Application of Real Options in Hydro Power Projects

iApplication of Real options in Hydro Power Projects

A Project submitted in partial fulfillment of the requirements For the award of

Post-Graduate Diploma in Management

By

Rajesh Vig

IMTPost Graduate Diploma in Management-Part Time

Institute of Management TechnologyGhaziabad 122 001

April, 2013

Application of Real options in Hydro power projects

ii

A Project submitted in partial fulfillment of the requirementsFor the award of

Post-Graduate Diploma in Management-Part Time

By

Rajesh Vig

Under the guidance of

Dr. GIREESH TRIPATHIAssociate Professor

IMT, Ghaziabad

IMTPost Graduate Diploma in Management-Part Time

Institute of Management TechnologyGhaziabad 122 001

April, 2013

Certificate

iii

This is to certify that Project titled "Application of Real Options in Hydro Power Projects" submitted by Rajesh Vig (Enrolment No- 10PT-036) for the partial fulfillment of the requirement of Post Graduate Diploma in Management-Part Time is a bonafide work carried out by him, under my guidance and supervision.

The work has not been submitted by him elsewhere for the award of any other degree/diploma.

Dated Signature of the guide

Dated.. Counter signed byChairperson, PGDM P/T

iv

ACKNOWLEDGEMENT

I express my deep sense of gratitude to Dr. GireeshTripathi for his expert guidance and valuable inputs that gave me an exquisite insight about the Project on Application of Real options in Hydro Power Projects

I am highly obliged and thus express my gratefulness to him.

I share the pleasure of this achievement with all my colleagues for moral and emotional support in completing this research work in the area of Finance, successfully.

(Signature)Rajesh Vig

PGDMIMT, Ghaziabad

iABSTRACT

This thesis investigates the application of real options to the Hydro Power Projects. The thesis

applies NPV, IRR, and binomial options pricing model to study a case on New Ganderbal Hydro

Electric Project. More specifically, a deferral option of Project is studied. When doing the real

options analysis, the thesis uses the electricity price as the underlying and finds that the

electricity price is an appropriate underlying for the options analysis.

On the pros side, the study confirms that options analysis overcomes the inadequacy of NPV

analysis in uncertain environments, at least partly. Options analysis can evaluate the flexibility

intrinsic or built into projects facing uncertain environments. Moreover, options analysis

develops contingency strategy in uncertain environments.

On the cons side, traditional options analysis requires the geometric Brownian motion

assumption of the uncertainties and relatively high quality of data. The applicability of options

analysis depends on the type of uncertainty of the environment and the data availability. The

deferral option in Project fits in the category where options analysis is applicable.

The thesis concludes that real options analysis using the electricity price as underlying is an

appropriate method for valuing the deferral options of Project and similar hydropower projects.

ii

TABLE OF CONTENTS

Page

ABSTRACT I

TABLE OF CONTENTS... Ii

LIST OF TABLES. Vi

LIST OF FIGURES.... Vii

ABBREVIATIONS.. Viii

CHAPTER 1: INTRODUCTION 01-04

1.1 Real options in Hydro Power Projects.01

1.2 Need for this Research..02

1.3 Objectives02

1.4 General Methods and Tools..03

1.5 Organization of this Thesis04

CHAPTER 2: LITERATURE REVIEW 05-16

2.1. Real Options.05

2.2 Review of Basic Models...06

2.3 Valuing Various Real Options..06

2.4 Several Important Issues Regarding Real Options Valuation...07

2.4.1 Underlying...07

2.4.2 Volatility..08

iii

2.4.3 Compound and Parallel Options...08

2.5 Real Options Applied in Energy and Natural Resources...09

2.6 Hydro Power Development in India..10

2.6.1 Overview of Indian Power sector..11

2.6.2 Plans for Future Development...12

2.6.3 Hydro power Potential in India.13

2.7 Concluding Remarks..15

CHAPTER 3: RESEARCH METHODOLOGY AND DATA

ANALYSIS 17-22

3.1 Introduction...17

3.2 Data Description.18

3.2.1 Risk Free Interest Rate..18

3.2.2 Volatility of Electricity Price.20

3.2.3 Market Return and Risk.21

CHAPTER 4: REAL OPTIONS THEORY 23-44

4.1 NPV and DCF..23

4.2 Real Options v/s Financial Options..23

4.3 Types of Real Options...25

4.3.1 The Option to Defer.25

4.3.2 The Option to Expand/ Contract (to Change Scale).25

iv

4.3.3 The Option to Abandon..26

4.3.4 The Option to Switch...26

4.3.5 The Option to Growth..27

4.3.6 The Compound Option.27

4.4 Real options Valuation Tools.28

4.4.1 Black and Scholes Model.29

4.4.2 Binomial Option Pricing31

4.4.2.1 Binomial Option Pricing Model.31

4.4.2.2 Risk Neutral Approach35

4.4.2.3 Estimating the Binomial Stock Price Process.37

4.4.3 Monte Carlo simulation..39

4.5 Frame work of Real Options Valuations..42

CHAPTER 5: CASE STUDY- NEW GANDERBAL HYDRO ELECTRIC

PROJECT 45-58

5.1 Introduction.45

5.2 Project Characteristics..47

5.3 Valuing New Ganderbal Hydro Electric Project..48

5.3.1 Traditional NPV..48

5.3.2 IRR..50

5.3.3 Real Option Analysis...50

5.3.3.1 A General Binomial Tree Framework for ROA.50

5.3.3.2 ROA with Electricity Price as Underlying..53

v 5.3.3.3 Binomial Tree.54

5.4 Summary of Results.57

CHAPTER 6: CONCLUSION 59-60

6.1 Summary and Conclusions.59

6.2 Limitations of the Research...59

6.3 Future Scope of the Research.60

APPENDECIES 61

Appendix1. All India Installed Capacity (MW) of Power Stations..61

REFERENCES 62-63

vi

LIST OF TABLES

Table No. Table Name Page No.

2.1

Long term forecasts of Electricity: All India (Public

utilities). 21

2.2

Basin-Wise Potential and its Status of Development at 60%

Load Factor as of 1 January 2005 22

3.1 Project Data Collected 26

3.2 Yearly Prices at IEX INR/KWH 27

3.3 BSE- Sensex Market Return 28

4.1 Financial v/s Real Options 30

5.1 Project Characteristics 50

5.2 Project NPV Analysis 52

5.3 Summary of Results 61

vii

LIST OF FIGURES

Figure No. Figure Name Page No.

2.1 Growth of Installed Hydro Power 15

3.1 10 Year GOI Bond Yield 19

4.1 Binomial One Period 32

4.2 Stock Price movement in Numerical Example 32

4.3 Binomial One Period Payoff 33

4.4 Stock Price Movements 35

4.5 Stock Price movement in Numerical Example 37

4.6 Binomial Two Period 38

4.7 Framework of Real Options Method 42

5.1 Analysis of a scenario on the event tree 51

5.2 Electricity Price Movement 55

viii

ABBREVIATIONS

BU Billion UnitsCEA Central Electricity AuthorityDCF Discounted Cash FlowsEA2003 Electricity Act 2003GW GigawattsGDP Gross Domestic ProductIRR Internal Rate of ReturnIEX Indian Energy ExchangeKWH KilowatthourNPV Net Present ValueNEP National Electricity PolicyNGHEP New Ganderbal Hydro Electric ProjectMW MegawattsROA Real Options Analysis

- 1 -

CHAPTER 1

INTRODUCTION

1.1. REAL OPTIONS IN HYDRO POWER PROJECTS

The uncertainty and irreversibility associated with the investments in Hydro power plants makes

their analysis a more difficult task, since traditional analysis methods, such as the net present

value (NPV), are not the most appropriate tools for the valuation of investments under these

conditions. These methods dont take into account the managerial flexibility embedded in a

project, and therefore, assume that investments are managed passively, and managers will not

review their decisions.

However, under the conditions of uncertainty and irreversibility, managerial flexibility may be

highly valuable and should be taken into account in a project valuation. The valuation of

flexibility calls for more sophisticated techniques, such as the Real options approach.

Recently, the literature on Real Options has grown a lot and these techniques have been applied

in a wide range of industry sectors using many different approaches. During the last twenty

years, however, the application of real options analysis to power generation investments has

increased significantly, mainly due to the liberalization process of electricity markets in many

countries.

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1.2. NEED FOR THIS RESEARCH

Real options analysis in power projects is one of the most important developments in business

decision analysis in the last two decades. As already mentioned, one of the major problems in

hydro power projects is uncertainty and irreversibility of the investments. Introduction of real

options analysis particularly, option to defer, scale, grow, abandon however seems to be solving

some of the problems in many sectors including power sector.

In spite of recent developments in the field of real options, it is apprehended that unless the

actual investors actively participate, the growth of this market would be limited. For increasing

investors participation, the process of Real option analysis should be easily understood by them.

This research aims at improvement in the understanding of the stakeholders in the Real Option

Analysis. This study focuses on analyzing, quantifying and then managing various risks

associated with the hydro power projects. The major risks are uncertainty of the electricity

prices, uncertainty of carbon credits, etc. The impact of each of these risks on the valuation of the

hydro power projects is to be estimated and incorporated in the form of option value.

1.3. OBJECTIVES

In view of the research problem discussed in section 1.2 above, the aim of this study is to present

the valuation of a hydropower power plant. We calculate the value of the option to defer using

electricity price as underlying and compare it with the traditional net present value (NPV) and

IRR method used in capital budgeting and explain how real options analysis is better than

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traditional methods in incorporating managerial flexibility of delaying the project till the

outcome becomes more favorable.

1.4. GENERAL METHODS AND TOOLS

The real options approach is based on the seminal work of Black, Scholes, and Merton that won

the Nobel Prize in 1997. Modern Finance theory provides abundant understanding of

uncertainties and how to deal with them. It also provides some very useful techniques that

engineers can learn to better "optimize" designs in an uncertain world.

Binomial tree and risk-neutral valuation should be introduced to engineers. Cox, Ross, and

Rubinstein developed the Binomial Tree Model in 1979. The model represents how the value of

an asset evolves where the value is monitored under successive short periods of time. In each

short period it is assumed that only two value movements either up or down, are possible. Risk-

neutral valuation, assuming the world is risk neutral, gives the correct value for all worlds, not

just in a risk-neutral world.

Modern computer technology removes most of the previous computing capacity problems for

system designers. People are able to establish huge optimization models on personal computers.

But are they fully utilizing the computing capacity they did not possess before? Taking into

account uncertainties systematically and productively in systems design has-been made possible

by the modern computer technology. The key to the success of this study is that, based on

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traditional optimization models, a simulation model with which options thinking can be

developed.

1.5. ORGANIZATION OF THIS THESIS

The remaining part of this thesis has been organized in the following sequence: Chapter 2

presents the literature review relevant to the study. Chapter 3 discusses the research methodology

to achieve the objectives. Identification of appropriate variables and sources and collection of

secondary data on the variables including analysis are also discussed in this chapter. Chapter 4 is

focused on options pricing tools and their assumptions Chapter 5 values NGHEP using NPV,

IRR and Real option analysis using electricity price as the underlying. The final Chapter 6

summarizes the work with conclusions, limitations of the study and further scope of research.

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CHAPTER 2

LITERATURE REVIEW

This study integrates two threads of research. One is real options research, and the other is hydro

power development in India. This chapter reviews the literature of these two threads.

2.1. REAL OPTIONS

The real options revolution arose in part as a response to the dissatisfaction of corporate

practitioners, strategists, and some academics with traditional capital budgeting techniques. Well

before the development of real options, corporate managers and strategists were grappling with

the elusive elements of managerial operating flexibility and strategic interactions. Early critics

e.g., Dean (1951), Hayes and Abernathy (1980), haves and Garvin (1982) recognized that

standard discounted cash flow (DCF) criteria often undervalued investment opportunities,

leading to myopic decisions, underinvestment and eventual loss of competitive position, because

they either ignored or did not properly value important strategic considerations. Decision

scientists further maintained that the problem lied in the application of wrong valuation

techniques altogether, proposing instead the use of simulation and decision tree analysis Hertz

(1964), Magee (1964) to capture the value of future operating flexibility associated with many

projects. Myers acknowledges that traditional DCF methods have inherent limitations when it

comes to valuing investments with significant operating or strategic options suggesting that

option pricing holds the best promise of valuing such investments.

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2.2. REVIEW OF BASIC MODELS

The quantitative origins of real options derive from the seminal work of Black and Scholes

(1973) and Merton (1973) in pricing financial options. Cox, Ross and Rubinstein (1979)

binomial model enabled a more simplified options in discreet time. Margarbe (1978) values an

option to exchange one risky asset for another, while Stulz (1982) analyzes options on the

maximum (or minimum) of two risky assets and Johnson (1987) extends it to several assets.

These papers opened up the potential to help analyze the generic options to switch among

alternative uses and related options. Geske (1979) values a compound option (i.e. an option to

acquire another option), which in principle may be applied in valuing growth opportunities

which become available only if earlier investments are undertaken. The above line of work

opened up the potential, in principle, to value investments with a series of investment outlays

that can be switched to alternative states of operation and particularly to eventually help value

strategic inter- project dependencies.

2.3. VALUING VARIOUS REAL OPTIONS

The number of seminal papers gave a boost to the real options literature by focusing on valuing

quantitatively- in many cases deriving analytic, closed form solutions- one type after another of a

variety of real options, although each option was analyzed in isolation. The option to defer has

been examined by McDonald and Siegel in valuing offshore petroleum leases and by Tourinho

(1979) in valuing reserves of natural resources. Ingersoll and Ross (1992) reconsider the decision

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to wait in light of beneficial impact of potential future interest rate decline on project value.

Majdand Pindyck values the option to delay sequential construction of projects that take time to

build, or there is a maximum rate at which the investment can proceed. Carr (1988) and

Trigeorgis (1993a) also deal with valuing sequential or staged (compound) investments.

Trigeorgis et al. examine options to alter operating scale or capacity choice. The option to

temporarily shut down and restart operations was analyzed by Mc Donald and Siegel (1985).

Myers and Majd analyze the option to abandon the project for its salvage value seen as an

American put option. Baldwin and Ruback (1986) analyze that future price uncertainty creates a

valuable switching option that benefits short lived projects.

2.4 SEVERAL IMPORTANT ISSUES REGARDING REAL OPTIONS VALUATION

2.4.1. Underlying

Financial options are based on underlying assets such as stocks, stock indices, foreign currencies,

debt instruments, commodities, and futures contracts. They are traded in markets. Despite the

fact that real options are not traded on markets, Mason and Merton (1985), and Kasanen and

Trigeorgis (1993) maintained that real options may be valued similarly to financial options. The

existence of a traded portfolio that has the same risk characteristics (i.e., is perfectly correlated)

as a non-traded real asset is sufficient for real options valuation. Kulatilaka (1993) used the

relative price of oil over gas to value the flexibility of a dual-fuel industrial steam boiler.

Luenberger (1998) showed an example using the gold price as the underlying assets to value a

real investment opportunity in a gold mine. Similarly, as shown in this thesis, it is possible to use

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energy price as the underlying asset to value a hydropower project under the assumption of a

complete energy market.

2.4.2. Volatility

Volatility is a measure of uncertainty, a key input of the options valuation. How to find the

volatility is one of the key difficulties of application of real options if there is no market traded

underlying. Luehrman [1998] described three approaches: an educated guess, historical data, and

simulation. Copeland and Antikarov [2001] suggested, by estimating first the stochastic

properties of variables that drive volatility, using Monte Carlo simulation to estimate it.

The estimate of volatility is often one of the weakest points of a real options valuation, while the

valuation is usually sensitive to the volatility. Because the volatility is the essence of a lot of

information, it is theoretically impossible to estimate it for some real options valuation simply

due to lack of data. Sometimes, therefore, the insights provided by a real options analysis are

more important than a specific quantitative result.

2.4.3. Compound Options and Parallel Options

Most real options are not well-defined simple options. They can be compound or parallel. They

are often options on options (compound options) and the interactions between options are

significant. So the methodology for valuing compound options is very important for the

applicability of real options methodology in the real world. Parallel options are different options

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built on the same project, where those options interact. For example, several possible

applications of a new technology or several possible target markets of a new product. Oueslati

(1999) described three parallel options for fuel cell development as automotive applications,

stationary power, and portable power.

Geske (1979) developed approaches to the valuation of compound options. Trigeorgis

(1993) focused on the nature of the interactions of real options. The combined value of a

collection of options usually differs from the sum of their separate values. The incremental value

of an additional option, in the presence of other options, is generally less than its value in

isolation, and declines as more options are present. Oueslati (1999) explored the evaluation of

compound and parallel real options in Fords investment in fuel cell technology.

2.5 REAL OPTIONS APPLIED IN ENERGY AND NATURAL RESOURCES

The real options concept has been successfully applied in the energy industry. Siegel, Smith, and

Paddock (1987) valued offshore petroleum leases using options, and provided empirical evidence

that options values are better than actual DCF-based bids. Since then, research on real options on

energy has been a hot topic. Dias (2002) gave a comprehensive overview of real options in

petroleum. Miltersen (1997) presented methods to value natural resource investment with

stochastic convenience yield and interest rates. Cortazar and Casassus (1997) suggested a

compound option model for evaluating multistage natural resource investment. Cherian, Patel,

and Khripko (2000) studied the optimal extraction of nonrenewable resources when costs

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accumulate. Goldberg and Read (2000) found that a simple modification to the Black-Scholes

model provides better estimates of prices for electricity options. Their modification combines the

lognormal distribution with a spike distribution to describe the electricity dynamics.

Pindyck (1993) studied the uncertain cost of investment in nuclear power plants. He derived a

decision rule for irreversible investments subject to technical uncertainty and input uncertainty.

The rule is to invest if the expected cost of completing the project is below a critical number. The

critical expected cost to completion depends on the type and level of uncertainty. Pindycks work

focused on finance issues of the project, the engineering model was apart from his interest.

Koekebakker and Sodal (2002) developed an equilibrium-based real options model of an

operating electricity production unit whose supply is given by a stochastic mean-reverting

process. Hlouskova et al. (2002) implemented a real options model for the unit commitment

problem of a single turbine in a liberalized market. Price uncertainty was captured by a mean-

reverting process with jumps and time-varying means to account for seasonality. Rocha,

Moreira, and David (2002) studied the competitiveness of thermo power generation in Brazil

under current regulations and used real options to assess how to motivate private investment in

thermo power.

2.6 HYDRO POWER DEVELOPMENT IN INDIA

Spurred by sustained economic growth, rise in income levels, and increased availability of goods

and services, Indias incremental energy demand for the next decade is projected to be among the

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highest in the world. This increasing energy demand also translates into higher demand for

electricity. It has been estimated that in order to support a growth rate of the gross domestic

product (GDP) of around 7% per annum, the rate of growth of power supply needs to be over

10% annually. This calls for rapid development of the countrys power sector, taking into

account, inter alia, considerations of long-term sustainability, environmental aspects and social

concerns.

India is endowed with rich hydropower potential; it ranks fifth in the world in terms of usable

potential. However, less than 25% has been developed or taken up for development. Thus

hydropower is one of the potential sources for meeting the growing energy needs of the country.

A judicial mix of hydropower in the energy portfolio can also contribute to energy security,

reduction of greenhouse gas emissions, meeting the peak demand and also increased flexibility in

grid operation. Besides, projects may also be conceived as multi-purpose ones contributing not

only to power but also to irrigation, flood control, navigation, etc. The Government of India is,

therefore, giving special emphasis to accelerated hydropower development in its power

development plans.

2.6.1 Overview of Indian Power Sector

The installed generating capacity in India (in utilities) as of 31 Dec. 2012 was nearly 210,952

megawatts (MW). This included thermal (coal, gas and liquid fuel), hydro, nuclear, and

renewable based generation. Hydropower constituted about 39,416 MW. Detailed energy

breakdown of the installed capacity in utilities in the five power regions of the country on a

sector-wise and mode-wise basis is given in Appendix 1. As may be seen there the hydro-thermal

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mix is low with hydropower constituting about 19% of the total capacity. Nearly 70% of the

installed capacity is in the public sector. In the case of hydropower, the public sector has a

predominant share of over 94%. Nearly 70% is in the state sector. The annual gross electricity

generation was about 855 billion units (BU) during 2011- 2012; the share of hydropower in this

was around 17%.

The demand for power has been growing at the rate of 9.6% in recent years. During 2010-2011

the demand was 862 BU in terms of energy and 122 (GW) in terms of peak power requirements.

The availability of power had been continually falling short of the demand and, as a result, the

country is experiencing power shortages of varying degrees in different parts of the country. The

shortages during 2011-2012 were 10.3% in energy and 12.9% in peaking power. Per-capita

consumption of electricity is relatively low, of the order of 600 kilowatt-hours (kWh). Presently,

over 84% of the villages are electrified; but only 52.5% of the rural households have access to

electricity.

2.6.2 Plans for future power development

India is pursuing a centralized system for power planning. EA 2003 requires CEA to prepare

anew in accordance with the National Electricity Policy notified by the Government and update

it once every 5 years. The plan is to be finalized taking into account suggestions and objections

from licensees, generating companies and the public. The plan is to be notified only after getting

the approval of the Government. CEA has also to formulate a perspective transmission plan for

inter-state and intra-state transmission systems. These plans would be continuously updated to

take care of the revisions in load projections and generation scenarios. Further detailed planning

by the Central and state transmission utilities has to conform to this plan.

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A draft NEP was notified in 2005 which was based on an all-India generation capacity addition

of around 40,000 MW during 20022007 and the demand projections shown in Table 2.1

Table 2.1 Long term forecasts of Electricity: All India (Public utilities).

Region Energy Requirement(MW) Peak Load (MW)

2011-2012 2016-1017 2011-20122016-2017

Northern Region 308528 429480 49674 69178

Western Region 299075 395859 46825 61966

Southern Region 262718 354599 42061 56883

Eastern Region 90396 117248 15664 20416

North-Eastern Region 14061 20756 2789 4134

A&N Islands 374 591 77 122

Lakshadweep 44 111 17 26

All India 975222 1318644 157107 212725Source: 16th Electric Power Survey Report Released January 2001

2.6.3 Hydropower Potential in India

India is endowed with rich hydropower potential; it ranks fifth in the world in terms of usable

potential. This is distributed across six major river systems (49 basins), namely, the Indus,

Brahmaputra, Ganga, the central Indian River systems, and the east and west flowing river

systems of south India. The Indus, Brahmaputra and Ganga together account for nearly 80% of

the total potential. In the case of Indus the utilization is, however, governed by the Indus Water

Treaty with Pakistan. The economically exploitable potential from these river systems through

medium and major schemes has been assessed at 84,044 MW at 60% load factor10

corresponding to an installed capacity of around 150,000 MW. As mentioned earlier, so far only

32,325 MW has been established. Tables 2.2 and 2.3 show the status of development of

hydropower on a region-wise and basin-wise basis. In addition, pumped storage sites with an

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aggregate capacity to the tune of 94,000 MW have also been identified, but only about 5,000

MW have so far been developed. The assessment of small hydro (up to 25 MW) potential has

indicated nearly 10,000 MW distributed over 4,000 sites. It is estimated there is still an

unidentified small hydro potential of almost 5,000 MW.

