1

Lecture Notes

ECON 437/837: ECONOMIC COST-BENEFIT ANALYSIS

Lecture Ten

2

MEASUREMENT OF

COSTS AND BENEFITS OF

TRANSPORTATION

INVESTMENTS

3

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

4

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

5

Cost Savings for Existing and New Traffic

Cost per vehicle-mile for type i

Traffic Volume of type i

cit

c`it

V`itVit

Di

D’i

E

FG

Cost Savings for Newly Generated

Traffic

Cost Savings for Existing Traffic

6

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

7

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.

8

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.

9

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.

10

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.

11

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:

where Vt is the expected volume of traffic in year t, V is traffic, i is a type of traffic, t is time.

Vt=Viti

12

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.

13

Step Six: Estimate M’ and M , which are the annual road maintenance costs with and without the road improvement.

Step Five: Estimate the benefits of savings in cost of travel due to road improvement in year t:

i(cit – c’it)*Vit

and the present value of these benefits at discount rate r:

(1+r)-t *(cit – c’it)*Vit t i

t t

14

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

Step Eight: Estimate the present value of total benefits due to improvement (when volume of traffic remains constant after improvement):

(Mt – M’t)

(1+r)-t* (cit – c’it)*Vit + (1+r)-t*(Mt – M’t)t i t

15

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.

Cost per vehicle-mile for type i

Traffic Volume of type i

cit

c`it

V`itVit

Di

D`i

E

F

G

EFG = ½(1+r)-t*(cit – c’it)*(V’it -Vit) t i

Gain in Consumer Surplus due to Improvement

16

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:

½(1+r)-t*(cit – c’it)*(V’it -Vit) t i

(1+r)-t*(cit – c’it)*Vit + (1+r)-t*(Mt – M’t)t i t

+

17

Need to take into account all external benefits and costs:

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.

Externalities Connected with Road Projects

iDit*(X’it - X0

it)

18

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.

Externalities Involving Traffic on Other Roads

19

• 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:

222**

S

aH

S

bVbVaH

SVS

VSH

VS

VH

20

• Excess of marginal social cost, MSC, over marginal private cost, MPC, can be expressed as:

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.

S

Sα

MPC

MPCMSC

SH

SH

SHa2

*

21

Externalities (Congestion) in Case of Complementary Road

D’D’ is an increase in traffic on the complementary road.

EFIJ is the external costs.

C

C’(private costs)

Cost per

vehicle-mile

Traffic Volume on Complementary Road

D

D’

S’ (social costs)

V0 V1

D

D’

E

J

I

F

External costs associated with traffic increase

C0

C1

22

Externalities in Case of Substitution Road

D*D* is a decrease in traffic on the substitute (competitive) road.

HGFE is the external benefits.

C

C’ (private costs)

Cost per

vehicle-mile

Traffic Volume on Substitute Road

D

S’ (social costs)

V0V*

D

D*E

H

G

F

External benefits associated with traffic decrease

D*

C0

C1

23

Calculation of Externalities for Complementary or Substitute Road

jk

jkjjk

j kjkjk s

saVfCE

0

00 ***

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.

24

Cost Benefit Analysis of Transportation Projects-- Introduction of New Roads --

Cost per vehicle-mile for type i

Traffic Volume of type i

C’it

V`it

Di

D’i

H

• 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.

25

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.

26

27

ANALYSIS OF THE PROJECT FROM ALTERNATIVE VIEWPOINTS

THREE POINTS OF VIEW

ARGENTINABRIDGE

CONCESSIONAIREURUGUAY

AdditionalTravel

Services

AdditionalTravel

Services

Toll

TransportationServices

Payments forGoods & Services

Sales ofGoods & Services

Toll

TransportationServices

Payments forGoods & Services

Sales ofGoods & Services

Rest of the WorldBrazil

Proj

ect

Fina

ncin

gDebt Service& Dividends

28

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

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• 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.

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).

Average Cost, $

BAC Bridge

O Bq

BVOC

BTC+

BC

BtN

R

J

P

K

BD

GCBD

Taxes and OtherDistortions on

VOCB and TCB

ImaxV

River Crossingper Year

30

• 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.

With no bridge, the demand for the alternative mode (the ferries) is shown as . 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).

DGC

wob

MC

A B

E F

G H

L M

O

AC

At

AVOC

ATC

+

wbq

wobq River Crossing

per Year

AlternativeMode

$

Taxes and Other Distortions

on VOCA

, TCA

, and MCA

GCwb

D

GC

wobD

31

Cargo: International Traded Goods

A D s A Q 0 s

A Q 1 d A Q 1 d

A Q 0 Q

P

w B B P cif

A S ' c A t S c A t S

' c t

c t

B D

B S

B A S '

B A S

s B Q s

AB Q 0 s AB Q 1 d

B Q Q

P

A B C D

Impact of Transportation Cost Reduction on International Traded Goods

Exporting Country A COUNTRY

Importing IMPORTING Country B

x A Q 0 x A Q 1

x A m

B Q Q 0 0 x A m

B Q Q 1 1

1 1 A A P fob 0 0 A A P fob

Net Gains in Exporting Country: ABCD Net Gains in Importing Country: Nil

32

Cargo: Regionally Traded Goods

A D

s A Q 0 s

A Q 1 d A Q 1 d

A Q 0 Q

P

A S

' c A t S

c A t S

B D

B S

B A S '

B A S

s B Q 0 d

B Q 0 Q

P

A B C D

E F

Impact of Transportation Cost Reduction on Regionally Traded Goods

Exporting Country A

d B Q 1

1 1 B B P cif

Importing Country B

H G

1 1 A A P fob

x A Q 0

x A Q 1

x A m

B Q Q 0 0

x A m

B Q Q 1 1 s B Q 1

' c t c t

Net Gains in Exporting Country: ABCD Net Gains in Importing Country: EFGH

0 0 B B P cif

0 0 A A P fob

33

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.

34

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.

35

Externalities Involving Railroad Traffic

36

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.

37

RailroadRoad

Project of Road Improvement

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:

ii

ii XRF )(

- is the fare or freight rate for the type of rail traffic

- is the marginal cost associated with carrying that traffic

- is the change in the volume, induced by the road improvement

- type of traffic on the railroad

iF

thi

iR

iX

c0

c1

DROAD

V0 V1 RQ1R

0Q

MC1

MC2

MC3

DR(C1)

DR(C0)

38

Volume of traffic on road

Unit Cost of

Travel onroad

M

RN P

1v '2v 2v

*2c

*1c

1D2D

'1D

'2D

'1C

'2C

1C

2C

2C '2C - after the improvement

1C '1C - the private unit costs of travel on the road

before the improvement

G J

H IO

F

Traffic level on railroad

Fare

'4D

'3D

3D

4D

Figure 2

1D '1D -the demand curve for services of the road

on the assumption that the railroad is operatingand charging the fare level OF (from Figure 2)

3D '3D

-the demand curve for the services of the road assuming the railroad has been abandoned

*1c

1v -the initial levels of unit costs and traffic volume on the road

*2c

2v -the equilibrium levels after the roadhas been improved and the railroad abandoned

4D '4D

-the demand curve for services of the railroad on the assumption that there is no improvement on the road - the demand curve for services of the railroad after improvement on the road

2D '2D

*2c '

2v - the equilibrium levels after the road has been improved but before railway abandoned

Figure 1

39

- the measure of direct benefits *1c MN

*2c

Volume of traffic on road

Unit Cost of

Travel onroad

M

RN P

1v '2v 2v

*2c

*1c

1D2D

'1D

'2D

'1C

'2C

1C

2C

*1c MR

*2c - 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 the road at unit cost of C1, but who would have it at unit cost of C2.

NPV2V’2 - represents cost incurred in the road by traffic because of the abandoned

railroad.

40

Volume of traffic on road

Unit Cost of

Travel onroad

M

RN P

1v '2v 2v

*2c

*1c

1D2D

'1D

'2D

'1C

'2C

1C

2C

G J

H IO

F

Traffic level on railroad

Fare

'4D

'3D

3D

4D

Figure 2

Figure 1

SUMMARY

a) The present values of cost savings to the users of the road (represented by area )*

1c MN *2c

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

plus e) The current market value in alternative uses of the properties to be abandoned

MC

41

COSTS AND BENEFITS OF

ELECTRICITY INVESTMENTS

42

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

43

Economic Value of Electricity For New Connections or For Reduction of

with Rotating Power Shortages

Assuming willingness to pay (WTP) of all customers are also evenly distributed from highest 0P’ to lowest P0

m:

Economic Value of Additional Power Supply = ((PMAX+ P0m)/2) * (Q’-Q0)

Shaded area = economic value of shortage power

(Q’-Q0) = Power shortage, evenly rotated to all customers

Q00

P0m

PMAX=P’ D

FC

D0

S 0

B

Quantity

$

Q’

44

Economic Value of Electricity Computation Formula

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

0

Pt

P’D

F

Q0

C

D0

S0

B

QuantityQ’

45

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

Estimated Cost of Power Failure

46

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 0.1720 min 8.81 13.56 1.66 0.151 hr 4.35 7.16 1.680.052 hr 3.75 7.35 2.520.034 hr 1.87 8.13 2.100.038 hr 1.80 6.42 1.890.0216 hr 1.45 4.96 1.75 0.02Average** 2.15 6.38 1.980.12All 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 %.

47

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) 0.23 (two generators + one fuel cost)

Average willingness to pay to Utility ($/kWh) 0.14

Average power retail price (gross of tax, $/kWh) 0.05

Own-Generation Cost and Willingness to Pay in Mexico

48

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 Commercial

Direct User 2.79 2.40

Employees of Direct User 0.21 0.09

Indirect User 0.12 0.13

Total 3.12 2.62

Multiples of Av Tariff** 62.4 52.4

Key West, Florida (rotating blackout for 26 days)*% of Cost MultiplesTime of Price

Nonresidential Users 4.8 $2.30/kwh 46.0

• Electric Power Research Institute study EPRI EA-1215, 1981, Vol. 2. • Average price in 1981 is 0.05 $/kwh.

49

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).

50

Summary:Average power outage cost ranges from 6 to 80 times of the average power price.

51

Investment in New Generation to Obtain Cost Savings

52

8760 hrs

CapacityMW

Load Duration Curve hours for Year

8760 hrs

CapacityMW

Load Curve hours for Year

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.

53

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.

54

2

3

4 MC1=0.03/kWh

Optimal Stacking of Thermal

MC2=0.04/kWh

MC3=0.05/kWh

MC4=0.08+ 400(0.15)/1000=0.14/kWh

H2 H3 H4

1000 1500 4500

CapacityKwH

Plant Capital Cost

Fuel Cost

4 $1000 $0.03

3 $700 $0.04

2 $600 $0.05

1 $400 $0.08

H4 solve for the minimum number of hours to run a plant 4 or the maximum number to run plant 3.

v = r+ d =0.15v(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

1

55

Stacking Problem: when do we replace a thermal plant?

Output of plant #5 that substitutes for plant #1 = Q1

H2

KW

1 (2)

2 (3)

3 (4)

4 (5)

Hydro storage

H1

H3

H4

Output of plant #5 that substitutes for plant #2 = Q2

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

Plant No. Marginal Running Cost per kWh

1 0.08

2 0.05

3 0.04

4 0.03

5 0.02

• 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.

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.

56

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 New Total CostH4 x 0.03 H4 x 0.02H3 x 0.04 H3 x 0.03H2 x 0.05 H2 x 0.04H1 x 0.08 H1 x 0.05Total B Total C

Total A = Total B -Total C. • We now compare total A with the annual capital cost of plant 5.

57

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

C(k) - the marginal running cost of a plant built in year kQ(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

58

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, 5-10% each year. Therefore with existing capacity economic rents will increase over time.

59

Load Curve for Hours of Day

• We start with the assumption that all we have are homogeneous thermal plants.

Qt0

Qt1

Hours of day

Capacity in KW

0

K0

• If demand increases to Qt1 we either ration the available electricity or we build more capacity.

60

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.

Qt0

0Hours of day

Capacity in K.W.

0

K0

• 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:

1

2

3

4

Surcharge cents

Si = Surcharge

m

iiiKS rent economic Total

• It is the economic rent accruing to the existing capacity.

61

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.

62

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

63

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

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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.

Supply of Electricity, 2001

World Canada

(1000GWh) (GWh)

•Nuclear 2,500 (16%) 70,652 (12%)

•Hydro 2,900 (18%) 334,120 (59%)

•Thermal 10,000 (64%) 141,838 (25%)

•Others 300 (2%) 22,928 (4%)

•Total 15,700 569,53865

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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 plant2400 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?

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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.

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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.

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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.

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A Case Study:

Public Private Partnership of

the Power Project

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.

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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.

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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.

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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.74

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. 75

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Concluding Remarks

• The financial evaluation of this project goes beyond the assessment of the proposed single cycle plant as a stand-alone 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.