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 1.Price of fuel 2.Price of electricity 3.Volumes that will be sold over the life of the project 4 possibilities for the investor 1.Don’t invest 2.Invest in a small plant 3.Invest in a larger plant 4.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): ◦ Q 1 : the volumes for a small plant ◦ Q 2 : the volumes for a large plant

Cash flow model PV(t E ) =  t A+ 1 T C(t)/( 1 +r) t-t E PV(t i ) = PV(t i+ 1 )/( 1 +r)+C(t i ) Cash flow, C: C 1,2 (t)= Q 1,2 (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=  (year in which plant is expanded, if option exercised)

Simplest Case: option to Abandon, only stochastic fuel price Start at t E Calculate PV(t E ) for each path/sample of Fuel price Calculate continuation value V C (t E ) Compare V C (t E ) to the value of abandoning V A (t E ) at time t E For paths where PV(t E )>V E, exercise abandonment, and update those paths with PV(t E ) = V A (t E ) For other paths PV(t E ) = V C (t E ) Go back 1 year (t E - 1 ) and repeat until t = 0, and calculate average

Calculation of Continuation Value V C V C is the expected value of the project conditional on the value of the fuel price. This is found by regressing PV(t E ) against Fuel (oil price) with a simple polynomial

The exercise boundary (trivial case)

Results for the simplest case Mean value of inflexible project: 101 Mean value flexible project: 116 (15% higher)

2 uncertain variables: Electricity Price and Fuel Price

Results for 2 uncertain variables Mean value of inflexible project: 101 Mean value flexible project: 128 (27% higher)

The option to expand

Results for project with option to expand Mean value of inflexible small plant: 91 Mean value of inflexible large plant: 101 Mean value flexible (abandonment/expansion) project: 187

The project with the option of expanding and abandoning

Results for multiple option case Mean value of inflexible small 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 Q 1 /Q 2, 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 Q 1,2 (market model) The role and the value of derivatives/contracts for such a project