DCF Financial Modeling: Terminal Value Sensitivity, Gordon Growth vs. Exit Multiple Discrepancies

## Quantitative DCF Valuation: Terminal Value Sensitivity

Discounted Cash Flow (DCF) modeling sizes an enterprise's value by discounting projected Unlevered Free Cash Flows (UFCF) to present value using the Weighted Average Cost of Capital (WACC).

### 1. Dual Terminal Value Formulations

Analysts utilize two primary methodologies to estimate enterprise residual value:

1. **Perpetual Gordon Growth Model**:
$$\text{TV}_{\text{Gordon}} = \frac{\text{UFCF}_{N+1}}{\text{WACC} - g} = \frac{\text{UFCF}_N \times (1 + g)}{\text{WACC} - g}$$
2. **Exit Multiple Method**:
$$\text{TV}_{\text{Multiple}} = \text{EBITDA}_N \times \text{Target Exit Multiple}$$

### 2. Solving for the Implied Perpetual Growth Rate

To stress-test an exit multiple assumption, invert the Gordon Growth equation to calculate the implied long-term growth rate:

$$g_{\text{implied}} = \frac{\text{TV}_{\text{Multiple}} \times \text{WACC} - \text{UFCF}_{N+1}}{\text{TV}_{\text{Multiple}} + \text{UFCF}_{N+1}}$$

If an 18x EV/EBITDA multiple implies an infinite perpetual growth rate of 4.8% when long-term GDP growth is 2.2%, the valuation assumption violates macroeconomic boundary conditions.