NPV & IRR Analysis Fundamentals

1. NPV Fundamentals

Net Present Value (NPV) is the gold standard for capital budgeting decisions. It measures the absolute dollar value a project adds to shareholder wealth by discounting all future cash flows to present value and subtracting the initial investment.

NPV Definition

Sum of discounted cash flows

Present value of all future cash flows minus initial investment.

Decision Rule

NPV > 0: Accept

Positive NPV means project creates shareholder value.

Key Advantage

Measures absolute value

Unlike IRR, NPV shows actual dollars of wealth created.

Discount Rate

WACC or hurdle rate

Use company's weighted average cost of capital.

NPV Formula

Net Present Value: NPV = -I₀ + CF₁/(1+r)¹ + CF₂/(1+r)² + ... + CFₙ/(1+r)ⁿ Or in summation notation: NPV = Σ [CFₜ / (1 + r)ᵗ] for t = 0 to n Where: I₀ = Initial investment at t=0 ($) CFₜ = Cash flow in period t ($) r = Discount rate (WACC, decimal) n = Project life (years)

NPV cash flow timeline diagram showing Year 0 initial investment as downward arrow, Years 1-n positive cash flows as upward arrows, discount factors beneath each period, and final year including salvage value and working capital release with NPV formula — NPV Cash Flow Timeline: Initial investment at Year 0, annual cash flows discounted to present value, with terminal value including salvage and working capital release.

Worked Example: Pipeline Expansion

Example: 20-mile NGL Pipeline Given: - Initial investment: $10,000,000 - Annual cash flow: $2,500,000/year for 8 years - Salvage value: $1,000,000 (Year 8) - Discount rate (WACC): 10% Solution using annuity factor: PV of annual cash flows = CF × [(1 - (1+r)⁻ⁿ) / r] PV = $2,500,000 × [(1 - 1.10⁻⁸) / 0.10] PV = $2,500,000 × 5.335 PV = $13,337,500 PV of salvage = $1,000,000 / (1.10)⁸ = $466,507 NPV = -$10,000,000 + $13,337,500 + $466,507 NPV = +$3,804,007 Decision: ACCEPT (NPV > 0)

NPV vs IRR: When They Conflict

Situation	Use NPV	Use IRR	Rationale
Mutually exclusive projects	Yes	No	NPV maximizes shareholder value; IRR can mislead
Different project sizes	Yes	No	IRR ignores scale; $50M project with 12% IRR may beat $5M project with 20% IRR
Non-conventional cash flows	Yes	No	Multiple sign changes create multiple IRRs
Single project go/no-go	Yes	Yes	Both give same accept/reject decision
Management communication	No	Yes	IRR as % is easier to communicate than NPV in $

NPV Rule: When NPV and IRR rank projects differently, always use NPV. NPV assumes cash flows are reinvested at WACC (realistic), while IRR assumes reinvestment at IRR itself (often unrealistic for high-IRR projects).

2. IRR & MIRR Methods

Internal Rate of Return (IRR) is the discount rate that makes NPV equal to zero. It represents the project's effective annual return. However, IRR has limitations that Modified IRR (MIRR) addresses.

IRR Formula

IRR Definition: Find r such that NPV = 0: 0 = -I₀ + CF₁/(1+IRR)¹ + CF₂/(1+IRR)² + ... + CFₙ/(1+IRR)ⁿ Decision Rules: - IRR > WACC → Accept project - IRR < WACC → Reject project - IRR = WACC → Indifferent (NPV = 0) IRR cannot be solved algebraically for n > 2. Use Newton-Raphson iteration or financial calculator.

NPV Profile Chart: NPV decreases with higher discount rates. IRR occurs where curve crosses zero. Accept projects when discount rate < IRR (NPV > 0).

Newton-Raphson Method for IRR

Iterative Solution: r(n+1) = r(n) - f(r) / f'(r) Where: f(r) = NPV(r) = Σ [CFₜ / (1+r)ᵗ] f'(r) = dNPV/dr = -Σ [t × CFₜ / (1+r)^(t+1)] Algorithm: 1. Initial guess: r₀ = 10% 2. Calculate NPV and derivative at r₀ 3. Update: r₁ = r₀ - NPV(r₀)/NPV'(r₀) 4. Repeat until |r(n+1) - r(n)| < 0.0001 Typically converges in 3-5 iterations.

Modified IRR (MIRR)

MIRR solves two IRR problems: (1) unrealistic reinvestment assumption and (2) multiple IRRs with non-conventional cash flows.

