1 / 20

Real Options Valuation of a Power Generation Project: A Monte Carlo Approach

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.

driley
Download Presentation

Real Options Valuation of a Power Generation Project: A Monte Carlo Approach

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 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

  2. Overview • Introduction of case study and objective • Valuation method explained • Some results • Conclusions

  3. 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

  4. 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

  5. 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)

  6. 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

  7. 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

  8. 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)

  9. 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

  10. 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

  11. The exercise boundary (trivial case)

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

  13. 2 uncertain variables: Electricity Price and Fuel Price

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

  15. The option to expand

  16. 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

  17. The project with the option of expanding and abandoning

  18. 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

  19. 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

  20. 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

More Related