# Presentation: 433259

## 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

## 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

## 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.

## 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

## Simplest Case  Black-Scholes 

- N(.) is the standard cumulative normal distribution.
- St is the current stock price,
-  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
- E is the exercise price.

## 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:
- dSt=Stdt + StdZt
-     where Zt is a standard arithmetic Brownian Motion process.

## 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{-r}EN(d2)
-      where d1=[ln(St/E) + (r+2/2)]/sqrt()
-      and     d2=d1-sqrt()

## 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’.

## 				N(.)

**is the standard cumulative normal distribution**
**no assumptions required**

## 				St

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

## 		r

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

## 				

**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**

##  				=T-t

**is the time to expiration**
**given R&D spending in 2002 $ and commercialization in 2050**
**time to expiration is 48 years**

## 				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**** **

## Assessment of Needed Benefits to Make R&D worthwhile

| Scenario | Exercise Price (in $B) | Cents/kWh (in 2002$) |
| --- | --- | --- |
| 20 years of introduction, 80% uptime, inflation, 0.4% adoption rate | 14,871 | 2.5 |
| 20 years of introduction, 80% uptime, inflation, 1% adoption rate | 37,180 | 1.7 |
| 50 years of introduction, 90% uptime, 1% adoption rate | 16,298 | 0.6 |

- See: DH Goldenberg and JD Linton, Energy Risk, January 2006

## Additional notes on Black-Scholes

- If the stock price, the expected savings, is desirable then the R&D 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

## Other Problems that can be considered using Real Options

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