MIRR Formula: MIRR = [(FV of positive CFs / |PV of negative CFs|)^(1/n)] - 1 Where: - Positive CFs compounded forward at reinvestment rate (typically WACC) - Negative CFs discounted back at finance rate (cost of debt or WACC) FV = Σ [CFₜ × (1 + r_reinvest)^(n-t)] for CFₜ > 0 PV = Σ [|CFₜ| / (1 + r_finance)^t] for CFₜ < 0 MIRR is always unique (single solution). MIRR < IRR when IRR > reinvestment rate (typical case).

Example: IRR vs MIRR Comparison

Pipeline Project: Cash flows: CF₀ = -$10M, CF₁...₈ = $2.5M/year WACC = 10% IRR Calculation: By iteration: IRR = 18.7% MIRR Calculation (reinvest at 10%): FV of positive CFs = $2.5M × [(1.10)⁷ + (1.10)⁶ + ... + 1.0] FV = $2.5M × 11.436 = $28.59M PV of negative CF = $10M (at t=0) MIRR = ($28.59M / $10M)^(1/8) - 1 MIRR = (2.859)^0.125 - 1 MIRR = 14.1% MIRR (14.1%) < IRR (18.7%) MIRR is more realistic because it assumes reinvestment at WACC (10%), not at IRR (18.7%).

Multiple IRR Problem

Cash Flow Pattern	IRR Count	Example	Solution
Conventional (-, +, +, +)	1 unique	Standard pipeline project	Use IRR normally
Non-conventional (-, +, +, -)	0, 1, or 2+	Mining with reclamation cost	Use NPV or MIRR
All negative	None	Pure cost project	Use cost-benefit analysis

Best Practice: Many midstream companies now require both IRR and MIRR for capital approval. MIRR provides a more conservative, realistic return estimate. Use MIRR when comparing projects with different cash flow timing patterns.

3. WACC & Discount Rates

The Weighted Average Cost of Capital (WACC) represents the blended cost of all capital sources. It is the appropriate discount rate for projects of average risk. Project-specific risk adjustments may be added.

WACC Formula

Weighted Average Cost of Capital: WACC = (E/V) × rₑ + (D/V) × r_d × (1 - T_c) Where: E = Market value of equity ($) D = Market value of debt ($) V = E + D = Total firm value ($) rₑ = Cost of equity (%) r_d = Cost of debt, before tax (%) T_c = Corporate tax rate (%) (1 - T_c) = Tax shield on interest Target capital structure: E/V = Equity weight (typically 50-70% for midstream) D/V = Debt weight (typically 30-50% for midstream)

WACC components diagram showing stacked bar with cost of equity (6.3%) and after-tax cost of debt (1.8%) summing to 8.1% WACC, capital structure pie chart showing 60% equity and 40% debt, CAPM formula for cost of equity calculation — WACC Components: Weighted average of cost of equity (via CAPM) and after-tax cost of debt, reflecting target capital structure.

Cost of Equity: CAPM

Capital Asset Pricing Model: rₑ = R_f + β × (R_m - R_f) Where: rₑ = Required return on equity (%) R_f = Risk-free rate (10-yr Treasury, ~4-5%) β = Beta (systematic risk vs. market) R_m = Expected market return (~10-11%) (R_m - R_f) = Equity risk premium (~5-7%) Midstream Beta Ranges: - Interstate pipelines: β = 0.6-0.8 (low risk) - Gathering/processing: β = 1.0-1.3 (commodity exposure) - Integrated midstream MLPs: β = 0.7-1.1 Example (gathering system): R_f = 4.5%, β = 1.2, (R_m - R_f) = 6.5% rₑ = 4.5% + 1.2 × 6.5% = 12.3%

Cost of Debt

After-Tax Cost of Debt: r_d (after-tax) = r_d (before-tax) × (1 - T_c) Methods to determine before-tax r_d: 1. Yield to Maturity (YTM) on existing bonds 2. Credit spread over Treasuries based on rating 3. Recent bank loan rates Credit Spreads by Rating (over 10-yr Treasury): - AAA/AA: +0.5-1.0% - A: +1.0-1.5% - BBB: +1.5-2.5% - BB: +2.5-4.0% Example (BBB-rated company): Treasury = 4.5%, Spread = 2.0% Before-tax r_d = 6.5% Tax rate = 25% After-tax r_d = 6.5% × (1 - 0.25) = 4.9%

