Equations and Variables in the ATB
Calculated Variables Equations
Capital Expenditures (CAPEX): expenditures required to achieve commercial operation of the generation plant.
$$ CAPEX = ConFinFactor \times (OCC + GCC) $$
Construction Financing Cost (CFC): dollar amount of all-in capital cost associated with construction period financing.
$$ CFC = (OCC + GCC) \times (ConFinFactor - 1) $$
Construction Finance Factor (ConFinFactor): portion of all-in capital cost associated with construction period financing.
$$ ConFinFactor = \sum_{y=0}^{y=C-1} FC_{i{y}} \times AI_{y} + FC_{e{y}} \times AE_{y} $$
Accumulated Interest (AI): a portion of the construction finance factor representing the interest on a construction loan.
$$ AI_{y} = 1 + [(1 + IDC)(year + 0.5) -1] $$
Accumulated Equity (AE): a portion of the construction finance factor representing the time value of equity on a construction loan.
$$ AE_{y} = 1 + [(1 + EDC)(year + 0.5) -1] $$
Capital Recovery Factor (CRF): ratio of a constant annuity to the present value of receiving that annuity for a given length of time. The ATB presents both a real and nominal CRF.
$$ CRF = WACC \times \left [ \frac{1}{\left ( 1 - \frac{1}{(1 + WACC)^{t}} \right )} \right ] $$
Weighted Average Cost of Capital (WACC): average expected rate that is paid to finance assets. The ATB presents both a real and nominal WACC, the equation below is for the real WACC.
$$ WACC = \frac{1 + [1-DF]\times[(1+RROE)(1+i)-1] + DF\times[(1+IR)(1+i)-1]\times[1-TR]}{1+i}-1 $$
Project Finance Factor (ProFinFactor): technology-specific financial multiplier to account for any applicable differences in depreciation schedule and tax policies; the investment tax credit (ITC) appears first to reduce the depreciable basis and a second time to apply the value of the credit (Ho et al., 2021). This formulation of the ProFinFactor leads to a before-tax, real, levelized cost of energy (LCOE) (Short et al., 1995).
$$ ProFinFactor = \frac {1 - TR \times PVD \times (1 - \frac{ITC}{2}) - ITC}{(1 - TR)} $$
Fixed Charge Rate (FCR): amount of revenue per dollar of investment required that must be collected annually from customers to pay the carrying charges on that investment. The FCR presented in ATB uses the real CRF.
$$ FCR = CRF \times ProFinFactor $$
Levelized Cost of Energy (LCOE): a summary metric that combines the primary technology cost and performance parameters: capital expenditures, operating expenditures, and capacity factor.
$$ LCOE = \frac{FCR \times CAPEX + FOM}{CF \times 8,760 (hours/yr)} + VOM + FUEL - PTC $$
Production Tax Credit (PTC): a before-tax credit that reduces LCOE; credits are available for 10 years, so it must be adjusted for a 10-year CRF relative to the full CRF of the project. This formulation of the PTC accounts for a pretax LCOE and aligns with the equation used for the ProFinFactor.
$$ PTC = \frac {PTC_{full} } {(1 - TR)} \times \frac{ CRF } {CRF_{10yrs}} $$
Total Battery System Cost: the total overnight capital cost of battery system after accounting for storage duration.
$$ TotalBatterySystemCost($) = TotalBatteryStorageCost($) + TotalBatteryPowerCost($) $$
$$ TotalBatteryStorageCost($) = BatteryStorageCapacity(kWh) \times BatteryEnergyCost($/kWh) $$
$$ TotalBatteryPowerCost($) = BatteryPowerCapcity(kW) \times BatteryPowerCost($/kW) + BatteryPowerConstant($) $$
Total Utility-Scale PV-Plus-Battery System Cost: LCOE equation for photovoltaic (PV)-plus-battery systems, which accounts for the potential effects of the PV and battery systems using various tax credits as well as the costs of charging the battery from the grid.
$$ PVPlusBatterySystemCost($/MWh) = FixedCosts($/MWh) + VOM($/MWh) + ChargingCosts($/MWh) $$
$$ FixedCosts = \frac {[AnnualPVSystemCost + AnnualBatterySystemCost + FOM($/kW-yr)]\times 1,000(kW/MW)}{CF\times 8,760(hours/yr)} $$
$$ AnnualPVSystemCost($/kW) = RROE \times PFF(PV) \times ConFinFactor \times [ PVSystemCost($/kW) \times 1 + GCC($/kW)] $$
$$ AnnualBatterySystemCost($/kW) = RROE \times PFF(Battery) \times ConFinFactor \times BatteryStorageCost($/kW) \times 1 $$
Input Variables
Input Variable Equations
Depreciation Factor (DepFac): a function of the discount rate:
$$ DepFac = \frac {1}{[(1+WACC) \times (1 + i)]^{y}} $$
The ATB uses the real WACC when calculating DepFac.
