Cost Calculation Module

Overview

The Cost Calculation Module (calculate_costs.py) is the financial analysis engine of the Plant Agent Model (PAM). It bridges detailed cost data (materials, energy, labor) with high-level economic assessments (NPV, LCOH, COSA) to enable informed decision-making:

  • Operational decisions: What to produce and at what cost, by computing unit production costs combining OPEX, carbon costs, and debt repayment for each furnace group.

  • Investment decisions: Whether to build new capacity and where, by evaluating business opportunities for capacity expansion through comprehensive NPV analysis.

  • Technology decisions: When to switch to cleaner or cheaper technologies, by calculating NPV and stranded asset costs (COSA) for all technology options.

  • Strategic decisions: How subsidies and carbon costs affect competitiveness, by modeling time-varying CAPEX, OPEX, and debt subsidies alongside carbon pricing impacts.

All calculations are normalized to per-unit-of-production basis, support time-varying subsidies, and account for debt financing with straight-line amortization, making this module central to realistic steel industry economic modeling.

Functional Modules

Subsidy Management

Handles time-varying subsidies for CAPEX, OPEX, cost of debt, and energy carriers. Subsidies are automatically filtered by year and applied to reduce costs. Bounds checking prevents costs from going negative or below floors (CAPEX/OPEX/Energy ≥ 0, Cost_of_Debt ≥ Risk_Free_Rate).

Four categories of subsidies are supported:

  1. CAPEX subsidies: Reduce upfront investment costs

    • Absolute: Fixed dollar amount per unit (e.g., $50/t)

    • Relative: Percentage reduction (e.g., 20% off)

  2. OPEX subsidies: Reduce operating costs

    • Absolute: Fixed dollar amount per unit (e.g., $10/t)

    • Relative: Percentage reduction (e.g., 15% off)

  3. Cost of Debt subsidies: Reduce interest rates

    • Absolute only: Percentage point reduction (e.g., -2% points)

    • Relative subsidies are ignored for debt

  4. Energy carrier subsidies: Reduce energy/feedstock costs for any carrier

    • Applies to any carrier in the energy_costs dict (hydrogen, electricity, natural_gas, coal, bf_gas, bof_gas, cog, etc.)

    • Absolute: Fixed amount in the carrier’s native unit (e.g., $1000/t H2, $0.02/kWh electricity)

    • Relative: Percentage reduction (e.g., 20% off)

    • Each carrier can have multiple subsidies that stack

All subsidies are time-bound with start_year and end_year, automatically filtered each simulation year.

Energy Carrier Subsidies — Dual-Sided Pricing

Energy subsidies modify both input and output energy cost dictionaries before downstream calculations, affecting BOM generation, energy VOPEX, reductant selection, by-product revenue, and NPV calculations.

A single subsidy simultaneously affects both sides:

Side

Formula

Effect

Input (consumption cost)

max(0, price - absolute_sum - price × relative_sum)

Cheaper to consume; floored at zero

Physical output (by-product revenue)

price + absolute_sum + price × relative_sum

More profitable to sell

Carbon output (co2_* carriers)

price - absolute_sum - price × relative_sum

Reduces storage cost / increases credit

get_subsidised_energy_costs() returns a 3-tuple: (input_costs, output_costs, no_subsidy_prices).

  • input_costs: Subsidised prices for consumption (input side)

  • output_costs: Subsidised prices for by-product revenue (output side)

  • no_subsidy_prices: Original unsubsidised prices for all carriers (not just subsidised ones)

Key behaviours:

  • Multiple subsidies stack (both absolute and relative are summed)

  • Input price floors at zero (free energy, but never negative)

  • Output prices have no floor (subsidy always increases revenue)

  • Carbon carriers (co2_*) use input-side formula for both sides (subsidy reduces cost, not increases revenue)

  • Zero-priced carriers are skipped (zero = free/absent; subsidy would create phantom revenue)

  • Original prices stored in energy_costs_no_subsidy on FurnaceGroup for baseline reference

  • LCOH calculations use unsubsidised electricity prices (by design)

Negative Subsidies (Taxes/Penalties)

Subsidies can have negative subsidy_amount values, which act as taxes or penalties that increase costs instead of reducing them.

Formula: cost_with_subsidy = cost - subsidy_amount

subsidy_amount

Calculation

Effect

+100 (positive)

500 - 100 = 400

Cost decreases

-100 (negative)

500 - (-100) = 600

Cost increases

-25% relative

400 - (400 × -0.25) = 500

25% cost increase

Use cases:

  • Carbon penalties on high-emission technologies

  • Environmental surcharges

  • Regulatory fees

Floor behaviour: The final input cost cannot go negative (no “money back”). CAPEX/OPEX floor at 0, COST OF DEBT floors at risk-free rate.

Functions:

  • filter_subsidies_for_year() - Filters subsidies to only those active in a specific year

  • collect_active_subsidies_over_period() - Collects unique subsidies active during any year in a period (with deduplication)

  • calculate_capex_with_subsidies() - Applies absolute and relative subsidies to CAPEX

  • calculate_opex_with_subsidies() - Applies absolute and relative subsidies to OPEX (floor at 0)

  • calculate_opex_list_with_subsidies() - Generates time-varying OPEX with year-specific subsidies

  • calculate_debt_with_subsidies() - Cost-of-debt subsidies; absolute point reductions only; floored at risk-free rate

  • calculate_energy_price_with_subsidies() - Applies absolute and relative subsidies to a single energy carrier price

  • get_subsidised_energy_costs() - Applies energy subsidies to all carriers; returns 3-tuple (input_costs, output_costs, no_subsidy_prices)

Subsidy Filtering Functions

Two functions handle subsidy filtering for different use cases:

filter_subsidies_for_year(subsidies, year) - Use for single-year filtering:

  • CAPEX subsidies (applied at construction start)

  • Debt subsidies (applied at financing decision)

  • Current-year OPEX tracking

collect_active_subsidies_over_period(subsidies, start_year, end_year) - Use for multi-year collection:

  • OPEX subsidies over plant lifetime (for NPV calculations)

  • Any scenario requiring subsidies across multiple years

The period function uses set() internally for deduplication - a subsidy spanning 2025-2030 appears once, not six times. The end_year is exclusive (matches Python range() convention).

Cost Breakdown Analysis

Extracts and processes bills of materials (BOM) to accurately assess the material and energy costs associated with production. Returns nested dictionaries with cost breakdowns by output product or feedstock.

Functions:

  • calculate_cost_breakdown() - Calculates normalised cost breakdown per unit of production

  • calculate_cost_breakdown_by_feedstock() - Detailed cost breakdown for each feedstock option

  • calculate_carbon_breakdown_by_feedstock() - Physical carbon intensity (tCO2/t-product) by feedstock. Sign convention: carbon_inputs negated (consumed), carbon_outputs positive (stored/slipped/utilised)

Data-driven cost-breakdown columns. calculate_cost_breakdown_by_feedstock() accepts an optional cost_breakdown_keys argument — the canonical list of normalised carrier/feedstock keys produced once at simulation start by walking dynamic feedstocks and consolidating via normalize_energy_key. The list is propagated through Environment.cost_breakdown_keys and onto each FurnaceGroup, then re-emitted by the post-processor as cost_breakdown - <key> columns (with deterministic column ordering and zero-padded missing keys). The previous hardcoded STANDARD_COST_BREAKDOWN_COLUMNS list and ad-hoc rename map (fluxes / lime → burnt lime) have been removed; new energy carriers and feedstocks now appear in the post-processed CSV automatically without code edits.

Operating Expenditure Calculation

Computes both variable and fixed operating expenditures based on input cost data and capital investment ratios. Returns 0 for unit costs when utilization is zero (no production means no unit cost).

Functions:

  • calculate_variable_opex() - Weighted average of material and energy costs. Accepts flexible input formats: unit_cost as float or {"Value": float, "Unit": str}, and uses demand or demand_share_pct for weighting.

  • calculate_unit_total_opex() - Sums variable and fixed OPEX per unit (returns 0 if utilization is 0)

  • calculate_unit_production_cost() - Total unit cost including OPEX, carbon costs, debt repayment, and secondary output adjustments

  • calculate_cost_adjustments_from_secondary_outputs() - Computes average per-unit cost adjustment from secondary outputs (by-products). Uses output_energy_costs (output-side subsidised prices) for energy carriers. Physical outputs generate revenue (negative adjustment via -abs(price)), except carriers in disposal_cost_outputs which keep their raw price sign (positive = disposal cost, e.g. steelmaking_slag). Carbon outputs (co2_*) may be a cost or credit depending on sign. This adjustment is included in all 4 NPV call sites (brownfield renovation, greenfield switch, new plant evaluation, expansion evaluation) and COSA baseline

Debt Repayment

Generates debt repayment schedules using straight-line amortization (constant principal, declining interest) and calculates debt payment breakdowns.

The module uses straight-line amortization with constant principal and declining interest:

  • Principal is repaid equally each year: Principal = Total Debt / Lifetime

  • Interest is calculated on average debt balance: Interest = ((Debt_Start + Debt_End) / 2) × Cost_of_Debt

  • Total repayment = Principal + Interest (declines over time as debt decreases)

This method differs from annuity loans where payments are constant. Here, payments start higher and decrease over time.

Functions:

  • calculate_debt_repayment() - Generates full yearly debt repayment schedule

  • calculate_current_debt_repayment() - Calculates single year’s debt payment

  • calculate_debt_report() - Breaks down debt into principal and interest components for reporting

Note: years_elapsed is 1-indexed (first operational year = 1). If lifetime_expired is True or debt == 0, returns 0.

Cash Flow Analysis

Calculates cash flows over time for profitability analysis and stranded asset cost calculations. Validates array lengths before operations and raises ValueError for mismatches (fail-fast for data consistency).

Functions:

  • calculate_gross_cash_flow() - Cash flow as (Revenue - OPEX) per period

  • calculate_net_cash_flow() - Subtracts debt from gross cash flow (for NPV)

  • calculate_lost_cash_flow() - Adds debt to gross cash flow (for COSA)

Note: If unit OPEX == 0 for a period, the model assumes no production and sets cash flow to 0 (revenue is not realized).

Investment Evaluation - NPV

Provides tools to calculate net present value (NPV) for technology investments, supporting both individual and batch calculations for business opportunities. Returns -1e9 for invalid inputs (NaN values in cash flows or cost_of_equity ≤ -1.0) to signal non-viability.

Functions:

  • calculate_npv_costs() - Basic NPV from equity investor perspective

  • calculate_npv_full() - Comprehensive NPV with construction lag, carbon costs, and infrastructure

  • calculate_business_opportunity_npvs() - Batch NPV calculation for multiple sites/technologies

Note: construction_time years are prepended to OPEX and debt schedules. price_series must include the same lead periods so its length matches the lagged OPEX/debt.

Stranded Asset Analysis

Calculates the Cost of Stranded Asset (COSA) when switching technologies before end-of-life, accounting for remaining debt obligations and foregone operating profits.

When switching technologies before end-of-life, COSA represents the NPV of:

  1. Remaining debt obligations - Must still be repaid even if asset is abandoned

  2. Foregone operating profits - Lost future revenue from current technology

Formula: COSA = NPV(Gross_Cash_Flow + Remaining_Debt)

COSA is subtracted from the NPV of the new technology to determine if a switch is economically viable.

Functions:

  • calculate_cost_of_stranded_asset() - NPV of losses from stranding an asset

  • stranding_asset_cost() - Full COSA calculation combining debt obligations and foregone profits

CAPEX Calculations

Handles capital expenditure calculations including subsidies and learning-by-doing cost reductions. Returns 1.0 (no reduction) when capacity_zero is 0 to avoid division by zero.

Functions:

  • calculate_capex_with_subsidies() - Applies absolute and relative subsidies to CAPEX

  • calculate_capex_reduction_rate() - Learning-by-doing cost reductions based on the learning curve logic (the more mature a technology, the cheaper its unit cost). The learning coefficient for CAPEX reduction is set to ca. -0.04, which corresponds to approximately 7% cost reduction per doubling of capacity.

Hydrogen Cost Calculations

Calculates levelized cost of hydrogen (LCOH) with regional ceilings and intraregional trade options.

For hydrogen-based technologies, LCOH represents the full cost of hydrogen production:

LCOH ($/kg) = Energy_Consumption (kWh/kg) × Electricity_Price ($/kWh) + CAPEX_OPEX ($/kg)

The module supports:

  • Regional hydrogen price ceilings (percentile-based)

  • Intraregional hydrogen trade with transport costs

  • Country-level LCOH calculations with electrolyzer efficiency curves

Note: This LCOH calculation is analogous to the one used in the geospatial model, but based on grid power prices instead of custom renewable energy costs. Functions are duplicated in geospatial_calculations.py and changes must be manually synchronized between both locations. See Priority Location Selection for more details on ceilings and trade.

Functions:

  • calculate_lcoh_from_electricity_country_level() - LCOH per country from electricity prices

  • calculate_regional_hydrogen_ceiling_country_level() - Regional hydrogen price ceilings (percentile-based)

  • apply_hydrogen_price_cap_country_level() - Applies price caps with intraregional trade options

Note: Functions are duplicated in geospatial_calculations.py and changes must be manually synchronized between both locations.

Energy and Reductant Selection

Identifies the most cost-effective reductant across different production paths based on energy costs.

Functions:

  • calculate_energy_costs_and_most_common_reductant() - Identifies most cost-effective reductant across all metallic inputs

Cross-Cutting Solutions

Cost Normalization

  • All costs normalized to per-unit-of-production basis for comparability

  • Handles both absolute ($/t) and relative (%) subsidies

  • Ensures minimum values: CAPEX/OPEX ≥ 0, Cost_of_Debt ≥ Risk_Free_Rate

Time Series Treatment

  • Construction time lags: Prepends zeros to schedules for projects under construction

  • Year-specific subsidies: Automatically filters subsidies active in each year

  • Variable time horizons: Supports both full lifetime and remaining lifetime calculations

Edge Case Handling

  • Zero utilization → Returns 0 for unit costs (no production means no unit cost)

  • Invalid NPV inputs → Returns -1e9 (large negative value signals non-viability)

  • Missing data → Returns 0 or empty collections (graceful degradation)

  • Array length mismatches → Raises ValueError (fail-fast for data consistency)

Integration Points

This module is called by the following PAM components:

Caller

Function Used

Purpose

FurnaceGroup.optimal_technology_name()

stranding_asset_cost(), calculate_npv_full()

Technology switching NPV analysis

FurnaceGroup.unit_production_cost

calculate_unit_production_cost(), calculate_current_debt_repayment()

Current operating cost

FurnaceGroup.debt_repayment_per_year

calculate_debt_repayment()

Debt schedule for COSA calculations

Plant.evaluate_expansion()

calculate_business_opportunity_npvs()

New plant investment analysis

PlantAgentsModel.run()

calculate_lcoh_from_electricity_country_level(), calculate_regional_hydrogen_ceiling_country_level(), apply_hydrogen_price_cap_country_level()

Hydrogen cost modeling