.025
Average WTP for power during outage = 78.4 times average power price.
Notes:* C.W. Gellings and J.H. Chamberlin, Demand-Side Management: Concepts and Methods,
Liburn, Georgia, The Fairmont Press, Inc., 1988.
** Based on system simulation model
*** Based on shares: 13.5/13.5/39.0/34.0 %.
45
Own-Generation Cost and Willingness to Pay
in Mexico
Own-generation cost of one generator +fuel ($/kWh) 0.18
- Capital cost ($/kWh): 0.05
- Fuel cost ($/kWh): 0.13
Maximum willingness to pay ($/kWh)
(two generators + one fuel cost)
0.23
Average willingness to pay to Utility ($/kWh)
0.14
Average power retail price (gross of tax, $/kWh)
0.05
46
Estimated Cost of Power Failure (cont'd)
2. Based on actual costs to users
San Diego (sudden outage of a few hours)*
(1981 US $/kwh)
Industrial
Direct User
2.79
Employees of Direct User
0.21
Indirect User
0.12
Total
3.12
Multiples of Av Tariff**
62.4
Commercial
2.40
0.09
0.13
2.62
52.4
Key West, Florida (rotating blackout for 26 days)*
Nonresidential Users
•
•
% of
Time
4.8
Cost
$2.30/kwh
Electric Power Research Institute study EPRI EA-1215, 1981, Vol. 2.
Average price in 1981 is 0.05 $/kwh.
Multiples
of Price
46.0
47
Estimated Cost of Power Failure (cont'd)
3. Based on linear relationship between GDP and electricity
consumption of industrial/commercial users*
Outage cost = 1.35 (1981$/kwh)
Or:
= 27 (multiples of the average power price)
*
M. L. Telson, “The Economics of Alternative Levels of Reliability for Electric
Power Generation Systems”, Bell Journal of Economics, (Autumn 1975).
48
Summary:
Average power outage cost
ranges from 6 to 80 times of
the average power price.
49
Investment in New Generation
to Obtain Cost Savings
50
Load Curve
hours for Year
Load Duration Curve
hours for Year
Capacity
MW
Capacity
MW
8760 hrs
8760 hrs
Peak hours
Off-Peak hours
A kilowatt is the measure of capacity.
1 K.W. of capacity can produce 8,760 Kilowatt hour (kWh) per year.
51
Calculation of Marginal Cost
of Electricity Supply
• During the off-peak hours when the capacity is not fully
utilized, the marginal cost in any given hour is the marginal
running cost (fuel and operating cost per kWh) of the most
expensive plant operating during that hour.
• During the peak hours, when generation capacity is fully
utilized, the marginal cost of electricity per kWh is equal to
the marginal running cost of the most expensive plant
running at the time plus the capital costs of adding more
generation capacity, expressed as a cost per kWh of peak
energy supplied.
52
Optimal Stacking of Thermal
Capacity
KwH
MC4=0.08+ 400(0.15)/1000=0.14/kWh
1
Plant
Capital
Cost
Fuel
Cost
4
$1000
$0.03
3
$700
$0.04
2
$600
$0.05
1
$400
$0.08
MC3=0.05/kWh
2
MC2=0.04/kWh
3
4
MC1=0.03/kWh
H2
H3
H4
1000
1500
4500
H4 solve for the minimum number of hours to run a plant 4 or
the maximum number to run plant 3.
v = r+ d =0.15
v(K4)+f4(H4)=v(K3)+f3(H4)
0.15(1000)+0.03(H4)=0.15(700)+0.04(H4)
(150-105)=0.04(H4)-0.03(H4)
45=0.01H4
H4=4500
53
Stacking Problem: when do we replace a
thermal plant?
KW
Plant No.
Marginal Running
Cost per kWh
Output of plant #5 that substitutes
for plant #1 = Q1
Hydro
storage
Output of plant #5 that
substitutes for plant #2 = Q2
1
0.08
2
0.05
1 (2)
3
0.04
2 (3)
H2
4
0.03
3 (4)
H3
5
0.02
4 (5)
H4
H1
Output of plant #5 that
substitutes for plant #3 = Q3
Output of plant #5 that
substitutes for plant #4 = Q4
Load curve for plants 2,3,4
after 5 is introduced
The question is whether or not we should build plant #5. We use the most efficient plant
first and then use the next most efficient and so on until the least efficient we need to
meet demand.
• Assume plant #5 has equal capacity to each of the other plants we would then have to
shift all of the plants up one stage in production, thus there is no need to use plant
number one now.
Benefits to Plant #5: It is going to be producing most of the time. Part of the time 5 is
effectively substituting for 4, part for 3, part for 2, and part for 1.
54
Two approaches to calculating benefits
A. The new plant is used to substitute for part of the other plants that
now do not produce as much as previously:
Benefits
Q4 x (0.03 – 0.02)
Q3 x (0.04 – 0.02)
Q2 x (0.05 – 0.02)
Q1 x (0.08 – 0.02)
Total A
B. Alternative approach
• Let H1, H2, H3, H4, be amount of electricity previously produced by plants 1
to 4.