Real Interest Rate (IR): assumed interest rate on debt:
$$ IR = \frac {1 +d}{1 + i} -1 $$
Present Value of Depreciation (PVD): a function of FD, f, and y:
$$ PVD = \sum (MACRS~FD) \times \frac {1}{[(1 + WACC) \times (1 + i)]^{y}} $$
The ATB uses the real WACC when calculating PVD.
Other Input Variables
| Input Variable | Value | Definition/Description |
|---|---|---|
| Construction duration (C) | Varies by technology | Number of years in construction period. |
| Capacity factor (CF) | Varies by technology | Generally, the ratio of actual annual output to output at rated capacity for an entire year. |
| Charging costs | For PV-plus-battery systems ($/megawatt-hour [MWh]) | Average cost of electricity to charge a PV-plus-battery system during the lowest-cost hour of each day. The default assumes the battery charges 75% of its energy from the PV system. |
| Nominal debt rate (d) | Varies by technology | The nominal debt rate varies by technology. It is fixed over time for the R&D financials and varies with time in the Markets and Policies financials. |
| Debt fraction (DF) | Varies by technology | Fraction of capital financed with debt; 1-DF is assumed financed with equity; also referred to as the leverage ratio. |
| Capital fraction (FC) | Varies by technology | Fraction of capital spent in each year of construction, 1 to C. FCi covers the capital fraction in that year spent on interest, and FCe is the percent spent on equity. |
| Depreciation fraction (FD) | Varies by technology | Fraction of capital depreciated in each year, 1 to M. |
| Equity during construction (EDC) | Varies by technology | Assumed nominal return on equity during project construction. (Typically greater than or equal to RROE for that technology) |
| Fixed operations and maintenance (FOM) expenses | ATB input ($/megawatt-year [MW-yr]) | Annual expenditures to operate and maintain equipment that are not incurred on a per-unit-energy basis. |
| Fuel | Heat rate (million British thermal units per megawatt-hour [MMBtu/MWh]) x fuel costs($/MMBtu) | Fuel costs, converted to $/MWh, using heat rates. |
| Grid connection costs (GCC) | Varies by technology ($/kilowatt [kW]) | Overnight capital costs include a nominal-distance spur line (<1 mile [mi]) for all technologies; for offshore wind, they include export cable and construction period transit costs for a 30-kilometer (km) distance from shore. Project-specific costs for lines that are based on distance to existing transmission are not included. |
| Inflation rate (i) | 2.5% | Assumed inflation rate based on historical data (CPI-U 1991–2022) (BLS, 2025). |
| Interest during construction (IDC) | Varies by technology | Assumed nominal interest rate during project construction. |
| Investment tax credit (ITC) | Varies by technology (%) | Tax credit received on the CAPEX of the system. |
| Depreciation period (M) | Varies by technology (years) | Number of years in modified accelerated cost recovery system (MACRS) depreciation schedule. |
| Overnight capital costs (OCC) | Varies by technology ($/kW) | CAPEX if plant could be constructed overnight (i.e., excludes construction period financing); includes on-site electrical equipment (e.g., switchyard), a nominal-distance spur line (<1 mi), and necessary upgrades at a transmission substation. |
| Production tax credit (PTC) | Varies by technology ($/MWh) | PTC value received by the project, normalized by the capital recovery period. |
| Capital regional multiplier (CapRegMult) | 1 | Multiplier to account for regional variation in capital costs; not used in the Annual Technology Baseline (ATB). |
| Rate of return on equity (RROE) | Varies by technology | Assumed rate of return on the share of assets financed with equity. The equations above use a nominal RROE. |
| Economic lifetime (t) or cost recovery period | 30 years (default); 20 years and technical life also available | Length of time for paying off assets. |
| Tax rate (TR) | 25.7% | Combined assumed marginal state and federal tax rate before the application of available federal tax credits for renewable generators. |
| Variable operations and maintenance (VOM) | Varies by technology ($/MWh) | Operations and maintenance costs incurred on a per-unit-energy basis. |
| Year index (y) | — | — |
Assumptions common to all technologies include the following:
- Variables are defined in the Financial Definitions worksheet in the ATB data spreadsheet, where two sets of financial assumptions are available in the following:
- Without Tax Credits Financial Assumptions case
- With Tax Credits Financial Assumptions case.
- Although the tax rate has been updated to include the changes in corporate taxes in both financial cases, the federal/state blended tax rate is not assumed to vary by technology in our calculations; in practice, depreciation schedules vary by technology based on the tax code.
References
The following references are specific to this page; for all references in this ATB, see References.