Table 2.2: Region Wise Potential and its Status of Development at

60% Load Factor as of 1 January 2005

RegionPotential

Assessed (MW)

Potential Developed

(MW)

Potential under Development(MW)

Balance Potential

(MW)

Balance Potential

(%)

Northern 30155 5150 2905 22100 73.29Western 5679 2270 1164 2245 39.53Southern 10763 5924 153 4686 43.54Eastern 5590 1364 201 4025 72.00North Eastern 31857 517 914 30426 95.51

Total 84044 15225 5337 63482 75.53Source: Indian National Hydro Power Association.

Table 2.3: Basin-Wise Potential and its Status of Development at60% Load Factor as of 1 January 2005

Basin Potential(MW)Potential

Developed (MW)

Potential under Development(MW)

Balance Potential

(MW)

Balance Potential

(%)

Indus Basin 19988 3731 1156 14701 73.55Ganga Basin 10715 1901 1367 7447 69.5Central Indian Rivers 2740 1060 1147 533 19.45West Flowing Rivers 6149 3704 41 2404 39.09East Flowing Rivers 9532 4168 144 5220 54.76Bhramputra Basin 34920 661 1085 33175 95

Total 84044 15225 5339 63480 75.33Source: Indian National Hydro Power Association.

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Hydropower development commenced over a century ago in India with the installation of a 130

kW power stations in the Darjeeling district of West Bengal, almost in pace with the worlds first

hydro-electric station in the United States. However, to date only about 20% of the countrys

vast hydro potential has been harnessed. The share of hydropower in the total installed capacity

has also decreased over the years; from over 50% in 1960-61 to nearly 26% now (Fig 1).

Figure 2.1 Growth of Installed Hydro Power

2.7 CONCLUDING REMARKS

As discussed earlier, in this chapter the relevant literature has been perused to find the possible

paths towards the achievement of the objectives of this research work. Although there is

increased interest in real options, research has not expanded its influence into the physical

engineering design, where uncertainty and flexibility are key in many circumstances. It would be

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exciting to look into building real options into the engineering design of water facilities

themselves, and develop some general methodology to build flexibility into engineering systems.

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CHAPTER 3

RESEARCH METHODOLOGY AND DATA ANALYSIS

3.1 INTRODUCTION

The literature review chapter helped in understanding the possible variables required for this

research work. In order to accomplish the objectives of this study, the relevance of these

variables on Hydro Power Projects is to be determined. This chapter is focused on identifying the

significant variables in the valuation of hydro power projects. The usage of these variables would

be discussed in subsequent chapters. The primary data regarding the New Ganderbal Hydro

Electric Project (NGHEP) has been collected through meetings with the people associated with

the project. Following data was sought during the meeting with them:

Project Cost Project Life Project Capacity Plant Load Factor Annual Production Free Power to State Operation and Maintenance Cost Generation Tariff Debt- Equity Ratio Cost of Debt Cost of Equity Taxable Depreciation Rate Working capital Requirement Incentives

The data collected is described in the table 3.1

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Table 3.1 Project Data Collected

PARAMETERS VALUE

Project life 35 years

Capacity 93MW

PLF 48%

Annual production 382.82 GWH

Free power to State 13%

Project Cost 8257.9 Million INR

O&M 2% of the project cost

Yearly increase in O&M cost 5%

Selling price for 1st year per KWH 5.19

Selling price levelised per KWH 4.34

Debt 70%

Equity 30%

Cost of debt 12%

Cost of Equity 15.50%

The above Data is used in calculation of Net Present Value (NPV), Internal Rate of Return (IRR)

and also used in Real Option Analysis (ROA).

The secondary data has been collected from sources like Indian Energy Exchange, BSE- Sensex,

Reserve Bank of India websites.

3.2 DATA DESCRIPTION

3.2.1 Risk Free Interest Rate

The yield on the Government of India Bond with maturity of 10 years has been chosen as the

representative risk free interest rate for this study. This is because it indicates a fairly long term

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rate and also this instrument is the most actively traded in the Indian fixed income market. There

are examples in literature as given by Kolbe and Zagast, 2006 which advocate the use of 10 year

maturity as a representative proxy instrument for interest rates in such studies. The required data

has been collected from the Reserve Bank of India (Indian central bank) web site and Handbook

of Statistics on Indian Economy and is plotted in the figure 3.1

Figure 3.1 10 Year GOI Bond Yield

7.727.747.767.78

7.87.827.847.867.88

7.97.92

Jan/

11

Apr/

11

Jul/

11

Oct

/11

Jan/

12

Apr/

12

Jul/

12

Oct

/12

Jan/

13

Apr/

13

10 YR GOI BOND YIELD

10 YR GOI BOND YIELD

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3.2.2 Volatility of Electricity Price

Data regarding the volatility of the electricity prices is collected from Indian Energy Exchange.

Yearly data of electricity price for last 5 years is collected and is captured in Table 3.1

Table 3.2 Yearly Prices at IEX INR/MWH

Year N1

2008 7541.12

2009 6030.42

2010 3641.76

2011 3389.122012 3169.98

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3.2.3 Market Return and Risk

The data for market return and market risk is collected from BSE- Sensex website. The data of

marker return for last 14 years is collected and captured in Table 3.3

Table 3.3 BSE- Sensex Market Return

Indices :Sensex

Year High Low Close

2012-2013 20203.66 15748.98 18861.54

2011-2012 19701.73 15175.08 17404.22010-2011 21004.96 16022.48 19445.222009-2010 17711.35 9901.99 17527.772008-2009 17600.12 8160.4 9708.52007-2008 20873.33 12455.37 15644.442006-2007 14652.09 8929.44 13072.12005-2006 11307.04 6134.86 11279.962004-2005 6915.09 4505.16 6492.822003-2004 6194.11 2904.44 5590.62002-2003 3512.55 2834.41 3048.722001-2002 3742.07 2600.12 3469.352000-2001 5541.54 3540.65 3604.381999-2000 5933.56 3245.27 5001.28

Source: http://www.bseindia.com/markets/keystatics

- 22 -

- 23 -

CHAPTER 4

REAL OPTIONS THEORY

4.1 NPV AND DCF

The traditional DCF methods are used in capital budgeting to calculate the net present value of

the projects. The optimal investment rule is to invest only if the NPV of the project is positive.

However the traditional DCF method has certain limitations. The first limitation is estimating the

discount rate, which can arbitrarily be kept high considering the risk associated with project. The

second drawback is estimating the projects future cash flows, which is not always possible to

forecast accurately. Thirdly the DCF method does not take into account the managerial

flexibilities which are embedded in the project such as option to defer the project, the option to

expand or contract the scale of the project, the option to switch the input or output of the project

and the option to abandon the project if the outcome is not favorable. Lastly the strategic value of

a project resulting from its interdependencies with future, follow up investments and from

competitive interaction.

4.2 REAL OPTIONS VS FINANCIAL OPTIONS

A financial option is an option to buy or sell a financial asset which already exists and is actively

traded in a financial market in a standard form (stocks, shares, bonds, etc.). Buying and selling a

financial option on the stocks or shares of a business is a private bet on its market price, between

two investors, and this has no effect on the business itself.

- 24 -

In contrast, a real option is an option to change the real physical or intellectual activity of a

business. A real option is effectively a deal between the business itself and the entire outside

world and it can change the economic value of the business.

Comparative analysis: Financial and Real options

The conceptual analogy between financial options and real options is quite intuitive, and the

table 4.1 summarizes the analogies that can be easily drawn.

Table 4.1 Financial v/s Real Options

Financial Option Variable Real Option

Exercise price E Costs to acquire the

asset

Stock price S Present value of future

cash flows from the asset

Time to expiration T Length of time option

is viable

Volatility of stock

returns

Riskiness of the asset

Risk free rate of return R Risk free rate of return

It appears less obvious that the mathematical concepts used to price financial options with all the

assumptions they rely on will also be applicable to real options. However in last two decades

there has been lots of work in real option developments far beyond the initial basic option

concepts (wait/defer, abandon, switch, grow, expand/contract, compound). This work has

- 25 -

delivered further important insights into the commonalities and differences between real options

and financial options.