Complete WACC Example

Midstream Company WACC: Capital Structure: E/V = 60% equity D/V = 40% debt Cost of Equity (CAPM): R_f = 4.5%, β = 1.0, ERP = 6.0% rₑ = 4.5% + 1.0 × 6.0% = 10.5% Cost of Debt: Before-tax r_d = 6.0% Tax rate = 25% After-tax r_d = 6.0% × 0.75 = 4.5% WACC Calculation: WACC = (0.60 × 10.5%) + (0.40 × 4.5%) WACC = 6.3% + 1.8% WACC = 8.1%

Risk-Adjusted Discount Rates

Project Type	Risk Level	Adjustment	Example Rate
Replacement/maintenance	Very Low	WACC - 2%	6%
Expansion (contracted)	Low	WACC	8%
Expansion (merchant)	Medium	WACC + 2-4%	10-12%
New basin development	High	WACC + 4-6%	12-14%
International/emerging market	Very High	WACC + 6-10%	14-18%

Discount Rate Sensitivity: A 2% change in WACC can swing NPV by 20-30% for long-lived infrastructure. For a 20-year project with $100M investment and $15M/year cash flows: NPV at 8% = $47M, NPV at 10% = $28M (40% lower). Always test sensitivity to discount rate assumptions.

4. Cash Flow Analysis

Accurate cash flow forecasting is the foundation of reliable NPV/IRR analysis. Free Cash Flow to Firm (FCFF) is the appropriate measure for project evaluation.

Free Cash Flow Formula

Free Cash Flow to Firm (FCFF): FCFF = EBIT × (1 - Tax) + Depreciation - CAPEX - ΔWC Or equivalently: FCFF = Revenue - OPEX - Taxes + Depreciation × Tax - CAPEX - ΔWC Where: EBIT = Earnings before interest and taxes Tax = Marginal corporate tax rate (21% federal + state) Depreciation = Non-cash charge (creates tax shield) CAPEX = Capital expenditures ΔWC = Change in working capital (increase = outflow) Note: Interest is NOT subtracted from FCFF. WACC already accounts for financing costs.

Depreciation Tax Shield

Depreciation reduces taxable income, creating a "tax shield" that increases after-tax cash flow. Accelerated depreciation (MACRS) provides higher tax shields in early years, increasing NPV.

Tax Shield Value: Annual Tax Shield = Depreciation × Tax Rate PV(Tax Shield) = Σ [Depreciationₜ × Tax Rate / (1+r)ᵗ] Depreciation Methods: 1. Straight-Line: Equal annual depreciation = Cost / Life 2. MACRS (IRS): Accelerated, front-loaded (higher early years) MACRS Classes for Midstream: - 5-Year: Vehicles, light equipment - 7-Year: Processing equipment, compressors - 15-Year: Pipelines, land improvements - 20-Year: Utility property, transmission lines

Bar chart comparing 15-year MACRS depreciation schedule for pipelines versus straight-line method, showing MACRS front-loads deductions with higher early year rates declining over time while straight-line maintains constant 6.67% annual rate — MACRS vs. Straight-Line Depreciation: MACRS front-loads deductions, providing higher tax shields in early years and increasing NPV compared to straight-line depreciation.

MACRS 15-Year Schedule (Pipelines)

Year	Rate	Year	Rate
1	5.00%	9	5.91%
2	9.50%	10	5.90%
3	8.55%	11	5.91%
4	7.70%	12	5.90%
5	6.93%	13	5.91%
6	6.23%	14	5.90%
7	5.90%	15	5.91%
8	5.90%	16	2.95%

Working Capital

Working Capital Treatment: Working Capital (WC) = Current Assets - Current Liabilities = Inventory + Receivables - Payables Year 0: WC investment = cash outflow Years 1-n: ΔWC = additional outflow if revenue grows Final Year: WC release = cash inflow (recovered at project end) Midstream WC Requirement: Typically 5-10% of annual revenue - Limited inventory (gas flows through) - Short collection cycles (monthly billing) - Long payment terms with suppliers

Terminal Value

Terminal Value Methods: 1. Salvage Value (asset-based): TV = Estimated market value at end of analysis Typical for pipelines: 20-40% of original cost Tax on gain: (Salvage - Book Value) × Tax Rate 2. Perpetuity Growth Model: TV = FCF(final) × (1 + g) / (WACC - g) g = perpetual growth rate (typically 0-2%) 3. Exit Multiple: TV = EBITDA(final) × EV/EBITDA multiple Midstream multiples: 8-12× EBITDA Terminal value often represents 30-50% of total NPV for long-lived infrastructure projects.

Cash Flow Accuracy: NPV is most sensitive to near-term cash flows due to discounting. A 10% error in Year 5 cash flow has 10× more impact than a 10% error in Year 25. Focus forecasting effort on Years 1-10; far-future cash flows can use simplified assumptions.

