ROI = (Net Benefits - Total Costs) / Total Costs × 100%

Project cost: $500,000
Annual benefits: $200,000 over 5 years

Total benefits: $1,000,000
ROI = ($1,000,000 - $500,000) / $500,000 × 100% = 100%

NPV = Σ (Cash Flow_t / (1 + r)^t) - Initial Investment

def calculate_npv(
    initial_investment: float,
    cash_flows: list[float],
    discount_rate: float = 0.10  # 10% typical
) -> float:
    npv = -initial_investment
    for t, cf in enumerate(cash_flows, start=1):
        npv += cf / ((1 + discount_rate) ** t)
    return npv

# Example: $500K investment, $200K/year for 5 years
npv = calculate_npv(500_000, [200_000] * 5, 0.10)
# NPV = $258,157 (positive = good investment)

def calculate_irr(cash_flows: list[float]) -> float:
    """
    cash_flows[0] is initial investment (negative)
    Returns the IRR as a decimal
    """
    from scipy.optimize import brentq

    def npv_at_rate(r):
        return sum(cf / (1 + r) ** t for t, cf in enumerate(cash_flows))

    return brentq(npv_at_rate, -0.99, 10.0)

# Example: -$500K initial, then $200K/year for 5 years
irr = calculate_irr([-500_000, 200_000, 200_000, 200_000, 200_000, 200_000])
# IRR ≈ 28.6%

Payback Period = Initial Investment / Annual Cash Flow

Investment: $500,000
Annual savings: $200,000
Payback = $500,000 / $200,000 = 2.5 years

## Build Option (3-Year TCO)

### Year 1
| Category | Cost |
|----------|------|
| Development team (4 FTEs × $150K) | $600,000 |
| Infrastructure setup | $50,000 |
| Tools & licenses | $20,000 |
| **Year 1 Total** | **$670,000** |

### Year 2-3 (Maintenance)
| Category | Annual Cost |
|----------|-------------|
| Maintenance team (2 FTEs) | $300,000 |
| Infrastructure | $60,000 |
| Technical debt | $50,000 |
| **Annual Total** | **$410,000** |

### 3-Year Build TCO: $1,490,000

---

## Buy Option (3-Year TCO)

| Category | Annual Cost |
|----------|-------------|
| SaaS license (100 users × $500) | $50,000 |
| Implementation (Year 1 only) | $100,000 |
| Training | $20,000 |
| Integration maintenance | $30,000 |
| **Year 1** | **$200,000** |
| **Year 2-3** | **$100,000/year** |

### 3-Year Buy TCO: $400,000

# Business Case: [Project Name]

## Executive Summary
[2-3 sentence summary of investment and expected return]

## Problem Statement
- Current pain points
- Quantified impact (hours lost, revenue impact, etc.)

## Proposed Solution
- What we're investing in
- Key capabilities

## Financial Analysis

### Investment Required
| Item | One-Time | Annual |
|------|----------|--------|
| Software license | | $X |
| Implementation | $X | |
| Training | $X | |
| Integration | $X | $X |
| **Total** | **$X** | **$X** |

### Expected Benefits
| Benefit | Annual Value | Confidence |
|---------|--------------|------------|
| Time savings (X hrs × $Y/hr) | $X | High |
| Error reduction | $X | Medium |
| Revenue increase | $X | Low |
| **Total** | **$X** | |

### Key Metrics
| Metric | Value |
|--------|-------|
| 3-Year TCO | $X |
| 3-Year Benefits | $X |
| NPV (10% discount) | $X |
| IRR | X% |
| Payback Period | X months |
| ROI | X% |

## Risk Analysis
| Risk | Probability | Impact | Mitigation |
|------|-------------|--------|------------|
| | | | |

## Recommendation
[GO / NO-GO with rationale]

## Appendix
- Detailed calculations
- Vendor comparison
- Implementation timeline

## NPV Sensitivity Analysis

| Scenario | Discount Rate | Year 1 Benefits | NPV |
|----------|---------------|-----------------|-----|
| Base case | 10% | $200,000 | $258,157 |
| Conservative | 15% | $150,000 | $102,345 |
| Optimistic | 8% | $250,000 | $412,890 |
| Pessimistic | 12% | $120,000 | $32,456 |