DCF Valuation Explained: Formula, Unlevered Free Cash Flow & Worked Example

1. The Theoretical Foundation of DCF Modeling

The intrinsic value of any commercial enterprise equals the sum of all future cash flows it can generate, discounted back to the present day at a rate reflecting the riskiness of those cash flows (the cost of capital):

Enterprise Value (EV) = \sum [ UFCF_t / (1 + WACC)^t ] + [ Terminal Value / (1 + WACC)^n ] Equity Value = Enterprise Value + Cash & Liquid Investments - Total Debt - Non-Controlling Interest Implied Share Price = Equity Value / Diluted Shares Outstanding

2. Deriving Unlevered Free Cash Flow (UFCF)

Unlevered Free Cash Flow (Free Cash Flow to Firm - FCFF) represents cash available to all capital providers (both debt holders and equity shareholders) after operating expenses, taxes, and reinvestment requirements:

Operating Income (EBIT) \times (1 - Effective Tax Rate) = Net Operating Profit After Taxes (NOPAT) + Depreciation & Amortization (D&A - Non-Cash Expense) - Capital Expenditures (CapEx - Reinvestment in PPE) - Δ Net Working Capital (ΔNWC = Operating Current Assets - Operating Current Liabilities) = Unlevered Free Cash Flow (UFCF)

3. Terminal Value: Gordon Growth vs. Exit Multiple

Because companies are assumed to operate indefinitely (going concern), a substantial portion of DCF valuation resides in the Terminal Value (TV) beyond the explicit 5-10 year projection horizon:

Gordon Growth Formula: TV = [ UFCF_(n+1) ] / (WACC - g) = [ UFCF_n \times (1 + g) ] / (WACC - g) Exit Multiple Formula: TV = Final Year EBITDA \times Target EV/EBITDA Multiple

Crucial Rule: The long-term perpetual growth rate g must not exceed the sustainable long-term GDP growth rate of the economy (typically 2.0% - 3.0%).

Step-by-Step Worked Valuation Case Study

Consider valuing Nordic Precision Tech, an industrial automation manufacturer with the following parameters:

Discount Rate (WACC): 9.5% • Perpetual Growth Rate (g): 2.5%
Projected 5-Year UFCFs:
Year 1: $40.0M • Year 2: $46.0M • Year 3: $52.0M • Year 4: $58.0M • Year 5: $64.0M
Balance Sheet Items: Cash = $35.0M • Total Debt = $80.0M • Diluted Shares = 10.0M
Step 1: Present Value of Explicit 5-Year Cash Flows
PV(Y1) = 40.0 / (1.095)^1 = $36.53M
PV(Y2) = 46.0 / (1.095)^2 = $38.36M
PV(Y3) = 52.0 / (1.095)^3 = $39.61M
PV(Y4) = 58.0 / (1.095)^4 = $40.35M
PV(Y5) = 64.0 / (1.095)^5 = $40.66M
Cumulative PV of Explicit Cash Flows = $195.51M
Step 2: Calculate Terminal Value (Gordon Growth)
UFCF(Y6) = 64.0 × (1 + 0.025) = $65.60M
Terminal Value = 65.60 / (0.095 - 0.025) = 65.60 / 0.070 = $937.14M
PV of Terminal Value = 937.14 / (1.095)^5 = $595.34M
Step 3: Enterprise Value & Share Price
Enterprise Value = $195.51M + $595.34M = $790.85M
Equity Value = $790.85M + $35.0M (Cash) - $80.0M (Debt) = $745.85M
Implied Share Price = $745.85M / 10.0M shares = $74.59 per share

Frequently Asked Questions

What is the difference between Levered and Unlevered Free Cash Flow?

Unlevered FCF is cash available to all capital providers before interest expenses, discounted at WACC to produce Enterprise Value. Levered FCF is cash remaining after debt interest and mandatory principal repayments, discounted at Cost of Equity to produce Equity Value directly.

Why does Terminal Value often represent 60% to 80% of total DCF value?

Because a healthy company operates for decades into the future. A large terminal value is mathematically normal, which is why sensitivity tables analyzing WACC vs perpetual growth rate are essential.

Technical Reference Notice: This article is published for educational and engineering reference purposes. Numerical calculations should be verified independently against manufacturer specifications, local regulatory codes, and company standards before making operational, financial, or safety-critical decisions.