The Cold War Legacy and Climate Change Motivation

This article explores the complexities of calculating energy costs, particularly for nuclear power, by delving into the time value of money, inflation, interest rates, and various cost components. It highlights how historical context and economic factors significantly influence these calculations.

The Cold War Legacy and Climate Change Motivation

The current state of nuclear technology is largely an artifact of the Cold War, not an optimally selected path. While climate change provides a strong motivation for nuclear power, its economic viability without this motivation is questionable due to high prices. Quantifying the damages from climate change is challenging, leading to an approach that considers "cost plus externalities," with the social cost of carbon (SCC) as a free parameter.

The SCC is difficult to define precisely due to feedback mechanisms and spreading uncertainties. Despite 125 years of scientific effort, this number remains unconstrained and is a time-dependent function. While the optimal level of CO2 abatement is not zero (as the marginal cost of abatement will eventually exceed its marginal benefit), the SCC serves as a heuristic to study the system's phenomenology. By varying the SCC, one can analyze its impact on carbon abatement and the technologies supported under different assumptions.

Understanding the Time Value of Money

To accurately compute the cost of energy, a thorough understanding of the time value of money is crucial. This involves interest rates, inflation, and the aggregation of costs incurred over different periods into a single lump sum.

Why Money's Value Changes

The value of money changes due to several factors:

1. Money Production: Banks create money through loans, a process that synthesizes a numerical representation of value. If this outpaces real economic productivity (labor, creativity), the value per unit dollar decreases, leading to inflation. Monetary policy aims for slight, continuous inflation to encourage spending and keep the economy active, preventing hoarding and economic stagnation.
2. Opportunity Cost: Lending money for a project means foregoing other potential investments. Lenders demand compensation for this lost opportunity, which is factored into interest rates.
3. Risk Factor: Investments carry risk. If a project fails, the lender might not recover their money. This risk is also incorporated into the interest rate, ensuring that, in expectation, the lender receives their principal back plus the opportunity cost.
4. Pure Preference for Early Consumption: Humans generally prefer receiving money today rather than tomorrow due to uncertainty about the future. This psychological preference also contributes to the time value of money. This effect is more pronounced for short-term horizons (today vs. tomorrow) and diminishes for longer periods (e.g., 2028 vs. 2030).

The Ramsey Rate and Social Discounting

In climate change economics, future damages are discounted. The Ramsey social discount rate approximates this discounting factor and comprises three terms:

• Pure Preference for Early Consumption (rho): Many argue this should be near zero, implying that future generations' well-being matters as much as the present. Psychological studies also suggest this preference is small over long time horizons.
• Elasticity of Marginal Utility with Consumption (eta): This unitless parameter measures how the usefulness of an additional unit of consumption changes as overall consumption increases. Generally, as consumption rises, the utility of additional consumption decreases (e.g., an extra dollar means less to a wealthy person).
• Growth Rate in Per-Capita Consumption (g): This represents how much society is getting richer over time. Selecting an appropriate 'g' is challenging due to growing wealth inequality. For instance, median household income in the US has periods of stagnation, while average income (GDP per household) rises more steadily, indicating that gains are disproportionately going to the wealthy.

Economists often use values like 1% for rho, 2 for eta, and 2 for g, leading to a general recommendation of a 5% annual social discount rate.

Nominal vs. Real Dollars and Interest Rates

• Nominal Dollars: Currency valued in the year it was spent. Reports often use nominal dollars unless otherwise specified.
• Real Dollars (Constant Dollars): Inflation-adjusted dollars, allowing for meaningful comparisons across different years. Most plots in this class will use constant dollars.

Interest Rates: * Nominal Interest Rate: The rate quoted by banks for loans, which includes an embedded inflation rate. Banks absorb the impact of inflation into this rate. * Real Interest Rate: The nominal rate minus the inflation rate. This reflects only the opportunity cost and risk of loans.

Historical Data and Forecasting

When analyzing historical projects, indices like the Producer Price Index (PPI), Consumer Price Index (CPI), and GDP deflator are used to adjust for inflation.

• CPI: Measures inflation for everyday consumer goods.
• PPI: Measures inflation for goods used in production (e.g., concrete, labor).
• GDP Deflator: A measure of the growth rate of GDP used to understand inflation when specific indices are unavailable.

For forecasting, historical average inflation rates (typically 2-3% per year) are used, though recent years have seen higher rates, especially for producer goods.

For loan interest rates, the 30-year Treasury bond rate (risk-free rate) plus a 5% risk factor is a quick estimate. Historically, this has been around 10%, but currently, it's closer to 8% for utility companies.

Compounding Interest

When combining interest rates, especially with different compounding periods, simple addition is incorrect. Specific formulas are needed to calculate equivalent rates or continuous compounding.

The Cost of Electricity: Capital Costs

Calculating the cost of electricity, particularly for forecasting, is complex. The Nuclear Energy Institute (NEI), a pro-nuclear industry advocacy group, often presents data showing nuclear as the cheapest form of electricity. However, these figures often represent only the production cost (marginal cost of generating the next unit of electricity), ignoring the substantial capital costs of building the power plant.

Cost Categories

Energy costs are typically categorized into:

• Capital Cost: The cost of building the power plant, usually specified per unit of energy-generating capacity (e.g., per kilowatt).
• Fixed Operations & Maintenance (O&M): Costs independent of electricity production, such as employee salaries, healthcare, and insurance, also typically per kilowatt of capacity.
• Variable O&M: Costs dependent on electricity production, such as fuel and some maintenance, typically per kilowatt-hour.

The total cost of producing electricity is a function of variable costs multiplied by the amount of electricity produced, plus fixed capital and O&M costs.

Data Sources for Capital Costs

• Energy Information Administration (EIA): The primary and most reliable source in the US. EIA collects data from utility companies (mandated by law) and other sources to provide statistics on power plant costs.
• Lazard: A private company that generates similar statistics.
• Government Accounting and Audit Offices: In other countries (e.g., France, India), these offices publish relevant data.
• Annual Reports and SEC Filings: For specific projects or when other data is unavailable.

EIA's Cost Estimates and "Technological Optimism"

EIA publishes data including:

• Projected Build Year: Costs change over time.
• Size: Cost depends on plant capacity.
• Lead Time: Construction duration.
• Baseline Capital Cost: The initial estimated cost.
• Technological Optimism Factor: A new factor introduced by EIA to adjust for potential underestimation of costs for less mature technologies. For example, offshore wind has a 25% optimism factor, meaning its estimated costs are arbitrarily increased by 25%.
• Total Overnight Cost: The baseline capital cost adjusted by the technological optimism factor.

Overnight Cost: This is the cost of building the hardware of the power plant, excluding all finance charges. It assumes the plant is built "overnight" to isolate the technology's cost from the financial environment.

Nuclear Power Plant Overnight Costs

EIA estimates the overnight cost for a light water reactor at $7,000 per kilowatt, adjusted to $7,777 with a risk factor. This factor is applied because few nuclear plants have been built in the US recently.

A wide range of estimates exists for nuclear overnight costs, spanning a factor of 11. Notably:

• Vendors (Westinghouse, Oklo, TerraPower): Consistently provide the lowest estimates, often seen as optimistic.
• Academics (e.g., MIT): Tend to be more optimistic than government estimates, though their estimates have become more pessimistic over time as they better understand the complexities and cost drivers.
• Government (via Sargent & Lundy): Sargent & Lundy, a major architectural engineering firm, provides estimates for the government. While they have expertise, they also have a vested interest in keeping estimates low to attract business.
• Vogtle: The actual cost of building the Vogtle plant in the US serves as a real-world benchmark, often significantly higher than initial estimates.

The wide disparity in estimates, even for the same reactor design (e.g., AP1000), highlights the challenges in forecasting nuclear project costs. Explanations for high costs often include "first-of-a-kind" issues or specific project mismanagement, but these are debated.

The Impact of Construction Delays

The overnight cost does not account for the time value of money during construction. Power plants are not built overnight; they involve years of expenditure.

The investment cost (or rate-based cost) is the total amount of the loan by the time the plant begins operation, including interest payments during construction. This is the balance due on the day of operation and is used to determine the electricity price needed to pay off the plant over its lifetime.

The intensity of spending during construction typically follows a parabolic shape, starting low, peaking in the middle, and then decreasing. This spending incurs inflation and interest charges. The formula for calculating the investment cost involves integrating the rate of spending over the construction period, factoring in inflation and the weighted average cost of capital (interest).

Crucially, construction delays significantly increase the investment cost. For example, a plant built in 6 years might cost 40% more than its overnight cost, but a 14-year construction (like Vogtle) can lead to costs 2.3 times the overnight cost. Projects like Flamanville and Olkiluoto, with 17-18 year construction times, cost about 3 times their overnight estimates. This underscores the importance of rapid construction, which motivates concepts like factory fabrication for nuclear plants.

Comparing investment costs across different technologies reveals that solar thermal is not very attractive, and nuclear remains expensive. However, this analysis only considers capital charges, not full costs including O&M, which will be explored further. Technologies like solar with tracking and batteries are becoming increasingly cost-effective.