What construction cost might prompt orders for new nuclear power plants in Texas?
Electricity generation deregulation has opened U.S. wholesale electricity markets to unregulated power producers. In this uncertain environment, how should a generating company evaluate the risk of investing in new capacity?1
Building upon the calculations in the sidebar (see p. 51) we can calculate the price trigger for new nuclear power capacity by considering the option of building an advanced boiling water reactor (ABWR) in Texas coming into commercial operation in 2010.2 This article: (1) provides a technique for estimating the mean and variance of net revenues from the power plant; (2) calculates the variance of net revenues; (3) determines a price trigger, or K*, that might trigger new orders for the current generation of nuclear power plants; and (4) discusses how to mitigate net revenue uncertainties in the form of controlling price risk, output risk, and cost risk.
ABWR Construction, Investment, Price, Output, and Cost
As an application of the real options approach to evaluating new nuclear power plants, public data is available to estimate construction cost, electricity prices, megawatt-hours generated, and operating costs for an ABWR in Texas. First, Table 1 (see p. 50) presents the average construction capital cost of a dual-unit ABWR built in the United States.3 The following summarizes the reactor supplier's statement regarding Table 1:
"The ABWR plant can be constructed in just four years for US$1,600/kWe and suppliers are willing to undertake a project on a fixed price, fixed schedule basis. As a result, the ABWR nuclear plant has proven itself in Japan and Chinese Taipei to be economically competitive with other power generation options and estimates indicate that it can be economic in other countries as well."
Let the construction cost (K) of the ABWR be $1,600/kWe (including financing charges) for a dual-unit 2,800-MW (gross) capacity plant (with 2,700 MW net). The plant could generate 23.65 M MWh each year at full capacity. The total investment, I, would be about $4,500 million (M).
Second, to forecast electricity prices over the life of the plant, consider energy sold in the Texas electricity market. The Texas market is unique in the U.S. because of its separation from the rest of the country into its own reliability region, known as ERCOT, the Electric Reliability Council of Texas. (Although all of ERCOT is in Texas, not all of Texas is in ERCOT.) Figure 1 shows Texas monthly electricity prices and natural gas prices from 1990 to 2003. Since the price spikes in 2000, the price of electricity (for example, "Type B Electric Energy" in ERCOT) has been higher and is likely to remain higher for the foreseeable future.
Figure 2 presents prices from 1990 to 2003 and simulated prices from 2004 to 2050. These simulated prices represent one of 1,000 Monte Carlo trials. In these trials, average price follows the parameters given in Figure 2. For each year there is a random draw from a normal distribution that adds variance to electricity prices. (The standard deviation of this normal distribution is $1.69.) In the particular simulation presented in Figure 2 the mean electricity price was $40.13 and the standard deviation was $1.62.
Figure 2 presents prices from 1990 to 2003 and simulated prices from 2004 to 2050. These simulated prices represent one of 1,000 Monte Carlo trials. In these trials, average price follows the parameters given in Figure 2. For each year there is a random draw from a normal distribution that adds variance to electricity prices. (The standard deviation of this normal distribution is $1.69.) In the particular simulation presented in Figure 2 the mean electricity price was $40.13 and the standard deviation was $1.62.
Third, during the 1980s and 1990s, capacity factors at U.S. nuclear power units improved dramatically. Figure 3 presents capacity factors from 1990 to 2002 at: (1) dual-unit BWRs in the U.S. that came into commercial operation after 1982; and (2) the Japanese ABWR that came into full commercial operation in 1997. Data for General Electric BWRs larger than 1,100 MW are used to simulate capacity factors at ABWRs operating in the United States. Ordinary Least Squares parameters were estimated with this sample of capacity factors. The estimated trend line is identified in Figure 3. Assuming ABWRs follow the same trend, the expected lifetime capacity factor would be about 86 percent. Using estimated parameters, a Monte Carlo simulation of capacity factors for a dual-unit ABWR is presented in Figure 4. (This is from the same simulation as in Figure 2.)
Fourth, Figure 5 presents C (operating cost at full capacity) for dual-unit BWRs in commercial operation in the United States after 1982 for the years 1990 to 2000 (inflated to mid-2001 dollars). Assuming ABWRs follow the same trend, Figure 6 presents a Monte Carlo simulation of variable expenses. In this simulation, the mean C is $16.38, with a standard deviation of $1.58. To summarize, expected net revenues might be (R is at the mean of the 1,000 Monte Carlo trials):
R = (($40.13/MWh . 86%) - $16.38/MWh) . 23.65M MWh/year = $430M/year.
The Value of a Dual-Unit ABWR in Texas
With a real discount rate of 7 percent, the capital recovery factor (d) is 0.0772 for 40 years. The NPV in 2010 (assuming both units are completed in 2010) is
NPV = (R / d )- I = ( $430M / 0.0772 ) - $4,500M = $1,100 M.
The NPV is positive, so the investor-generator would build the ABWR under traditional investment criteria.
However, net revenues are uncertain. Simulations of the electricity prices, generation output, and input costs can be combined to determine the probability distribution of net revenues. Figure 7 presents a simulation of revenues for each year from 2010 to 2050, based on the particular simulation in Figures 2, 4, and 6. Figure 8 presents a histogram of 1,000 simulations of NPV. Average NPV is $740M with a standard deviation of $160M. Underlying this NPV are average net revenues of $430M per year. How might an investor-generator evaluate this probability distribution for NPV?
Following the real options analysis, the variance of percentage changes in net revenues was 4.2 percent in the 1,000 simulations represented in Figure 8. With a variance of 4.2 percent, f = 60%.4 So,
I* = ( f /d ) R* = (60% / 0.0772) $430M = $3,340M and
K* = ($3,340M / 2,800MW) . (1,000 MW/kWe) = $1,200/kWe.
Alternatively, the capital recovery factor could be adjusted to reflect the uncertainty in NPV, i.e., (d/f) = 0.1287, inferring a real discount rate of 12 percent, or a risk premium of 5 percent. (A 12 percent cost of capital yields a 12.87 percent capital recovery factor for a 40-year life.) This represents a decrease of about 25 percent from construction cost in Table 1. Therefore, if investors implicitly discount nuclear power because of these uncertainties, new nuclear power deployment requires lower construction cost.
Mitigating the Risks of Nuclear Investment
Three risks were considered: price risk, output (capacity factor) risk, and cost risk. This section examines the sensitivity of the trigger K* to mitigating each of these risks and what nuclear power plant owner-operators might be willing to pay for real and financial assets to mitigate each of these risks.
To examine the sensitivity of K*, each risk can be suppressed in the Monte Carlo simulation. For example, if the owner-operator could contract with a buyer to guarantee the price of all output at $40/MWh (real) for 40 years, the standard deviation of the price could be reduced to zero and the trigger price (K*) would rise. Each of the three risks can be held to zero; two of the three can be held to zero; or all three can be held to zero.
As a benchmark, with the assumptions and simulations described in this paper, holding most revenue-related risk to zero, the nuclear power plant supplier could sell new nuclear power plants on a fixed-construction cost basis for a breakeven price of $1,980/kWe including IDC (see Table 2, p. 51). Controlling output and cost risk, price risk alone reduces K* by $200/kWe. Controlling output and price risk, cost risk alone reduces K* by $320/kWe. Controlling both price and cost risk, output risk alone reduces K* by $380/kWe.
Further, controlling output risk, price plus cost risk together reduce K* by $500/kWe. (Because of the slight correlation between price risk and cost risk in the simulations, there is an economy of risk reduction, compared to controlling price and cost risk separately for the equivalent of $520/kWe.) The influence of each pair of risks on K* can be calculated (see Table 2). Finally, to trigger sales with no risk mitigation (output, price, or cost risk), K* is about $780/kWe lower than the benchmark, i.e., $1,200/kWe (as found above).
These values for mitigating risk give an opportunity to consider bargaining among nuclear power industry participants to share risk and returns from new nuclear power plants. For example, the owner-operator might be willing to reduce the price of firm power below the expected spot market price to encourage very long-term contracts. According to the assumptions here, the owner-operator might be willing to pay up to the equivalent of $200/kWe to eliminate price risk. (This is a price per megawatt-hour difference of about 10 percent, holding all else equal.)
Under electric utility rate-of-return regulation, price risk was reduced by giving electric utilities price increases to cover increases in reasonable costs of operation and capital. In deregulated markets, price risk is shared between the owner-operator and the electricity consumer. Further research should determine the willingness-to-pay of electricity consumers for firm power under very long-term contracts.
A related question concerns output risk (because risk-mitigating measures to control price risk require the delivery of firm power). The owner-operator must backup committed output with either: (1) financial instruments or contracts for purchases on the spot market; or (2) physical assets, such as natural gas peaking units. The owner-operator should be willing to pay up to $500/kWe to eliminate both output and price risk. Future research should consider alternative real asset and financial portfolios to best mitigate these two forms of risk simultaneously for new nuclear power plants.
The remaining risk to the investor is cost risk, which could be eliminated through contracting. For example, nuclear fuel (which has an asset life of decades) could be leased at a fixed price for a finite period and returned to the lessor. Also, an operations management company could operate the plant under contract. But the transaction cost of monitoring an operating contract is likely to be prohibitive. Therefore, cost risk should be assigned to the party best able to mitigate cost risk on a day-to-day basis-the owner-operator. Future research should consider how much cost risk can be mitigated and how much equity in the project might be required of the owner-operator to create optimal incentives to deliver cheap, reliable, and safe electricity.
Three risks influence annual net revenues (revenues before payments on construction expenditures) from operating nuclear plants: output risk, price risk, and cost risk. Currently operating nuclear power plants were built under rate-of-return regulation. Future nuclear power plants likely will be built in deregulated environments. These environments put competitive pressure on nuclear power plant suppliers to lower new nuclear power plant construction cost and to develop a new business model for new plants. Future research should examine risk-mitigating components of this new business model. Until a new business model is created and implemented, it is unlikely that there will be new orders for nuclear power plants in Texas (or anywhere in the United States).
Endnotes
- A more detailed explanation of the techniques used here can be found in Geoffrey Rothwell, "What Construction Cost Might Trigger New Nuclear Power Plant Orders?" (March 2004) at http://siepr.stanford.edu/papers. On deregulated electricity markets, see Geoffrey Rothwell and Tomas Gomez, (2003, IEEE Press with John Wiley).
- Two ABWRs have been operating in Japan since 1997 and four units are under construction in Japan and Chinese Taipei. The ABWR has been certified by the U.S. Nuclear Regulatory Commission for construction in the United States.
- See Nuclear Energy Agency. Reduction of Capital Costs in Nuclear Power Plants (2000, Paris: OECD): pp. 96-99. In their 2003 edition Brealey and Myers dropped their discussion of "Misusing Simulations" (part of which is quoted here) and added a new section, "Real Options and Decision Trees."
- Here g = 1/2 . {1+[1+(8.0.077/0.042)]1/2 } = 2.5 and f = (g - 1) /g = 0.60
- The capital recovery factor, d, is equal to [erT (er - 1)]/( erT - 1), where r is the generator's cost of capital and T is the economic life of the plant (ignoring tax effects, see next).
- Neglecting income taxes is not likely to influence the primary conclusions of this paper under competitive market conditions, low corporate income tax rates, and the use of accelerated depreciation. However, the error will increase with increases in the cost of capital.
- Consider Robert Brealey and Stewart Myers, Principles of Corporate Finance (2000, Irwin/McGraw-Hill); p. 275): "Finally, it is very difficult to interpret a distribution of NPVs. Since the risk-free rate is not the opportunity cost of capital, there is no economic rationale for the discounting process. Because the whole edifice is arbitrary, managers can only be told to stare at the distribution until inspiration dawns. No one can tell them how to decide or what to do if inspiration never dawns." Hopefully, this analysis will provide some inspiration for identifying sources of risk and how to mitigate them. It also provides a method for calculating the risk premium.
- Avinash Dixit and Robert Pindyck, Investment Under Uncertainty (1994, Princeton University Press): pp. 65 and 148.
- Here, f equals [( g - 1)/ g] where g = 1/2 ? {1 + [1 + (8 d / s 2 )]1/2}, see Rothwell (2004, Appendix. 2). This formula for g assumes that financial markets price risk consistently across assets, including assets in a portfolio that is perfectly correlated with ("spans") net revenues for new power plants.
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