1. The Economics of Nuclear Fusion R&D Jonathan Linton Desmarais Chair in the Management of Technological Enterprises School of Management University of Ottawa Ottawa, On David Goldenberg Rensselaer Polytechnic Institute Troy, NY

2. 2 What Fusion is worth, depends on the future cost of energy : If perpetual motion machines become available, energy prices decline…... Nuclear fusion could becomes valueless If reserves decline for traditional energy sources and demand continues to grow, energy prices increase… …Nuclear fusion becomes very valuable

3. 3 Application of Capital Budgeting Need to assume that costs and revenues are known in the future. It is not possible to accurately forecast demand, supply or price of commodities far into the future. It is not possible to forecast the degree of success of an R&D program in the future or the rate of improvement in technology in the future. Attempts to do so are needed, but easily challenged.

4. 4 An Alternative Approach Consider R&D as insurance against the possibility of high future energy prices Invest in R&D or an R&D portfolio To purchase protection against unattractive energy costs and/or cost volatility

5. 5 Simplest Case Black-Scholes n N(.) is the standard cumulative normal distribution. n S t is the current stock price, n r is the annualized risk-free rate,  is the annualized instantaneous volatility of percentage rates of return on the stock,  T-t is the time to expiration, and n E is the exercise price.

6. 6 Assumptions of the Black-Scholes Pricing Formula The model assumes that the underlying asset follows a stationary log-normal diffusion process described by the stochastic differential equation: dS t =  S t dt +  S t dZ t where Z t is a standard arithmetic Brownian Motion process.

7. 7 The Black-Scholes Option Pricing Formula The Black-Scholes formula gives the current value of a European call option, C(S t ), as: C(S t )=S t N(d1)-exp{-r  }EN(d2) where d1=[ln(S t /E) + (r+  2 /2)  ]/  sqrt(  ) and d2=d1-sqrt(  )

8. 8 Assumptions (cont.) Under this description the log-normal diffusion process is essentially Geometric Brownian Motion. Black, Scholes, and Merton won the Nobel prize in economics for this model in 1997 under the title ‘for a new method to determine the value of derivatives’.

9. 9 N(.) n is the standard cumulative normal distribution n no assumptions required

10. 10 StSt n is the current stock price n not available for real assets n Consequently, we calculate the real stock price that makes the option attractive

11. 11 r n is the annualized risk-free rate n we utilize the average annualized Treasury Bill yield.

12. 12  n is the annualized instantaneous volatility of percentage rates of return on the stock n this is typically the most difficult part of calculating any option price n historical volatility of same or similar assets is used

13. 13  =T-t n is the time to expiration n given R&D spending in 2002 $ and commercialization in 2050 n time to expiration is 48 years

14. 14 E n is the exercise price n the exercise price is the cost of obtaining the benefit n cost of building and decommissioning nuclear fusion facilities – to meet demands for first fifty years of commercialization n note this involves all fixed costs

15. 15 Assessment of Needed Benefits to Make R&D worthwhile ScenarioExercise Price (in $B) Cents/kWh (in 2002$) 20 years of introduction, 80% uptime, inflation, 0.4% adoption rate 14,8712.5 20 years of introduction, 80% uptime, inflation, 1% adoption rate 37,1801.7 50 years of introduction, 90% uptime, 1% adoption rate 16,2980.6 See: DH Goldenberg and JD Linton, Energy Risk, January 2006

16. 16 Additional notes on Black-Scholes n If the stock price, the expected savings, is desirable then the R&D should be conducted n Note the stock price does not take into account fixed costs of introduction, these are addressed in the exercise price n The stock price considers time-adjusted revenue minus variable costs

17. 17 Other Problems that can be considered using Real Options n Advantage and value of conducting research into more than one technology (Max-min option) n Considering R&D as a series of sequential options (Compound option) n Value of postponing certain investments, but maintaining option of conducting R&D at a later time (American option) n Value of developing/maintaining domestic capabilities (Various)