Energy Systems

, Volume 5, Issue 3, pp 423–447 | Cite as

Multi-commodity real options analysis of power plant investments: discounting endogenous risk structures

  • Wilko RohlfsEmail author
  • Reinhard Madlener
Original Paper


The value of power generation technologies can be derived from the investment cost, the plant’s expected lifetime, and the discounted cash flows, the latter of which typically are a combination of several underlyings, such as the price of fuel, electricity, and CO\(_2\). To determine this value, most studies assume predefined, uniform, and constant discount rates, irrespective of the fact that the specific risk strongly varies with the technology concerned and also over time. In order to endogenize the technology-specific risk, we develop a new model that explicitly accounts for the (likewise technology-specific) combination of the underlyings. More specifically, we use a multivariate binomial tree real options approach for analyzing the value of different power plants (gas-fired and coal-fired, with and without carbon capture and storage (CCS); hydro; wind; photovoltaics) and for taking into account technical change. We further investigate the influence of alternative CO\(_2\) policies on the plants’ values, modeling the CO\(_2\) price in three different ways and for three different carbon price levels (5, 25, 45 €/t\(_\mathrm{CO_2}\)): (1) as a stochastic process (geometric Brownian motion), reflecting the price development in the Emissions Trading Scheme of the European Union (EU ETS); (2) as a (constrained) stochastic process with a price floor, and (3) as a deterministic carbon tax. From the model application, using data from German exchange-based markets and a much-cited pilot study on future energy strategies and scenarios in Germany, we find a strong preference for hard-coal power plants in the low CO\(_2\) price scenario (\(P_{2015}=\) €5) and a low value of waiting in case of using the real options model. For all price scenarios, the value of waiting is much higher for both the CO\(_2\) permits with a price floor and the CO\(_2\) tax policy. This leads, for the medium and high CO\(_2\) price scenario, to a dominance of the CCS power plants. In the high CO\(_2\) price scenario (\(P_{2015}=\) €45), the value of waiting only delays the investment decision in the case of the floored CO\(_2\) permit prices. For the two other policies, the model predicts an immediate investment in CCS power plants once the CCS technology becomes commercially available in 2020.


Real options CAPM Multivariate binomial tree  Carbon tax Energy technology choice Endogenous discount rate 



The authors gratefully acknowledge helpful comments received on earlier versions of the paper from participants at the INFORMS 2011 (November 13–16, Charlotte, North Carolina) and the INREC 2012 (March 6–7, Essen, Germany) conferences.


  1. 1.
    Reinelt, P., Keith, D.: Carbon capture retrofits and the cost of regulatory uncertainty. Energy J. 28(4), 101–127 (2007)CrossRefGoogle Scholar
  2. 2.
    Bellman, R.E.: Dynamic Programming. Princeton University Press, Princeton (1957)Google Scholar
  3. 3.
    Black, F., Scholes, M.: The pricing of options and corporate liabilities. J. Polit. Econ. 81(3), 637–654 (1973)CrossRefGoogle Scholar
  4. 4.
    Dixit, A.K., Pindyck, R.S.: Investment Under Uncertainty. Princeton University Press, Princeton (1994)Google Scholar
  5. 5.
    McDonald, R., Siegel, D.: The value of waiting to invest. Q. J. Econ. 101, 707–727 (November 1986)Google Scholar
  6. 6.
    Boyle, P.P., Evnine, J., Gibbs, S.: Numerical evaluation of multivariate contingent claims. Rev. Fin. Stud. 2(2), 241–250 (1989)CrossRefGoogle Scholar
  7. 7.
    Siddiqui, A., Fleten, S.-E.: How to proceed with competing alternative energy technologies: a real options analysis. Energy Econ. 32(4), 817–830 (2010)CrossRefGoogle Scholar
  8. 8.
    Fleten, S.-E., Näsäkkälä, E.: Gas-fired power plants: investment timing, operating flexibility and \(\text{ CO }_2\) capture. Energy Econ. 32(4), 805–816 (2010)CrossRefGoogle Scholar
  9. 9.
    Rohlfs, W., Madlener, R.: Valuation of CCS-ready coal-fired power plants: a multi-dimensional real options approach. Energy Syst. 2(3–4), 243–261 (2011)CrossRefGoogle Scholar
  10. 10.
    Gahungu, J., Smeers, Y.: Multi-assets real options, CORE Discussion Papers 2009/51. Center for Operations Research and Econometrics (CORE). Universitè Catholique de Louvain, Belgium (2009)Google Scholar
  11. 11.
    Abadie, L.M., Chamorro, J.M., Gonzàlez-Eguino, M.: Valuing investments to enhance energy efficiency. In: Real Options Meets Practise: 14th Annual International Conference, 16–19 June, Rome (2010)Google Scholar
  12. 12.
    Abadie, L.M., Chamorro, J.M., Gonzàlez-Eguino, M.: Optimal abandonment of EU coal-fired stations. Energy J. 32(3), 175–208 (2011)CrossRefGoogle Scholar
  13. 13.
    Kienzle, F., Andersson, G.: Valuing investments in multi-energy generation plants under uncertainty: a real options analysis. In: Proceedings of the 10th IAEE European Conference, 7–10 Sep, Vienna (2009)Google Scholar
  14. 14.
    Rohlfs, W., Madlener, R.: Assessment of clean-coal strategies: the questionable merits of carbon capture-readiness. Energy 52, 27–36 (2013)CrossRefGoogle Scholar
  15. 15.
    Cox, J., Ross, S., Rubinstein, M.: Option pricing: a simplified approach. J. Fin. Econ. 7(3), 229–263 (1979)CrossRefzbMATHGoogle Scholar
  16. 16.
    Abadie, L.M., Chamorro, J.M.: Valuing flexibility: the case of an integrated gasification combined cycle power plant. Energy Econ. 30(4), 1850–1881 (2008)CrossRefGoogle Scholar
  17. 17.
    Gamba, A., Trigeorgis, L.: An improved binomial lattice method for multi-dimensional option problems. Appl. Math. Fin. 14(5), 453–475 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    Rubinstein, M.: Return to Oz. Risk 7(11), 67–71 (1994)Google Scholar
  19. 19.
    Sharpe, W.: Capital asset prices: a theory of market equilibrium under conditions of risk. J. Fin. 19(3), 425–442 (1964)MathSciNetGoogle Scholar
  20. 20.
    Lintner, J.: The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Rev. Econ. Stat. 47, 13–37 (May 1965)Google Scholar
  21. 21.
    von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior. Princeton University Press, Princeton (1944)zbMATHGoogle Scholar
  22. 22.
    Kahneman, D., Tversky, A.: Prospect theory: an analysis of decisions under risk. Econometrica 47(2), 263–292 (1979)CrossRefzbMATHGoogle Scholar
  23. 23.
    Hogg, R.V., Craig, A.T.: Introduction to Mathematical Statistics. Macmillan Publishing, New York (1978)Google Scholar
  24. 24.
    Hull, J.C.: Options, Futures and other Derivatives, 7th edn. Pearson, Prentice Hall (2008)Google Scholar
  25. 25.
    Nitsch, J., Pregger, T., Scholz, Y., Naegler, T., Sterner, M., Gerhardt, N., von Oehsen, A., Carsten, P., Saint-Drenan, Y.-M., Wenzel, B.: Langfristszenarien und Strategien für den Ausbau der erneuerbaren Energien in Deutschland bei Berücksichtigung der Entwicklung in Europa und global, Leitstudie 2010. Bundesumweltministerium BMU, FKZ 03MAP146 (2010)Google Scholar
  26. 26.
    McCoy, S.T.: The Economics of \(\text{ CO }_2\) Transport by Pipeline and Storage in Saline Aquifers and Oil Reservoirs. PhD thesis, Carnegie Mellon University, Pittsburgh (2008)Google Scholar
  27. 27.
    Wood, P.J., Jotzo, F.: Price floors for emissions trading. Energy Policy 39(3), 1746–1753 (2011) Google Scholar
  28. 28.
    Brunner, S., Flachsland, C., Luderer, G., Edenhofer, O.: Emissions trading systems: an overview. PIK Potsdam Institute for Climate Impact Research, Potsdam (2009)Google Scholar
  29. 29.
    Gardner, S.: Analysis: Europe—Little Support for Carbon Floor Price. Ethical Corporation, London (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Faculty of Mechanical Engineering, Institute of Heat and Mass TransferRWTH Aachen UniversityAachenGermany
  2. 2.Institute for Future Energy Consumer Needs and Behavior (FCN), School of Business and Economics/E.ON Energy Research CenterRWTH Aachen UniversityAachenGermany

Personalised recommendations