business-case-analysis

# Business Case Analysis

Financial frameworks for justifying investments, evaluating projects, and comparing alternatives.

## Key Financial Metrics

### Return on Investment (ROI)

Simple measure of profitability relative to cost.

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

**Example:**
```
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%
```

**Limitation:** Does not account for time value of money.

### Net Present Value (NPV)

Gold standard for project evaluation—discounts future cash flows to present value.

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

Where:
- `t` = time period
- `r` = discount rate (cost of capital)

**Example:**
```python
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)
```

**Decision Rule:**
- NPV > 0: Accept (creates value)
- NPV < 0: Reject (destroys value)
- NPV = 0: Indifferent

### Internal Rate of Return (IRR)

The discount rate at which NPV equals zero.

```python
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%
```

**Decision Rule:**
- IRR > hurdle rate (cost of capital): Accept
- IRR < hurdle rate: