The Economics of Nuclear Fusion R

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The Economics of Nuclear Fusion RD

• 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

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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
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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 RD program in the future or the
  rate of improvement in technology in the future.
• Attempts to do so are needed, but easily
  challenged.

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An Alternative Approach
Consider RD as insurance against the
possibility of high future energy prices
Invest in RD or an RD portfolio To purchase
protection against unattractive energy costs
and/or cost volatility
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Simplest Case Black-Scholes

• N(.) is the standard cumulative normal
  distribution.
• St is the current stock price,
• r is the annualized risk-free rate,
• s is the annualized instantaneous volatility of
  percentage rates of return on the stock,
• tT-t is the time to expiration, and
• E is the exercise price.

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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
• dStmStdt sStdZt
• where Zt is a standard arithmetic Brownian
  Motion process.

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The Black-Scholes Option Pricing Formula
The Black-Scholes formula gives the current
value of a European call option, C(St), as
C(St)StN(d1)-exp-rtEN(d2) where
d1ln(St/E) (rs2/2)t/ssqrt(t) and
d2d1-sqrt(t)
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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.

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N(.)

• is the standard cumulative normal distribution
• no assumptions required

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St

• is the current stock price
• not available for real assets
• Consequently, we calculate the real stock price
  that makes the option attractive

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r

• is the annualized risk-free rate
• we utilize the average annualized Treasury Bill
  yield.

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s

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

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tT-t

• is the time to expiration
• given RD spending in 2002 and
  commercialization in 2050
• time to expiration is 48 years

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E

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

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Assessment of Needed Benefits to Make RD
worthwhile
See DH Goldenberg and JD Linton, Energy Risk,
January 2006
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Additional notes on Black-Scholes

• If the stock price, the expected savings, is
  desirable then the RD should be conducted
• Note the stock price does not take into account
  fixed costs of introduction, these are addressed
  in the exercise price
• The stock price considers time-adjusted revenue
  minus variable costs

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Other Problems that can be considered using Real
Options

• Advantage and value of conducting research into
  more than one technology (Max-min option)
• Considering RD as a series of sequential options
  (Compound option)
• Value of postponing certain investments, but
  maintaining option of conducting RD at a later
  time (American option)
• Value of developing/maintaining domestic
  capabilities (Various)