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Real Options Valuation of a Power Generation Project: A Monte Carlo Approach. Bruno Merven ( 1 ) , Ronald Becker (2) ( 1 )Energy Research Centre-University of Cape Town & International Resources Group Ltd. (2) Maths department, University of Cape Town. Overview.
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Real Options Valuation of a Power Generation Project:A Monte Carlo Approach Bruno Merven(1), Ronald Becker(2) (1)Energy Research Centre-University of Cape Town & International Resources Group Ltd. (2) Maths department, University of Cape Town
Overview • Introduction of case study and objective • Valuation method explained • Some results • Conclusions
Case Study • A peaking OCGT plant in an open market • Uncertainties • Price of fuel • Price of electricity • Volumes that will be sold over the life of the project • 4 possibilities for the investor • Don’t invest • Invest in a small plant • Invest in a larger plant • Invest in a small plant + pay a premium to have the possibility of expanding at a later stage
The case for Real Options • Provides a possibility for the valuation of the flexibility that exists within projects • In theory, more sound setting of the discount rate • Potentially less arbitrary definition of uncertainty
Valuation methods for Real Options • Closed form (Black-Scholes) • Lattice (Binomial/finite difference methods) • Monte Carlo (normally only for European-type) • Practitioners’ type (combination of the above) • Method presented: The Least-Squares Monte Carlo approach (provides the possibility of valuation when early exercise is possible)
The Least Squares Monte Carlo (LSM) method explained • Generate paths for uncertain variables over life of project • Start at the last date where expansion/abandonment option can be exercised • Move back in time, and each time (each year) compare the PV of exercising the various options (abandon/expand/continue) for each path • Take the average in year 0, where initial decision is taken
Generating Risk Neutral Paths • Fuel Price, F: Geometric Brownian Motion (GBM), r: Oil Futures, s: historic volatility • Electricity Price, P: GBM, r: futures market, s: historic volatility. P +ve correlation to F. • Volumes sold: 2 different paths generated (also GBM, but with –ve correlation to P): • Q1: the volumes for a small plant • Q2: the volumes for a large plant
Cash flow model • PV(tE) = tA+1TC(t)/(1+r)t-tE • PV(ti) = PV(ti+1)/(1+r)+C(ti) • Cash flow, C: C1,2(t)= Q1,2 (P(t)-V(t))-F(t)-tax(t)-I(t) • T: life of project • r: risk free rate • V: variable cost (function of fuel price F) • F: fixed costs • I: investment – non-zero at t=0 and t=t (year in which plant is expanded, if option exercised)
Simplest Case: option to Abandon, only stochastic fuel price • Start at tE • Calculate PV(tE) for each path/sample of Fuel price • Calculate continuation value VC(tE) • Compare VC(tE) to the value of abandoning VA(tE) at time tE • For paths where PV(tE)>VE, exercise abandonment, and update those paths with PV(tE) = VA(tE) • For other paths PV(tE) = VC(tE) • Go back 1 year (tE- 1) and repeat until t = 0, and calculate average
Calculation of Continuation Value VC • VC is the expected value of the project conditional on the value of the fuel price. • This is found by regressing PV(tE) against Fuel (oil price) with a simple polynomial
Results for the simplest case • Mean value of inflexible project: 101 • Mean value flexible project: 116 (15% higher)
Results for 2 uncertain variables • Mean value of inflexible project: 101 • Mean value flexible project: 128 (27% higher)
Results for project with option to expand • Mean value of inflexiblesmall plant: 91 • Mean value of inflexible large plant: 101 • Mean value flexible (abandonment/expansion) project: 187
Results for multiple option case • Mean value of inflexiblesmall plant: 91 • Mean value of inflexible large plant: 101 • Mean value flexible (abandonment/expansion) project: 211
Conclusions • The LSM method was used to evaluate a project with embedded flexibilities • The method is quite versatile and can handle more than one uncertain variable, and more than one option, without significantly increasing the level of complexity • In the particular case study, results were quite sensitive to the variables: the discount rate and Q1/Q2, • The difficulty lies in parameterising the stochastic variables • The method can only handle “uncertainty that can be parameterized”, but MC is quite versatile
Possible extensions • Valuation of fuel switching options • Valuation of option to expand to CCGT • Incremental addition/abandonment of units • A more detailed model for Q1,2 (market model) • The role and the value of derivatives/contracts for such a project