5. Sensitivity & Risk Analysis

Sensitivity analysis tests how NPV/IRR change with key input variables. For midstream projects, the primary sensitivities are typically throughput volume, commodity prices (for processing plants), CAPEX, and discount rate.

One-Way Sensitivity (Tornado Chart)

Sensitivity Analysis Process: 1. Identify key variables (typically 5-8 drivers) 2. Define range: ±10%, ±20%, or min/max bounds 3. Vary one variable, hold others at base case 4. Calculate NPV at each scenario 5. Rank by impact (tornado diagram) Example Results ($100M pipeline, base NPV = $50M): Variable | -10% | Base | +10% | Swing ------------------|---------|--------|--------|------- Throughput volume | $18M | $50M | $82M | $64M Discount rate | $68M | $50M | $35M | $33M CAPEX | $60M | $50M | $40M | $20M OPEX | $56M | $50M | $44M | $12M Ranking: Volume > Discount Rate > CAPEX > OPEX

Tornado sensitivity diagram for NPV analysis showing variables ranked by impact with throughput volume most sensitive at top, followed by CAPEX, discount rate, tariff/price, and OPEX least sensitive, with bars extending from base case NPV of $50M showing low and high scenario impacts — Tornado Sensitivity Diagram: Variables ranked by NPV impact. Throughput volume is the primary driver; OPEX has minimal effect. Red/green bars show NPV range from low to high scenarios.

Scenario Analysis

Scenario	Volume	Tariff	CAPEX	NPV	IRR
Optimistic (P10)	240 MMcf/d	$0.55	$90M	$95M	22%
Base Case (P50)	200 MMcf/d	$0.50	$100M	$50M	16%
Pessimistic (P90)	160 MMcf/d	$0.45	$110M	$8M	11%
Downside Stress	120 MMcf/d	$0.40	$120M	-$25M	7%

Breakeven Analysis

Key Breakeven Calculations: 1. Breakeven Volume (NPV = 0): Find Q such that NPV(Q) = 0 Simplified: Q_BE = [CAPEX × CRF + OPEX] / [Tariff × 365] CRF = Capital Recovery Factor = r / [1 - (1+r)^-n] 2. Breakeven Tariff (NPV = 0): Tariff_BE = [CAPEX × CRF + OPEX] / [Q × 365] 3. Maximum CAPEX (IRR = WACC): CAPEX_max = PV of all future cash flows at WACC Example: Base: Q = 200 MMcf/d, Tariff = $0.50, CAPEX = $100M WACC = 10%, n = 20 years CRF = 0.10 / [1 - 1.10^-20] = 0.1175 Annual required revenue = $100M × 0.1175 + $10M OPEX = $21.75M Breakeven Q = $21.75M / ($0.50 × 365) = 119 MMcf/d Project fails if volume < 119 MMcf/d (41% below base).

Monte Carlo Simulation

Probabilistic Analysis: Define probability distributions for uncertain variables: - Volume: Log-normal (mean 200, std dev 30 MMcf/d) - CAPEX: Triangular (min $90M, mode $100M, max $120M) - Tariff: Uniform ($0.45 to $0.55/Mcf) Run 10,000+ iterations: - Sample each variable from its distribution - Calculate NPV for each iteration - Build probability distribution of outcomes Results: - Expected NPV (mean): $48M - Standard deviation: $25M - P(NPV > 0): 85% - P(NPV > $50M): 45% - VaR (P10): NPV > $8M with 90% confidence Decision: 85% probability of positive NPV is acceptable for most corporate risk tolerances (>70% threshold).

Risk Factors by Project Type

Project Type	Primary Risk	Mitigation
Fee-based pipeline	Volume/throughput	Minimum volume commitments, anchor shipper contracts
Gas processing plant	NGL prices, plant utilization	Hedge NGL prices, long-term processing agreements
LNG terminal	Henry Hub/LNG spread, CAPEX	20-year offtake contracts, cost-reimbursable EPC
Storage facility	Storage rates, utilization	Firm storage contracts, seasonal spreads
FERC-regulated	Allowed ROE (rate case)	Regulatory precedents, prudent cost management

Industry Practice: Most midstream companies require projects to show positive NPV in both base case and pessimistic (P90) scenarios before approval. The "sanction hurdle" is typically IRR > WACC + 2-3% to provide buffer for execution risk and model uncertainty.

NPV & IRR Analysis

NPV > 0, IRR > WACC

8-14%

3-7 years

Contents

Use this guide when you need to: