Comprehensive Methodology for Calculating Discount Rate in Levelized Cost of Electricity (LCOE)

I. Core LCOE Formula and the Role of Discount Rate

The Levelized Cost of Electricity (LCOE) represents the average cost per unit of electricity generated over a project’s lifetime. The formula is:

• C_t: Total costs in year $t$ (CAPEX, OPEX, residual value, etc.)

• E_t: Electricity generation in year $t$ (kWh)

• r: Discount rate (reflects capital time value and risk)

• n: Project lifetime (years)

The discount rate (r) determines the present value weight of future cash flows, directly impacting LCOE outcomes.

II. Determining the Discount Rate

1. Weighted Average Cost of Capital (WACC)

• E: Equity value

• D: Debt value

• V: Total value ($V=E+D$)

• r_e: Cost of equity (calculated via CAPM)

• r_d: Cost of debt

• T_c: Corporate tax rate

Example:
For a solar project with 60% equity ($r_e=12\mathrm{\%}$), 40% debt ($r_d=6\mathrm{\%}$), and 25% tax rate:

2. Risk-Adjusted Approach

• Risk-free rate: Government bond yield (e.g., 10-year U.S. Treasury ≈ 4.3%)

• Risk premium: Industry-specific risk (typically 3%-8% for solar)

• Final discount rate: Risk-free rate + Risk premium
  → 4.3% + 5% = 9.3%

III. Step-by-Step Calculation (25-Year Solar Plant Example)

1. Input Parameters

2. Present Value of Costs (Numerator)

• C₀: Initial investment ($1,200,000 at $t=0$)

• OPEX_t: Annual OPEX ($15,000)

• S: Residual value ($50,000 at $t=25$)

Calculation:

3. Present Value of Energy (Denominator)

Accounting for 0.5% annual degradation:

Total energy present value:

4. LCOE Result

IV. Sensitivity Analysis of Discount Rate

Conclusion: A 1% increase in $r$ raises LCOE by ~7-8%.

V. Engineering Best Practices

1. Nominal vs Real Discount Rate:

   • Use nominal rate if costs/prices include inflation.

   • Use real rate for inflation-adjusted values:

     $$r_{\text{real}}=\frac{1+r_{\text{nominal}}}{1+i}-1$$
     

     (where $i$ = inflation rate)

2. Risk-Tiered Discounting:

   • Apply higher rates (e.g., 12%) to high-risk phases (e.g., construction years).

   • Lower rates (e.g., 8%) for stable operational phases.

3. Multi-Stakeholder Scenarios:

   • Calculate LCOE separately for equity/debt holders to reflect differing capital costs.