The commonalities between the two include the following generic basis:

1. Investment in uncertainty

2. Irreversibility

3. The ability to choose between two or more alternatives

4.3 TYPES OF REAL OPTIONS

4.3.1. The Option to Defer

The deferral option, or option of waiting to invest, derive its value from reducing uncertainty by

delaying a investment decision until more information has arrived. It is an American call option

on the project value at the exercise price. A carmaker may want to delay the decision to build a

new manufacturing plant for the new model until a better understanding of the market

performance of the product has developed and to outsource the manufacturing in the meantime.

4.3.2. The Option to Expand/ Contract (to change scale)

The option to change scale acknowledges managerial flexibility to alter capacity in order to

respond to market conditions. The option to expand is an American call option whereas the

option to contract is the American put option. For e.g. an existing airline company may consider

- 26 -

expanding by increasing the frequency of flights on established routes or by adding new

connections to its existing network.

4.3.3. The Option to Abandon

The option to abandon is an American put option, the right to dispose of the stock or an asset

and to recover the salvage value once market conditions change or market expectations remain

unfulfilled. The sale of an asset compensates for losses and permits investments in new assets or

more valuable real options.

4.3.4. The Option to Switch

The option to switch captures the managerial flexibility to alter the modus operandi of any

business. This includes exchanging input or output parameters, volume, processes, and global

locations. Brenner and Schwartz pioneered the option to switch in the mining industry by

analyzing the closing and opening of the mine as the two switching extremes of operations.1

Similarly, Dixit examines the value of managerial flexibility to enter or exit any given market as

a switching option.2 The basic component of the switching option that derive its value includes

the cost saved or additional cash flows generated by having the ability to respond to future

uncertainties and change a cost-driving operational parameter.

- 27 -

4.3.5. The Option to Growth

A company acquires a growth option by making an initial investment in a new market, a new

product line, or a new technology. Such an investment often requires more initial outlays than the

expected revenues would justify. However the value of this investment opportunity comes from

creating future growth opportunities. Growth options create infrastructure and opportunities for

future expansion and hence are of strategic value. They are sequential options that link distinct

growth and expansion steps but always preserve managerial flexibility to embark on the next

expansion step, depending on the prevailing market conditions.

4.3.6. The Compound Option

These are also called as options on options. By investing and completing each step management

buys the option, but not the obligation to take the project to the next level. Geske was the first to

price a compound option. He valued the call option on the stock as a call option on a call option

of the firms assets. A good example of a compound option situation in the real world is a

pharmaceutical drug development program.

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4.4 REAL OPTIONS VALUATION TOOLS

The valuation methods usually employed, likewise, are adapted from techniques developed

for valuing financial options. One should note that, in general, while most "real" problems allow

for American style exercise at any point (many points) in the project's life and are impacted by

multiple underlying variables, the standard methods are limited either with regard to

dimensionality, to early exercise, or to both.

Closed form, Black-Scholes like solutions are sometimes employed. These are applicable

only for European styled options or perpetual American options.

The most commonly employed methods are binomial lattices. These are more widely

used given that most real options are American styled. Additionally, and particularly,

lattice-based models allow for flexibility as to exercise, where the relevant rules may be

encoded at each node. Note that lattices cannot readily handle high-dimensional

problems.

Specialized Monte Carlo Methods have also been developed and are increasingly, and

especially, applied to high dimensional problems. Note that for American styled real

options, this application is somewhat more complex; although recent research combines

a least squares approach with simulation, allowing for the valuation of real options which

are both multidimensional and American styled

- 29 -

4.4.1 Black and Scholes Model

The Black- Scholes- Merton analysis is based on no arbitrage condition. The model was

designed to value European options, which are non dividend paying. Thus neither the possibility

of early exercise nor the payment of dividend affects the value of options.

In deriving the formula for option valuation, Black and Scholes (1973) made a series of

assumptions as follows:

1) The share price follows a random walk in continuous time and has a lognormal distribution

2) The growth rate and variance of the stock return are constant

3) The option is European type and pays no dividends.

4) There are no transaction costs in buying and selling the stock or the option

5) Borrowing at short-time interest rate is possible.

6) Short selling is permitted and involves no penalties.

The value of a call option in the Black-Scholes model can be written as a function of the

following variables:

S = Current value of the underlying asset

K = Strike price of the option

t = Life to expiration of the option

r = Riskless interest rate corresponding to the life of the option

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2 = Variance in the ln (value) of the underlying asset

The model can be written as:

Value of call = (1) (2)

Where

1 = ln + +

2 = 1

And N(x) is the cumulative probability distribution function for a variable that that is normally

distributed with a mean of zero and a standard deviation of 1.0.

- 31 -

4.4.2. BINOMIAL OPTION PRICING

Binomial option pricing is a simple but powerful technique that can be used to solve many

complex option-pricing problems. In contrast to the Black-Scholes and other complex option-

pricing models that require solutions to stochastic differential equations, the binomial option-

pricing model (two state option-pricing Model) is mathematically simple. It is based on the

assumption of no arbitrage.

The assumption of no arbitrage implies that all risk-free investments earn the risk-free rate of

return and no investment opportunities exist that require zero dollars of investment but yield

positive returns. It is the activity of many individuals operating within the context of financial

markets that, in fact, upholds these conditions. The activities of arbitrageurs or speculators are

often maligned in the media, but their activities insure that our financial markets work. They

insure that financial assets such as options are priced within a narrow tolerance of their

theoretical values.

4.4.2.1. Binomial Option Pricing Model

Assume that we have a share of stock whose current price is $100/share. During the next month,

the price of the stock is either going to go up to $110 (up state) or go down to $90 (down state).

No other outcomes are possible over the next month for this stock's price.

- 32 -

Beginning Value End of Month Value

$110

$100

$90

Figure 4.1 Binomial One Period

Now assume that a call option exists on this stock. The call option has a strike price of $100 and

matures at the end of the month. The value of this call option at the end of the month will be $10

if the stock price is $110 and 0 if the stock price is $90. The payoff at maturity (one month from

now) for this call option is:


$10 given a stock price of $100

Call Price today

$ 0 given a stock price of $ 90

Figure 4.2 Stock Price movement in Numerical Example

The question is: what should be the price of the call option today?

Consider what happens when we make the following investments in the stock and the call option.

Assume we buy one-half share of stock at $50 (.5 share times $100), and at the same time, we

write one call option with a strike price of $100 and maturing at the end of the month. Our

- 33 -

investment then is $50 less the current price of the call option. The payoff from this position at

the end of the month would be as follows: if the stock price is $110, our stock position is worth

$55, and we would lose $10 on the option. The return would thus be $45 if the stock price

reached a price of $110. On the other hand, if the stock price should go down to $90, the value of

our stock position would be $45 and the value of our option position would be 0. The payoff in

this case would also be $45

Investment Payoff

$55 [110 100,0] = $45

$50 $45 [90 100,0] = $45

Figure 4.3 Binomial One Period Payoff

The net effect of taking this particular position on this stock with this payoff structure is that our

payoff is $45 regardless of what happens to the stock price at the end of the month. The effect of

buying 1/2 a unit of the stock and writing a call option was to change a risky position into one

that is risk free with a payoff of $45 regardless of the stock price at the end of the month.

Assuming no arbitrage opportunities, an investor who makes this investment should earn exactly

the risk-free rate of return.

- 34 -

Thus, we know that the investment, $50 minus the call option price, has to be equal to the

present value of $45, the payoff, discounted for 1 month at the current risk-free rate of return.

In order to find the current price of the call option, we need only solve the following equation for

the option price:

$50 = $45.

= $50 $45.

Where Rf is the risk-free rate and T is the time to maturity in years. Assuming that the current

risk-free rate of return is 6% per annum and a time to maturity of one month, T=.08333, the

current option price of this call option should be $5.22.

The process used to price the option in this example is exactly the same procedure or concept

used to price all options, whether with the simple binomial option model or the more

complicated Black-Scholes model. The assumption is that we find and form a risk-free hedge

and then price the option off of that risk-free hedge. The key assumption is that the riskless

hedge will be priced in such a way that it earns exactly the risk-free rate of return, which is

where arbitrageurs come in to play. It is the activity of these individuals, looking for

opportunities to invest in a risk less asset and earn more than the risk-free rate of return that

insures that options are priced according to the no-arbitrage conditions.

- 35 -

4.4.2.2. Risk Neutral Approach

The basic argument in the risk neutral approach is that since the valuation of options is based on

arbitrage and is therefore independent of risk preferences; one should be able to value options

assuming any set of risk preferences and get the same answer. As such, the easiest model is the

risk neutral model.

In the risk less hedge approach, the probability of the stock price increasing, Pu, or the

probability of the stock price decreasing, Pd = 1-Pu, did not enter into the analysis at all. In the

risk neutral approach, given a stock price process (tree) we try to estimate these probabilities for

a risk neutral individual and then use these risk neutral probabilities to price a call option. For

example, we will use the same price process as the original risk less hedge example.


$95

$ 75

$63

Figure 4.4 Stock Price Movements

- 36 -

If an individual is risk neutral, then they should be indifferent to risk and as such for them the

current stock price is the expected payoff discounted at the risk free rate of interest. Assuming a

6% risk free rate, a risk neutral individual would make the following assessment:

$75 = [. $95 + (1 ). $63].

If we solve for Pu,

= $75. $63$95 $63

If RF = 6% and T=.08333, then Pu = .38675. This is the risk neutral probability of the

stock price increasing to $95 at the end of the month. The probability of it going down to $63 is

1-.38675= .61325. Now given that if the stock price goes up to $95, a call option with an

exercise price of $65 will have a payoff of $30 and $ 0 if the stock price goes to $63, a risk

neutral individual would assess a .38657 probability of receiving $30 and a .61325 probability of

receiving $ 0 from owning the call option. As such, the risk neutral value would be:

= [. $30 + (1 ). $0]. ..8Call Option Value = $11.54

- 37 -

4.4.2.3. Estimating the Binomial Stock Price Processes.

One of the difficulties encountered in implementing the binomial model is the need to specify the

stock price process in a binomial tree. While it is not transparent, when we use the Black-Scholes

model we are assuming a very explicit functional form for the stock price. If we are willing to

make the same assumptions when we are using the binomial model we can construct a binomial

model of the price process by using the volatility , to estimate up, u, and down, d, price

movements. This is done in practice as

= =

Where is annual volatility and t is the time between price changes. For example, assume a

current stock price of $55, a volatility of .20, = .20 and that the time to between price changes

is 1 month, t = .08333. Then u = et= e.20 .08333 = 1.0594 and then d = e-s Dt = e-.20 .08333

= 0.9439 and the stock price process over the one month interval would be:


$45 x 1.0594 = $47.67

$ 45

$45 x .9439 = $42.47

Figure 4.5 Stock Price Movement in Numerical example

- 38 -

If we keep the same ending point but let the price change every 2 Week = .04167, then =

= .. = 1.04167And

= = .. = 0.96

And the stock price process over the one month interval would be:

Now 2 weeks 1 month

$46.88 x 1.04167 = $48.83

$45 x 1.04167 =$46.88

$45.00 $46.88 x 0.96000 = $45.00

$43.20 x 1.04167 = $45.00 $ 45 x .96 = $ 43.20

$ 43.20 x 0.9600 = $41.47

Figure 4.6 Binomial Two Period

In the limit we could allow the price change for the example used above to change every week

(four times during the month and Dt = 1/52 = .01923) or daily (twenty-one times during the

- 39 -

month4 and Dt = 1/252 = .00397). Thus, given a volatility estimate we can construct the price

process for that security.

Once the price process for the underlying security is determined it is possible to use the binomial

model to price options on that security.

4.4.3. Monte Carlo Simulation

Simulation is a procedure in which random numbers are generated according to probabilities

assumed to be associated with a source of uncertainty, such as a new products sales or, stock

prices, interest rates, exchange rates or commodity prices. Outcomes associated with these

random drawings are then analyzed to determine the likely results and the associated risk.

Oftentimes this technique is called Monte Carlo simulation, being named for the city of Monte

Carlo, which is noted for its casinos.

Monte Carlo simulation is a widely used technique for dealing with uncertainty in many aspects

of business operations. For our purposes, it has been shown to be an accurate method of pricing

options and particularly useful for path-dependent options and others for which no known

formula exists.

To facilitate an understanding of the technique, we shall look at how Monte Carlo simulation has

been used to price standard European options. Of course, we know that the Black-Scholes model

is the correct method of pricing these options so Monte Carlo simulation is not really needed. It

- 40 -

is useful, however, to conduct this experiment because it demonstrates the accuracy of the

technique for a simple option of which the exact price is easily obtained from a known formula.

The assumptions of the Black-Scholes model imply that for a given stock price at time t,

simulated changes in the stock price at a future time t + t can be generated by the following

formula:

= +

Where S is the current stock price, S is the change in the stock price, rf is the continuously

compounded risk-free rate, is the volatility of the stock and t is the length of the time interval

over which the stock price change occurs. The variable is a random number generated from a

standard normal probability distribution. Recall that the standard normal random variable has a

mean of zero, a standard deviation of 1.0 and occurs with a frequency corresponding to that

associated with the famous bell shaped curve.

After generating one standard normal random variable, you then simply insert it into the right

hand side of the above formula for S. This gives the price change over the life of the option,

which is then added to the current price to obtain the price of the asset at expiration. You then

compute the price of the option at expiration according to the standard formulas, Max (0, ST - X)

for a call or Max (0, X - ST) for a put, where X is the exercise price and ST is the asset price at

expiration. This produces one possible option value at expiration. You then repeat this procedure

many thousands of times, take the average value of the call at expiration and discount that value

- 41 -

at the risk-free rate. Some users compute the standard deviation of the call prices in order to

obtain a feel for the possible error in estimating the price.

Let us price a call option. The stock price is 180, the exercise price is 185, the risk-free rate is

0.05, the volatility is 0.29 and the time to expiration is 0.9523. Inserting the above approximation

formula for a standard normal random variable in any cell in an Excel spreadsheet produces a

random number. Suppose that number is 0.264166. Inserting into the formula for S gives

180(.05) (.9523) +180(.29) (.264166) .9523 =21.92.

Thus, the simulated value of the stock at expiration is

180 + 21.92 = 201.92.

At that price, the option will be worth

Max (0, 201.92 -185) = 16.92 at expiration.

We repeat this procedure several thousand times, after which we take an average of the simulated

option prices and then discount that average to the present using the present value formula.

.

4.5. FRAMEWORK OF REAL OPTIONS VALUATION

Before using real options to evaluate a project, people first need to understand

decision to be made and check if it is advantageous to use this approach

method. If so, the valuation can be divided into 5 steps, as shown i

Figure 4.7

The first step, most important drivers and uncertainties of the project should be found out.

- 42 -

FRAMEWORK OF REAL OPTIONS VALUATION

Before using real options to evaluate a project, people first need to understand

decision to be made and check if it is advantageous to use this approach over traditional

method. If so, the valuation can be divided into 5 steps, as shown in Figure 4.2:

4.7 Framework of Real Options Method


Before using real options to evaluate a project, people first need to understand clearly what

over traditional NPV


- 43 -

Usually uncertainties include market risk (such as the market demand, price of the product,

economic cycle), technical risk (such as if the project can be finished on time, if the project can

achieve its technical objectives).

The second step, an approximate probability distribution should be assigned to each uncertainty.

In many cases, a lognormal distribution is used for a market risk. If there are other project-

specific risks associated with the project, their probability distributions should be studied case by

case.

The third step, the most important options should be identified. Possible options practical to the

project studied can be identified with reference to the types of real options.

The fourth step, appropriate method among Black-Schools formula, binomial model, and

simulation is identified and applied to obtain the value of the options.

The fifth step, by comparing the value of the options and cost to obtain options, a set of strategies

and decisions can be reached.

Meanwhile, the mind-set regarding flexibility available and different is established. Valuators

need to be careful of the false precision of the value of an option, because the value is established

on many approximations and assumptions. This is why a sensitivity analysis is sometimes

needed. Nevertheless, the mind-set to value the flexibility is one of the major gains of this

project.

- 44 -

- 45 -

CHAPTER 5

CASE STUDY: NEW GANDERBAL HYDRO ELECTRIC PROJECT

5.1 INTRODUCTION

The New Ganderbal Hydro Electric Project (NGHEP) is envisaged as a run-of-the river scheme,

between Preng and Ganderbal along left bank of the Nallah Sindh, a tributary of River Jhelum.

The diversion site is located at Preng having the latitude of 34 16 21.29 N and longitude of 74

52 27.23 E in the Ganderbal District of Jammu and Kashmir, about 40 km away from Srinagar

along the Srinagar-Leh National Highway. The powerhouse is located 20 km downstream of

diversion site at Ganderbal having the latitude of 34 13 15.50 N and longitude of 74 46 46.98

E. This new hydropower development has been contemplated because the existing Ganderbal

HEP (GHEP), commissioned in 1955, with an installed capacity of 15 MW, located along the

same bank of the Nallah, has now outlived its normal life.

The Ganderbal Power Station is the last of the Hydro Stations at the tail end of Nallah Sindh, a

tributary of River Jhelum and was commissioned in 1955. The Station is located at Ganderbal,

about 20 km from Srinagar city on Srinagar Leh Highway. The site is connected by AA class

Road. The installed capacity of the station is 15 MW consisting of 2 units of 4.5 MW and 2 units

of 3 MW. The station has served 57 years and thus outlived its normal life. The station has also

been giving recurring trouble and units have been derated and remain under regular outage due

to O& M problems. It was considered appropriate by Power Development Corporation (J&K

Govt.) to take effective measures to improve the power generation at this power station.

- 46 -

For taking effective measures to improve the power generation at Ganderbal power station,

engineering studies were carried out and two reports were developed, one for renovating the

existing water conductor system to improve its carrying capacity and the other for renovating and

overhauling the equipments to improve the station performance. Any renovated machine cannot

be expected to perform the same way as new units and their life cannot be expected to be as long

considering that the age of the units. It has therefore been considered that it is better to build a

new station and utilize these existing derated units till the new ones are commissioned.

The studies on the New Ganderbal Hydro Electric Project in Jammu and Kashmir State were

initiated in 1984 as a part of the investigation to replace the existing station and at the same time,

to augment the capacity to the extent possible. M/S. Thaper Hydra Consult had prepared a pre-

feasibility report in November 1988 for the project. Subsequently they were appointed as

consultants to prepare feasibility report for development of the project proposal.

- 47 -

5.2 PROJECT CHARACTERISTICS

The data regarding the project is captured in Table 5.1

Table 5.1 Project Characteristics

PARAMETERS VALUE

Project life 35 years

Capacity 93MW

PLF 48%

Annual production 382.82 GWH

Free power to State 13%

Project Cost 8257.9 Million INR

O&M 2% of the project cost

Yearly increase in O&M cost 5%

Selling price for 1st year per KWH 5.19

Selling price levellised per KWH 4.34

Debt 70%

Equity 30%

Cost of debt 12%

Cost of Equity 15.50%

- 48 -

5.3 VALUING NEW GANDERBAL HYDRO ELECTRIC PROJECT (NGHEP)

In this chapter, I have applied binomial lattice method to study the case on NGHEP, more

specifically a deferral option of the project. To understand the pros and cons and the applicability

of the real options method in the valuation of the project, the NPV and IRR are compared with

the real options method.

5.3.1 Traditional NPV

Table 5.2 Project NPV Analysis

Details / Years

Construction

period 1 10 15 25 35

Cash Outflow -8257.90 0.00

Cash Inflow

Profit After Tax 578.61 796.20 678.32 534.55 463.79

Interest on term loan 693.66 48.17 0.00 0.00 0.00

Interest on working capital 0.00 0.00 0.00 0.00 0.00

Depreciation 233.77 233.77 233.77 233.77 0.00

Total -8257.90 1506.04 1078.14 912.09 768.32 463.79

The NPV is INR 141.81 Million using the discount rate of 12.58% for initial 10 years and

19.49% for next 25 years. With such an analysis, because the NPV is greater than 0, Project

should be carried out immediately.

- 49 -

Note in the above net present value analysis, there are three very important assumptions:

1, the power plant will produce to full capacity, and all the electricity produced can be sold.

2, the price is fixed and will not change in 35 years.

3, here a12.58% discount rate is used for 1st ten years and 19.49% discount rate is used, which is

the WACC of the project.

These three assumptions are hard to defend:

1. How can a plant always produce at full capacity and sell all the electricity produced for a

period of 35 years? It is not only a simplified case, but also the most optimistic case and

apparently not realistic.

2, it seems unreasonable to assume that the price for electricity does not change over life of the

project i.e. 35 years.

3, the choice of discount rate is always a problem when evaluating public projects, there is no

concrete logic or proof for a specific discount rate chosen.

Although there are apparently unrealistic assumptions behind the NPV method, the method is

still ubiquitous. The reason is the computation difficulty of more refined models, and the NPV is

much better than nothing.

- 50 -

5.3.2. Traditional Internal Rate of Return (IRR)

The Internal Rate of Return (IRR) for Project can also be calculated. It is 13.72%. IRR provides

a better measure than NPV because it avoids the problem of choice of discount rate, and makes it

possible to compare the project with the expected return or capital cost to decide what to do.

Applying the traditional IRR valuation, the conclusion is that as long as the capital cost is less

than 13.72 %, the best strategy is to build the dam immediately.

5.3.3. Real Option Analysis

In this section I have used the Binomial tree model to calculate the value of the deferral option

using electricity price as the underlying.

5.3.3.1. A General Binomial Tree Framework for ROA

This section introduces the general binomial tree framework for ROA, and the following sections

will study the real options value with electricity price as the underlying.

- 51 -

Binomial Tree

Firstly, a binomial tree needs to be built based on some underlying describing the market

uncertainty. After building the binomial tree, a series of scenarios are developed with

probabilities, and what happens in each scenario can be analyzed. So a binomial tree can be

thought as an event tree in essence. To get such an event tree describing the market uncertainty,

one way is to lay out the scenarios of different NPVs, another way into present the evolution of

the electricity price.

Analysis of each scenario

Given the scenarios of underlying evolution, the expected payoff of each option can be

established. As Figure 5-1, a project with option 1, option 2 option n1 is valued. Given the

underlying value M, payoffs for each of those options can be calculated. The hold value is

calculated by discounted the expected value of next phase of the binomial tree.

M

Payoff for option 1

Payoff for option 2

Payoff for option 3

Hold value

Figure 5-1 Analysis of a scenario on the event tree

- 52 -

In the case of analyzing the deferral option for Project A, there is only one option. Only the

exercise value and hold value are entered into Figure 5-1.

Roll back

After establishing the options values for each scenario, the tree can be rolled back to get the

value of the option. The value for each scenario is:

Max (payoff for option 1, payoff for option 2, payoff for option n, the hold value)

Beginning from rightmost scenarios, the up probability pu and down probability pd are applied

to roll back to get the hold value for any scenario. Note the discount rate used must be risk

adjusted. The way to risk adjust the discount rate is to simulate the IRR and get the standard

deviation of the IRR. Note that different discount rates need to be applied to different cash flows

with distinct risk properties.

After rolling back the leftmost scenario, not only the value of options but also contingency

strategy can be developed.

- 53 -

5.3.3.2. ROA with Electricity Price as Underlying

The first step in ROA with electricity price as underlying is to calculate the volatility of the

electricity price and the drift rate r. For the options on stocks, the drift rate r is the risk-free

interest rate. If the underlying is electricity price, however, the drift rate cannot use the risk free

rate, it should be the expected change of electricity price per period of time.

5.3.3.2.1 Volatility

Can be calculated as standard deviation ofln , where P1 is the price of electricity at year 1 and P0 at year 0. The standard deviation for 5 years is 5e. The standard deviation is calculated

from the change in last 5 years prices traded at Indian Energy Exchange.

5e = .2051

Or

e = 9.17%

5.3.3.2.2. Risk Adjusted Discount Rate

For risk free rate, I have checked the Indian government 10 year bond which has an annual rate

of 7.82% but we are taking as 8% for the calculation simplicity. According to Sensex the

expected value and the standard deviation of the market rate of return are approximately 16.5%

and 40%. So the market price of the risk

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= ( )Or

= 0.2125Substituting rf, p, and into capital market line equation, the discount rate for the project is

= + . 2 = .0 + 0.2125 0.16 = .114

The risk-adjusted discount rate r is 11.4% which represents the intrinsic risk profile of the

project.

5.3.3.3. Binomial Tree

Though the life span of the project is 35 years and if a stage of 1 year is used, then there will be 35 stages, so the stage is taken to be 5 years

With r = 11.4% and e = 9.17%

The various parameters per stage are as follows:

= 5. = 1.22

= 1 = 0.1

=

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= 0.74 = 1

= 0.26

The electricity price movement is established as the binomial tree in figure.5.2

Year 0 Year 5 Year 10 Year 15 Year 20

9.61

7.88

6.46 6.38

5.29 5.29

4.34 4.34 4.34

3.51 3.51

2.85 2.85

2.30

1.87

Figure 5.2 Electricity Price Movements

This event tree gives different scenarios of electricity price market. For each scenario the

exercise price and deferral value is calculated.

The exercise value is just the expected NPV of starting Project A given the specific price in the

scenario. Given the starting price of electricity in a specific scenario, the Project Ancash flow

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simulation model can be used to get the expected value in this scenario. For example, for the

scenario in which the electricity price is 3.51/kWh, 3.51 are put as the starting price of electricity

in the Project cash flow simulation model, and the expected NPV of the project is 1069.32

Million INR.

The deferral value is the expected value if the option is not exercised. The deferral value is:

( 5 ). + ( 5 ). (1 + )5= 527.3

= = 35.5

5.4. Summary of Results

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With all the above analysis using different methods, the following results for the Project are

obtained as in Table 5-3

Table 5.3 Summary of Results

NPV IRR ROA

Value 141.81 13.72 527.3

Option value N/A N/A 385.5

Decision Go Go Wait

Using traditional NPV method, the project value without flexibility is studied. Then real options

analysis using electricity price as underlying are used to obtain the value of the project with

flexibility (the deferral options). The difference between the project value with flexibility and the

value without the project flexibility is the deferral options value.

The conclusion is that the ROA with electricity pricing as underlying gives the most accurate

valuation as 385.5 Million INR, and it gives a strategy to develop the project, contingency plan

regarding what to do under different scenario. Given the high volatility of price the best strategy

is to wait until the price of electricity is mostly resolved. If the price is high then beginning

building the plant, if it is low then still wait.

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CHAPTER 6

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CONCLUSIONS

6.1. SUMMARY AND CONCLUSIONS

The Recommended methodology for New Gander bal Hydro Electric Project is ROA with

electricity price as underlying because it takes into account the flexible decisions that managers

can make after the project begins and not the NPV or IRR method which gives the primitive

financial evaluation and also miss the value of flexibility and they cannot provide the

contingency strategy for the projects.

6.2 LIMITATIONS OF THE RESEARCH

Although attempts have been made to give a sound options valuation model for the use of

stakeholders through this research, yet there have been certain limitations which might have

posed some impact on the soundness of the results. Some of the constraints faced during the

research and corresponding limitations are discussed below.

1. This research work is linked to a technique which is complex, the option theories and

models such as, the partial differential equation, the dynamic processes people use to

think that the options are the work of rocket scientists. In developing countries, what

makes things even worse is that financial options are not traded in local financial

markets. This is because the trade of options is very easy to foster fraudulence in a weak

legal system. If a person does not establish an understanding of financial options, he/she

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will find it very hard to develop the idea of what the real options are and to have

confidence in the method.

2. Options analysis needs a lot of historical data to do objective analysis. In developed

countries, the abundant historical data on financial market provides the power of options

analysis - there is little subjective element in the analysis, and the magic of market tells

all. However, in developing countries, there is no complete financial market, and

consequently, the data is incomplete. Even with some data, the financial market is

decided by too much government interference so the information is highly distorted.

Although the difficulties in helping managers understand the methodology and the availability of

data problems, the real options method will be able to spread fast in developing countries

because of its insights into uncertainty and flexibility. The thinking is invaluable, nevertheless.

6.3 FUTURE SCOPE OF THE RESEARCH

The application of real options analysis to the hydro power projects is not limited to the type of

decision evaluated in this study. Other applications of real option analysis include of plant

dispatch, valuation of transmission assets, product pricing and structuring and various aspects of

risk management.

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APPENDIX 1

ALL INDIA INSTALLED CAPACITY ( IN MW) OF POWER STATIONS LOCATED IN THE

REGIONS OF MAIL LAND AND ISLANDS( As on 31.12.2012)

(UTILITIES)

RegionOwnership

Sector

Mode Wise BreakupGrand TotalThermal Total

ThermalNuclear

Hydro (Renewable)

RES (MNRE)Coal Gas Diesel

Northern Region

State 14213 2219.2 12.99 16445.19 0 7052.55 1203.21 24700.95

Private 5610 108 0 5718 0 2148 3420.03 11286.03

Central 11500.5 2344.06 0 13844.56 1620 6256.2 0 21720.76

Sub Total 31323.5 4671.26 12.99 36007.75 1620 15456.75 4623.24 57707.74

Western Region

State 16957.5 1915.72 17.28 18890.5 0 5480.5 444.42 24815.42

Private 15404 2805.5 0.2 18209.7 0 447 8005.62 26662.32

Central 10738 3533.59 0 14271.59 1840 1520 0 17631.59

Sub Total 43099.5 8254.81 17.48 51371.79 1840 7447.5 8450.04 69109.33

Southern Region

State 11382.5 555.7 362.52 12300.72 0 11353.03 1343.63 24997.38

Private 2760 4047.5 576.8 7384.3 0 0 10753.15 18137.45

Central 9640 359.58 0 9999.58 1320 0 0 11319.58

Sub Total 23782.5 4962.78 939.32 29684.6 1320 11353.03 12096.78 54454.41

Eastern Region

State 7010 100 17.06 7127.06 0 3168.92 330.16 10626.14

Private 5421.38 0 0.14 5421.52 0 0 106.55 5528.07

Central 10176.5 90 0 10266.5 0 713.2 0 10979.7

Sub Total 22607.88 190 17.2 22815.08 0 3882.12 436.71 27133.91

North Eastern Region

State 60 424.7 142.74 627.44 0 340 243.25 1210.69

Private 0 24.5 0 24.5 0 0 0.03 24.53

Central 0 375 0 375 0 860 0 1235

Sub Total 60 824.2 142.74 1026.94 0 1200 243.28 2470.22

Islands

State 0 0 50.02 50.02 0 0 5.25 55.27

Private 0 0 20 20 0 0 0.85 20.85

Central 0 0 0 0 0 0 0 0

Sub Total 0 0 70.02 70.02 0 0 6.1 76.12

ALL INDIA

State 49623 5215.32 602.61 55440.93 0 27395 3569.92 86405.85

Private 29195.38 6985.5 597.14 36778.02 0 2595 22286.22 61659.24

Central 42055 6702.23 0 48757.23 4780 9349.4 0 62886.63

Sub Total 120873.4 18903.05 1199.75 140976.2 4780 39339.4 25856.14 210951.7

Sourcehttp://www.cea.nic.in/power_sec_reports

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Application of Real Options in Hydro Power Projects