# Probability Distributions of Net Present Values for U.S. Nuclear Power Plants

# Introduction

From the dawn of electricity deregulation in the United States until mid-1998,

a pessimistic cloud hung over the nuclear power industry. This was expressed

in early 1998 by the CEO of Commonwealth Edison, James O’Connor, after three

other plants (Haddam Neck, Maine Yankee, and Big Rock Point) had closed before

the end of their licensed lifetimes in 1996 and 1997:

“Our decision to close Zion Station is based on economics. A thorough analysis

of the projected costs to produce power at the station and the expected price

of electricity in a deregulated market led us to one conclusion: Zion Station

will not be able to produce competitively priced power in a deregulated marketplace

over the remaining useful life of the plant.”

On June 25 of 1998, Commonwealth Edison paid up to $6,000 per megawatt-hour

(MWh) in the fiercely competitive marketplace. The pessimistic cloud lifted.

The last nuclear power plant to retire was Millstone 1 in July 1998 after being

inoperable since December 1995.Two nuclear power plant operators began to aggressively

purchase plants in 1998 and 1999. AmerGen, a joint-venture between PECO (originally

Philadelphia Electric Company, operator of Limerick 1 & 2 and Peach Bottom 1

& 2) and British Energy (operator of 15 Advanced Gas Reactors in the United

Kingdom) won bids to acquire Three Mile Island 1, Clinton, and Oyster Creek.

Entergy (operator of Arkansas Nuclear One 1&2, Grand Gulf in Mississippi, and

River Bend and Waterford in Louisiana) bought Pilgrim. Announced prices per

kilowatt (kW) ranged from $128 to $16 (Table 1). Similar offers were made for

Nine Mile Point 1 & 2 ($117 for Unit 1 and $136 for Unit 2) and for Vermont

Yankee ($44), but these sales were suspended in the belief that these plants

were worth more than what was being offered.

Soon after AmerGen concluded these purchases, PECO announced its intended merger

with Commonwealth Edison (operator of 11 nuclear units in Illinois) to become

Exelon. The following year Carolina Power & Light Company (operator of Brunswick

1&2, Robinson, and Shearon Harris) merged with Florida Power Corporation (operator

of Crystal River) to form Progress Energy.

##### Table 1 – Nuclear Power Plant Sales, 1998-2001.

see larger image

Also in 2000, Entergy acquired Fitzpatrick and Indian Point 3 (jointly) at

an announced price of $450/kW and Indian Point 1 & 2 at an announced price of

$372/kW. In 2001 two more nuclear power operators acquired plants. Dominion

(originally Virginia Electric & Power Company, operator of North Anna 1 & 2

and Surry 1 & 2) paid $640/kW for Millstone 1, 2, & 3. Constellation (originally

Baltimore Gas & Electric Company, operator of Calvert Cliffs 1 & 2) paid $524/kW

for Nine Mile Point 1 & 2. Further, Entergy concluded the purchase of Vermont

Yankee for $290/kW.

Announced prices should be adjusted for:

• Fuel Inventory Payments,

• Purchase Power Agreements, and

• Decommissioning Costs and Trust Funds^{1}.

Once these adjustments are made, the sale prices for plants during 1998 and

1999 ranged from $46/kW for Clinton to -$74/kW for Oyster Creek (Table 1). (A

negative sales price implies that the seller paid the buyer to accept ownership

of the plant’s assets and liabilities.) Were these prices reasonable? Did they

reflect the Net Present Values of these plants? What is the probability that

these NPVs were negative?

# The Net Present Value of Nuclear Power Plants

The Net Present Value of any project is total revenues, TR, minus total costs,

TC, from each year of the project, discounted to the present and summed2. For

the electricity generators (TR — TC) is equal to the price of electricity,

P, minus Average Variable Cost, AVC, in dollars per megawatt-hour ($/MWh) times

the quantity of electricity sold, Q (in MWh).

Under deregulation, the price of electricity is determined in the market. AVC

is equal to the sum of (1) fuel costs per MWh plus (2) Operation and Maintenance

expenses per MWh plus (3) Capital Additions per MWh. (Capital Additions include

all “going-forward,” depreciable investments.) The quantity of electricity is

equal to the Capacity Factor times the size of the plant (in MW) times the number

of hours in the year (usually 8,760). As discussed in Rothwell^{3},

we can transform AVC into a “minimum” AVC/MWh (this is AVC/MWh at a 100 percent

Capacity Factor) divided by the Capacity Factor. For example, with an average

variable cost of $30/MWh at an 80 percent capacity factor, the “minimum” value

of average variable cost would be $24/MWh at a 100 percent capacity factor.

