Example of discounting

The present value of £1 at a discount rate of 10%.

Principals of Economic Cost-Benefit AnalysisEdit

Even if the primary goal of an ADSR is to transmute long-lived radioactive waste, it is generally considered that the ADSR will have to be capable of selling electricity to help pay for the cost of its construction and its running costs. Predicting these costs is approached from one of two ways, the top‑down or the bottom‑up. These are both forms of cost-benefit analysis. Top‑down analysis starts with the construction and running costs of similar power stations and accordingly scales, includes or excludes values as necessary to represent the cost of the ADSR. Bottom‑up analysis microscopically calculates the cost of each component and employee etc. that the ADSR requires.

Typically the cost associated with generating electricity is quoted in terms of the Levelised Cost of Electricity (LCOE). The total LCOE takes into account every cost associated with the power station and divides it by the energy produced over its entire lifetime. It is typically quoted in £/ MWh or pence / kWh (or Euros, dollars, etc.). Sometimes mills per kWh is quoted, where a mill (also called: mille or mil) is 1/1000th of a pound (or euro, dollar etc.). Within these LCOE calculations, the time value of money is taken into consideration.

The time value of money takes into account the principal that a given quantity of money today has a different value to the same quantity of money in the future (or in the past). For example, if £100 today is invested in a savings account with a 2% annual interest rate, in 10 years time there will be £122 in the account. In this example receiving £100 today has the same economic value as receiving £122 in 10 years time, however receiving £100 in 10 years time has less value than receiving it today. All financial costs and revenues can be discounted from a nominal value to their Present Value (PV). Continuing with the same example, the nominal sum of money of £122 in 10 years time can be equivalently described in terms of its PV by using a discount rate of 1.96%. The discount rate, $ d $, and the interest rate, $ i $, are linked by the equation: $ d = i/(1+i) $. The real PV value of the nominal sum of £122 is then calculated by the equation: $ DPV = NFV \times (1-d)^n $, where $ DPV $ is the Discounted Present Value (£100) and $ NPV $ is the Nominal Future Value (£122).

The figure to the right highlights the affect a discount rate of 10% has on the value of a nominal sum of £1. Discount rates are invariably positive and therefore intrinsically place greater value on near-term cash flows rather than future cash flows. This has significant implications for the economic case of nuclear power stations, which in the near-term require significant up front capital expenditure to construct, and only in the long-term return revenue for small running costs. Discounting also minimises the financial importance of the costs involved with decommissioning a power station and the cost of geological disposal of radioactive waste. In the commercial power industry it is typical for the discount rate to be anywhere between 5-15%.

The design of an ADSR will be influenced by the cost associated with unanticipated shutdowns of the reactor. The structure of electricity markets is therefore important. The UK electricity market is discussed [McClay 2008]; other developed liberalised electricity markets are similar.

Electricity Market

UK electricity market structure for arranging electricity contracts. Taken from [McClay 2008].

The figure on the right shows the structure of the UK electricity market. Electricity is bought and sold in 30 minutes intervals (termed periods; there are therefore 48 periods per day). Due to the low running costs of nuclear power stations, their owners will typically arrange long-term forward contracts for the electricity sold. These might be settled weeks to months in advance of the delivery time of the electricity. If the power station is shut down for unscheduled reasons then the owner will not be able to provide the electricity that they have already contracted to sell.

If there is warning of an impending unscheduled shutdown it is possible to arrange contracts with other electricity suppliers. In this instance the revenue returned from the original contracted electricity sales is approximately equal to the cost of the required supply contracts. No profit or loss is made, however the owner will not be making the profit it had expected to make if the shutdown had not occurred, therefore there is an opportunity cost.

One hour prior to delivering a 30 minute period of electricity the “gate” is closed; no more contracts may be arranged. If a reactor should experience an instantaneous unplanned shutdown then there is no opportunity to even try to arrange contracts with other electricity suppliers. When a power station scheduled to sell electricity shuts down without having contracts arranged to cover its supply shortfall, the owner defaults to having the national grid operator supply the electricity. The price that the national grid charges is the System Buy Price (SBP). The SBP is volatile, it can be less than the going rate for electricity, but it can also be as much as multiple orders of magnitude greater. In the contemporary UK electricity market, a power station selling 600 MWe into the market might expected business-as-usual gross profit of $ ∼ $£630,000, the loss made during a 24 hour failure of the power station is expected to be £270,000 (with a standard deviation of £430,000 and a skew $ ∼ $1.7). These numbers suggest that (roughly speaking and with significant volatility) in order to return a marginal profit a nuclear power station must successfully generate electricity for > 30% of its scheduled sales. To then offset the capital cost of constructing an ADSR, it will have to successfully deliver electricity for significantly more than 30% of its scheduled sales [Steer et al. 2009].

Steer, S.J., Nuttall, W.J., Parks, G.T. and Gonçalves, L.V.N., 2009, “A Projected Cost of Accelerator System Failures in a Commercial Accelerator Driven Subcritical Reactor”, University of Cambridge Electricity Policy Working Group Working Paper, [online]. Number 0927, Available at: [Accessed 3rd Feb 2010] (Final version of paper submitted to Energy Economics, 2010)

McClay, C. (British Energy) 2008, “Risk Management in Electricity Companies”, Presentation slides from British Energy. [Slides provided by Hall, C. (British Energy)] (Personal Communication, 30 January 2009)

The Expected Cost of Constructing and Operating ADSRsEdit

Two dedicated studies of the economic case for commercial ADSRs have been identified. One is by Fernández et al. [Fernández et al. 1996] and the other is by Steer et al. [Steer et al. Submitted 2010]. Both studies are for a standalone ADSR, selling 600 MWe into an electricity market. Both works consider the first-of-a-kind ADSR, (the Fernández et al. study looks at nth-of-a-kind ADSRs as well, but that is not discussed presently. Costs in the Fernández et al. study are quoted in 1996 US dollars, in the Steer et al. study they are in 2006 UK pounds. In this document the Fernández et al. cost values have been converted to UK pounds using an exchange rate of $1 = £1; the 1996 value is then escalated to 2006 money using the UK historical consumer price index (£ (1996),math>\times<\math>1.27 = £ (2006)). The cost values are highly sensitive to the chosen exchange rate. It has been assumed that $1 in the USA has the same purchasing power as £1 in the UK. The Steer et al. study was presented for a real discount rate of 10%; a range of discount rates are given by the Fernández et al. study. To enable direct comparison, this document discusses the Fernández et al. costs for a 10% discount rate.

The Fernández et al. analysis is a hybrid of bottom up and top down analysis it is based on the Energy Amplifier design of Carlo Rubbia et al. [Rubbia et al. 1995]. In support of the economic case of ADSRs, emphasis is placed on the simplicity of the design, its passive operation and its extended fuel cycle. The analysis assumes that the reactor runs continuously for 5 year periods between refuelling, for its ~28 tons of fuel this corresponds to a power output of 100 GW days / tone of oxide fuel. The ~10,000 tons of lead coolant is intended to flow through natural convection without the need for pumping and the proton beam is provided by a 12.5 MW 3-stage cyclotron.

The Steer et al. study takes a higher level approach to the design of the ADSR, frequently extrapolating cost values from expectations of Generation III reactors the European Pressurised Reactor (EPR) and the Advanced Passive reactor 1000 (AP1000). It is suggested that the highest achievable capacity factor will be 85%, but that the performance of the accelerator system may limit this to a lower value. The study considers an ADSR driven by a single LINAC accelerator and also one with a redundant second accelerator. The single accelerator ADSR is the subject of the numbers presented in this document.

The table below summarises some of the key design parameters and cost values from the two economic studies. The Fernández et al. study considers both a 30 and 50 year lifetime for the ADSR. In the years 31 to 50 the affects of financial discounting are severe to the point that the additional 20 years in plant life make only a very small difference to the cost of generating electricity. The 50 year life has been used in the table. The maximum capacity factor considered by Steer et al. , 85%, is quoted in the table.

Fernández et al. (1996)

Steer et al. (2010)

Comparison of two first of a kind ADSR economic assessments in 2006 money.

Capacity factor



Thermal efficiency


Not Specified

Lifetime of reactor

50 years

40 years

Power of accelerator

12.5 MW

10 MW

Total capital expenditure before first revenue

£1715 million

(£2858 / kWe)

£2091 million

(£3485 / kWe)

Cost of construction of accelerator proper (excluding cost of capital)

£235 million


£290 million


Decommissioning Cost

Not included

£513 million

Operations and maintenance cost

£7.99 / MWh

£21.22 / MWh

Fuel cost

£3.29 / MWh

£1.10 / MWh

Total levelised cost of electricity

£46.99 / MWh

£58.53 / MWh

2009 price of wholesale electricity in the UK (in 2006 money): £34.08 / MWh

For the numbers presented in the above table the ADSR is assumed to be 100% reliable. Other comparisons between the two studies are that the Fernández et al. assessment assumes that there is little or no need to address long term geological storage of radioactive waste and therefore its cost is not included. The Steer et al. study treats the cost of geological disposal conservatively, using the same cost as for Generation III reactors. Steer et al. suggest the larger of the two operations and maintenance costs. A significant fraction of this cost derives from assuming that a first of a kind ADSR accelerator will require comparable manpower to contemporary accelerator facilities. The Fernández et al. study claims that the passive nature of the reactor core and the ability to replace accelerator components during operation (thus giving the accelerator a very high reliability) will allow for an ADSR to be operated by less staff than contemporary PWRs.

Fernández, R., Mandrillon, P., Rubbia, C. and Rubio, J.A., 1996, “A preliminary Estimate of the Economic Impact of the Energy Amplifier” European Organisation for Nuclear Research CERN/LHC/96-01 (EET)

Steer, S.J., Cardin, M-.,A., Nuttall, W.J., Parks, G.T., Gonçalves, L.V.N., Submitted 2010, “Hedging Against Technology Risks of the Accelerator System of a First of a Kind Accelerator-Driven Subcritical Reactor” Submitted to the University of Cambridge Electricity Policy Research Group Working Paper Series (2010)

Rubbia, C., Rubio, J.A., Buono, S., Carminati, F., Fiétier, N., Gálvez, J., Gelès, C., Kadi, Y., Klapisch, R., Mandrillon, P., Revol, J.P. and Roche. Ch., 1995, “Conceptual Design of a Fast Neutron Operated High Power Energy Amplifier” CERN/AT/95-44 (ET)