Original Total Cost
H4 x 0.03
H3 x 0.04
H2 x 0.05
H1 x 0.08
Total B
•
New Total Cost
H4 x 0.02
H3 x 0.03
H2 x 0.04
H1 x 0.05
Total C
Total A = Total B -Total C.
We now compare total A with the annual capital cost of plant 5.
55
The Situation where variations in the efficiency
of thermal plants are taken into account
The optimum price to charge at any hour is the marginal running cost
of the oldest (least efficient) thermal plant that is in operation during that
hour.
In this case, the benefits attributable to an investment in new capacity
turn out to be the savings in system costs that the investment makes
possible; and the present value of expected benefits is
¥
j-1
å åQ(k, t ) [C(k ) - C( j )] (1 + r)
j-t
t= j+1 k=1
C(k) - the marginal running cost of a plant built in year k
Q(k,t) - the number of kilowatt-hours in the production of which a new
plant would substitute for plants built in year k
C(j) – running cost of plant j
56
Marginal Cost Pricing
of Electricity
• Efficient pricing of electricity.
The basic assumption that we make is that the
demand for electricity is increasing over time, 510% each year. Therefore with existing capacity
economic rents will increase over time.
57
Load Curve for Hours of Day
• We start with the assumption that all we have are
homogeneous thermal plants.
Capacity
in KW
K0
Qt1
Qt0
0
Hours of day
• If demand increases to Qt1 we either ration the available electricity or we
build more capacity.
58
Load Curve for Hours of Day (cont'd)
• By varying the price of electricity through time we can spread out demand so
that it does not exceed capacity.
Surcharge
cents
Capacity
in K.W.
K0
4
Si = Surcharge
3
Qt0
0
2
1
0
Hours of day
• It is possible to keep quantity demanded constant by varying the price with
the use of a surcharge.
• Let Ki be the length of time each surcharge is operative. Si is the difference
between MC and the price charged, then:
m
Total economic rent   Si K i
i
• It is the economic rent accruing to the existing capacity.
59
Example
• Assume the capital cost is $400/kw of capacity and the social
opportunity cost of capital plus depreciation = 12% per year, we need
$48 of rent per year before installing an additional KW of capacity.
• As demand increases through time, a higher surcharge is required to
contain capacity. Price is used to ration capacity.
• This will generate more economic rent, and if this rent is big enough
it would warrant an expansion of capacity.
• The objective of pricing in this way is to have it reflect social
opportunity cost or supply price.
• In practical cases the price does not vary continuously with time but
we have surcharges that go on and off at certain time periods.
60
Example (cont’d)
• The “Load Factor” = kWh generated/8760 kwh
• Capital costs of per KW of capacity = $400/KW
• Social opportunity cost of capital plus depreciation
(10% + 2%) = $48/yr
• Marginal running costs = 3 cents per kWh
• Peak hours are 2,400 out of the year
• Off peak optimal charge is 3 cents per kWh
• On peak optimal charge is 5 cents per kWh
• Implicit rent of any new capacity = 2,400 x 2 cents
= $48/year
61
Choice of different types of Electricity
Generation Technologies to make
Electricity Generation System
• Thermal Generation
–
–
–
–
Nuclear
Large fossil fuel plants
Combined cycle plants
Gas turbines
• Hydro Power
– Run of the Stream
– Daily Reservoir
– Pump Storage
62
Thermal vs. Hydro Generation
• The thermal capacity is relatively homogeneous.
• In general, if capacity costs for generating
electricity are higher, fuel costs are lower.
• With hydro storage or use of the stream every
particular site is different.
63
Supply of Electricity, 2001
World
(1000GWh)
Canada
(GWh)
• Nuclear
2,500 (16%)
70,652 (12%)
• Hydro
2,900 (18%)
334,120 (59%)
10,000 (64%)
141,838 (25%)
• Thermal
• Others
• Total
300 (2%) 22,928 (4%)
15,700
569,538
64
Run of the Stream
• No choice of when the water will come. The water is
channeled through turbines to generate electricity.
• Water comes at a zero marginal cost and therefore should
use it when it comes.
• Suppose river runs for 8760 hrs. at full generation capacity.
• We will assume that the highest potential output during the
year of the run of stream is less than total demand (peak
hours = 2400 and off peak hours = 6360). Some thermal is
being used.
• Savings as compared to thermal plant
2400 x 5¢ = 120.00 Peak rationed price = 5¢
6360 x 3¢ = 190.80 off peak MRC of thermal = 3¢
310.80 per year
• Question: Is US$ 310.80 per year enough to pay for run of
stream capital plus running costs?
65
Daily Reservoir
• Constructed to meet the peak day hours.
• To store water during the off peak for use during the
peak hours.
• We don't generate any more electricity but we use the
same amount of water and use it to produce peak priced
electricity, i.e. (5¢) instead of off peak (3¢) electricity.
• Instead of
2400 x 5 ¢
= $120.00
6360 x 3 ¢
= $190.80
= $310.80
• We get 8760 x 5 ¢ = $438.00. Net benefits = $127.20
• The costs are that of building the reservoir and the
additional hydro generating capacity so as to generate
more electricity in the peak hours.
66
Daily Reservoir (cont’d)
• If previous run of stream generated 100 KW for 24
hours, now we will generate 300 KW for 8 hours.
• The gain from this switch in water is what we compare
with the extra cost of building the reservoir and additional
turbine capacity.
67
Pump Storage
•
We use off peak electricity to pump water up to a high area so that it can
be released to produce electricity during peak demand periods.
Example:
•
It takes 1.4 kWh off peak to produce 1 kWh on peak
•
Off peak value = 3 ¢ kWh, Peak value = 5 ¢ kWh
•
There is a profit here of [(5¢ - 3¢*1.4) = 0.8 ¢/kWh of peak hour generated
•
Pump storage is becoming feasible because of the existence of nuclear
and very large fossil fuel plants.
•
These plants are very costly to shut off and on. Therefore, their surplus in
off peak hours is very cheap electricity.
•
With large storage at top and bottom of till, a very small stream is all that
is needed to produce a very large power station and use nuclear power to
pump water back up on off peak hours.
68
A Case Study:
Public Private Partnership of
the Power Project
69
Issues and Objectives
Issues:
• More than 60% of installed capacity of power is hydro.
• A power deficit occurs due to:
- drought and low level of water in reservoirs
- high demand for power because of the expected high
annual GDP growth rate at 7-10%
Objectives:
• A 126 MW single cycle gas turbine plant is proposed
• Assess if the project is financially viable and bankable
• Evaluate if the project is economically viable and if there
are alternative options.
70
Key Project Parameters
• A foreign Independent Power Producer (IPP) proposes to
build a 126 MW single cycle electricity generation plant.
• The project will cost US$134 m in 2008 prices: it is
expected to start operation in 2010 and lasts for 20 years.
• The project will enter a power purchase agreement (PPA)
with the State Owned Utility, which:
- is the off-taker of the power generated,
- pays capacity payment and provides availability
incentive payment, and
- supplies the required fuel for the operation of the plant.
• The investor has approached AfDB to finance 70% of the
total investment cost.
71
Financial Appraisal
Key Assumptions:
• The initial plant load factor is 80% in 2010 and expected to
decline at 3.4% per year to reach 40% by the end of the
project, 2030.
• Real exchange rate, 1.21 rupees/US$, remains unchanged.
Inflation rates: 3% in the US and 8.9% in host country.
• Loans are denominated in US dollars; it is repaid in 14 equal
instalment. The annual interest rate is 6% real.
• Corporate income tax rate is 25%.
• Required rate of return by the investor is 13% real.
72
Financial Appraisal (cont’d)
Proposed Single Cycle Plant:
• ADSCR is 1.24 in yr 1, 1.43 in yr 2.
LLCR is 1.51 in yr 1, 1.56 in yr 2.
• FNPV @13% = 0.37 m rupees in 2008 prices.
• For the State Utility, it pays transmission and distribution
cost and charge tariff for end users. FNPV @10% = - 257
m rupees, if the cost of oil is US$49/barrel.
Alternative, Combined Cycle Plant:
• Capital cost is estimated at 40% higher than the single cycle
plant while the energy transformation efficiency is 60% (vs
32% for single cycle plant).
• For the State Utility, FNPV @10% = - 123 m rupees.
• The higher the oil price, the more it saves with the
combined cycle plant.
73
Economic Appraisal
Assumptions:
• Costs are measured in resource cost.
• The economic discount rate is estimated at 12% real.
Results:
• A cost-effectiveness analysis is undertaken.
• The levelized cost is computed as the PV of total economic
costs incurred over the project life divided by the PV of
electricity generated.
• The levelized cost of energy (if the cost of oil is
US$49/barrel): 14.6 rupees/kWh for combined cycle plant and
18.3 rupees for single cycle plant.
• The higher the price of oil, the more efficient in implementing
the combined cycle plant. 74
Concluding Remarks
• The financial evaluation of this project goes beyond the
assessment of the proposed single cycle plant as a standalone project. It is also carried out from the utility’s
perspective under alternative combined cycle technology
due to its financial arrangement to pay fuel costs.
• As the capital costs are explicit in the PPA and fuel costs
are not, it might appear to decision makers that the single
cycle is less costly, while in fact it is much more costly
taking full life cycle costs.
• Given the electricity generated by the two alternative
technologies over the same period, cost-effectiveness
analysis has been employed. The resource cost of the
combined cycle plant for the source of electricity
generation is lower due to its lower fuel requirement as
compared to the single cycle option.
75