Therefore, to forecast the NPV of an NPP we need for each year (t)

1. An appropriate discount rate, r (percent),

2. Projected prices of electricity, Pt ($/MWh),

3. The size of the plant, W (MW)

4. Projected Capacity Factors, CFt (percent),

5. Projected “minimum” Fuel costs per MWh, minFt ($/MWh),

6. Projected “minimum” O&M expenses per MWh, minO&Mt

($/MWh)

7. Projected “minimum” Capital Additions per MWh, minKt ($/MWh).

For example, assuming constant values, if the P is $35/MWh, minAVC is $24/MWh,

CF is 80 percent, and W is 1000MW, then profit (without considering annual payments

for plant construction and financing) is $35 million per year. Assuming a discount

rate of 9 percent (real, i.e., not including inflation) and a remaining lifetime

of 15 years, the Present Worth Factor would be about 8.0; so the NPV would be

$280 million Further, dividing by the number of kW (i.e., 1 million), the NPV/kW

is $280. If the market price of the plant is less than $280/kW, the buyer gains.

If the book value of the plant is greater than the market price, the difference

is either written off as a loss (to the shareholders) or recovered as a stranded

asset (from the customers), or distributed between the shareholders and the

customers.

To estimate the NPV/kW for each NPP:

• I forecast the Capacity Factor, “minimum” Fuel, “minimum” O&M expenses,

and “minimum” Capital Additions with a simple Ordinary Least Squares estimate

of a plant or unit-specific constant and a time trend, controlling for plant

or unit type, age, and size^{4}, and

• I use U.S. Energy Information Administration forecasts of deregulated

electricity prices for each state^{5}.

These projections are given for a discount rate of nine percent (real) in

the last column of Table 1. Table 1 shows that both the adjusted price per kW

and the estimated NPV/kW for Pilgrim and Oyster Creek were negative, the adjusted

price per kW for Pilgrim and Clinton are similar, but for Three Mile Island

1 and Oyster Creek differ by factors of more than 10, and the adjusted price

per kW for Fitzpatrick plus Indian Point 3 falls between the forecast NPVs of

each of these units. To investigate the robustness of these forecasts, the next

section discusses the probability distributions of the estimated NPVs.

# NPV Probability Distributions

Of course, any estimate involves forecasting error. Fortunately, with econometrics

the forecasting error can be calculated. Given the simple statistical structure

of the forecasting equations, I can calculate the variance associated with the

forecast of Capacity Factor, Fuel, O&M, and Capital Additions. It is equal to

the variance of the plant or unit-specific constant plus the variance of the

residual (Rothwell, 20004). Also, there is variance in electricity prices. To

proxy this variance I use the variance in the average electricity revenue from

residential customers for each state, available in EIA Form 826 for 1990-1997.

With the forecasts of annual net revenue and these variances, I simulate the

probability distribution of the NPV for each NPP unit using Monte Carlo techniques.

This is done 1,000 times by sampling from the five probability distributions

for electricity price, Capacity Factor, Fuel, O&M, and Capital Additions for

each remaining year of the NPP licensed life, calculating the net revenue, and

discounting the net revenue to the present.

When discounting probabilistic outcomes, the recommended discount rate is the

risk-free rate of interest. According to Brealey and Myers:^{6}

“First, we should explain what is meant by a distribution of NPVs. The cash

flows for each iteration of the simulation model are trans lated into a net

present value by discounting at the risk-free rate. Why are they not dis counted

at the opportunity cost of capital? Because, if you know what that is, you don’t

need a simulation model, except perhaps to help forecast cash flows. The risk-free

rate is used to avoid prejudging risk. The ‘expected NPV’ includes no allowance

for risk. Risk is reflected in the dispersion of the NPV distribution.”

Figures 1, 2, and 3 present NPV distributions for Indian Point 3, Fitzpatrick,

and Fitzpatrick plus Indian Point 3 using a risk-free rate of 3 percent. The

expected NPV at a discount rate of three percent for Indian Point 3 was $58/kW

with a standard deviation (SD, the square root of variance) of $201/kW. In the

1,000 simulations, the NPV for Indian Point 3 was negative 37 percent of the

time: P(NPV<0)=37 percent. On the other hand, the expected NPV for Fitzpatrick
was $335/kW with a standard deviation of $175/kW. In the 1,000 simulations,
the NPV for Fitzpatrick was negative in only 20 simulations (two percent of
the time). With these plants operating together and facing the same random price
of electricity:
• The expected NPV is a weighted average of the expected values of each
unit (where weights are equal to unit capacity divided by plant capacity).

• The standard deviation is lower than the standard deviation for either

unit, because randomly higher costs at one unit can be balanced by randomly

lower costs at the other unit.

• The probability of a negative NPV, nine percent, is closer to the value

for Fitzpatrick, because of the lower standard deviation.

##### Figure 1 – The NPV Probability Density for Indian Point 3 at a three percent

Discount Rate.

##### Figure 2 – The NPV Probability Density for Fitzpatrick at a three percent

Discount Rate.

This is the portfolio effect: portfolios of generating units reduce the risk

associated with random cash flows from a single unit. A well-known result of

modern finance theory is that for each level of return from a portfolio of assets,

diversifying the portfolio can reduce risk. As nuclear power plant owners attempt

to maximize profit in a deregulated environment, they will seek ways to diversify

their portfolios. One way is to buy other nuclear power plants. Which plants

should they buy?

##### Figure 3 – The NPV Probability Density for Fitzpatrick plus Indian

Point 3 at a three percent Discount Rate.

# Implications for Future Nuclear Power Plant Sales

Table 2 presents the results of probability analysis described above applied

to every nuclear power plant in the United States. Three-quarters (77/103) of

all U.S. nuclear power plants have less than a 10 percent chance of having a

negative NPV. This is true for nuclear power plants in states that have not

passed deregulation legislation (32/43) and states that have passed deregulation

legislation (45/60). Of the 12 units that have been sold, 60 percent (7/12)

had a less than 10 percent chance of having a negative NPV, but the other 40

percent had a higher chance of having a negative NPV (two of them were Pilgrim

and Oyster Creek). Sales of these poorly performing units depressed prices in

the nuclear power plant purchasing market in 1998 and 1999. Although 12 operating

units have been sold in states that have started to deregulate, there are 48

units that have not been sold. Most of them have less than a 10 percent chance

of having a negative NPV, but eight of them have greater than a 50 percent chance

of having a negative NPV. The owners of these units should either sell them

or merge with better managed nuclear power plant owners.

##### Tab. 2 Probability of Negative NPV

Further, because of portfolio effects and because it appears to be difficult

to receive full value on nuclear power plant sales, owners who can profitably

manage one unit or one plant should either buy other units or merge with owners

of well-managed plants. As more states deregulate and either require their utilities

to sell generating assets or allow their utilities to merge, the nuclear power

plant industry will become more concentrated. Although this might increase market

power in some generating markets, it will surely increase the market power of

the utilities in the nuclear services market.

As the nuclear power industry becomes more profitable, the probability of a

new nuclear power plant order will increase. But until prices of “used” nuclear

power plants (until now about $500/kW) approach the cost of constructing and

financing a new nuclear power plant (about $2000/kW), new orders are unlikely.

Therefore, sales prices in the deregulated nuclear power plant market signal

the future of the nuclear power industry.

##### Acknowledgments

*I thank R. Hagen and E. O’Donnell and participants at my
presentations to the Society for Risk Analysis Annual Meeting, Arlington, Virginia
(December 3-8, 2000), the Western Economics Association Annual Meetings, San
Francisco, California (July 4-8, 2001), and the Department of Nuclear Engineering,
University of California, Berkeley, for helpful suggestions. Of course, any
errors are my own.*

#### Footnotes

1 D. Donoghue, D. Haarmeyer, and R.T. McWinney, “The US Nuclear

Plant Market: The Search for Value,” Nuclear News, June 2000.

2 T. Gomez, and G.S. Rothwell, “Principles of Electricity Economics: Regulation

and Deregulation,” IEEE Press, forthcoming.

3 G.S. Rothwell, “Profitability Risk Assessment at Nuclear Power Plants under

Electricity Deregulation,” The Utilities Project, sponsored by PricewaterhouseCoopers,

www.UtilitiesProject.com, 2000.

4 G.S. Rothwell, “The Risk of Early Retirement of US Nuclear Power Plants under

Electricity Deregulation and CO2 Emission Reductions.” The Energy Journal 21(3),

2000.

5 U.S. Energy Information Administration, “Competitive Electricity Prices: An

Update,” Issues in Midterm Analysis and Forecasting, 1998.

6 R. Brealey and S. Myers, “Principles of Corporate Finance,” McGraw-Hill, 1981.