Firm Valuation

Firm Valuation: Steps and Building a Financial Model (with Calculations)

Firm valuation is the process of determining the economic value of a business or an asset. It's an essential component for investors, company management, and stakeholders, whether it’s for mergers and acquisitions, capital raising, or investment analysis. One of the most common approaches to firm valuation is Discounted Cash Flow (DCF) analysis, along with comparable company analysis and precedent transactions. This guide will explain how to value a company, specifically using a DCF model, and walk through all the calculations involved.

### Steps for Firm Valuation

1. Understanding the Business

- Industry Analysis: Understand the company’s industry, competitors, and market position.

- Business Model Analysis: Study how the company generates revenue, its cost structure, capital expenditures (CapEx), and growth potential.

2. Choosing the Valuation Approach

- Discounted Cash Flow (DCF): Values the firm by forecasting its free cash flows and discounting them to present value using the appropriate discount rate (often the weighted average cost of capital or WACC).

- Comparable Company Analysis: Compares the firm to similar public companies using valuation multiples like P/E ratio, EV/EBITDA, etc.

- Precedent Transactions: Looks at similar M&A transactions to derive a company’s valuation.

3. Forecasting Free Cash Flow (FCF)

To perform a DCF analysis, you need to forecast free cash flows over a period (typically 5-10 years). Free Cash Flow to Firm (FCFF) is calculated as follows:

FCFF = EBIT (1 - Tax Rate) + Depreciation & Amortization - CapEx - Change in Working Capital

- EBIT (Earnings Before Interest and Taxes): The company’s operating income. It’s found on the income statement.

- Tax Rate: Usually the effective tax rate of the company.

- Depreciation & Amortization: Non-cash expenses that are added back to EBIT.

- Capital Expenditures (CapEx): Investments in property, plant, and equipment (PP&E). Found on the cash flow statement.

- Change in Working Capital: The difference in current assets (excluding cash) and current liabilities. Positive changes reduce cash flow, while negative changes increase it.

4. Calculate the Terminal Value (TV)

The DCF model assumes that the company will generate cash flows indefinitely. To capture the value of cash flows beyond the forecast period, we calculate the Terminal Value (TV) using the Gordon Growth Model:

TV = FCFF_last year × (1 + g) / (WACC - g)

Where:

- g = the long-term growth rate of the company (often aligned with GDP growth or inflation).

- WACC = the Weighted Average Cost of Capital, which we’ll calculate next.

5. Discount Cash Flows to Present Value

Once we have projected the cash flows and calculated the terminal value, we discount these amounts to their present value using the WACC. The formula for discounting a single cash flow (for a given year) is:

PV = CF_t / (1 + WACC)^t

Where:

- CF_t is the cash flow in year t.

- WACC is the discount rate.

6. Calculate the Weighted Average Cost of Capital (WACC)

The WACC represents the company’s blended cost of equity and debt, reflecting the overall risk of investing in the company. The formula for WACC is:

WACC = (E/V × Re) + (D/V × Rd × (1 - Tc))

Where:

- E = Market value of equity.

- V = Total value of the firm (E + D).

- Re = Cost of equity (calculated using the Capital Asset Pricing Model (CAPM)).

- D = Market value of debt.

- Rd = Cost of debt.

- Tc = Corporate tax rate.

Cost of Equity (Re) is usually derived using the CAPM model:

Re = Risk-Free Rate + Beta × (Equity Market Risk Premium)

Where:

- Risk-Free Rate: Often the yield on long-term government bonds.

- Beta: A measure of how much the stock moves compared to the market.

- Equity Market Risk Premium: The additional return investors require for investing in the stock market over a risk-free rate.

7. Summing the Present Values

After discounting all forecasted cash flows and the terminal value, sum all present values to calculate the Enterprise Value (EV):

Enterprise Value (EV) = PV(FCFF_1) + PV(FCFF_2) + ... + PV(FCFF_n) + PV(Terminal Value)

8. Calculate Equity Value

To get the Equity Value of the company, subtract the company’s net debt (debt minus cash) from the enterprise value:

Equity Value = Enterprise Value - Net Debt

9. Determine Share Price

Finally, to find the company’s intrinsic share price, divide the Equity Value by the number of outstanding shares:

Share Price = Equity Value / Shares Outstanding

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### Detailed Example of Building a DCF Model

Let's assume you want to value a company with the following financials:

- EBIT (Operating Income): $200 million

- Tax Rate: 25%

- Depreciation & Amortization: $50 million

- Capital Expenditures (CapEx): $40 million

- Change in Working Capital: $10 million

- WACC: 10%

- Growth Rate (g): 3%

- Years for Projection: 5 years

#### Step 1: Calculate Free Cash Flow for Each Year

For Year 1:

- EBIT = $200M

- FCFF = $200M × (1 - 0.25) + $50M - $40M - $10M

FCFF for Year 1 = $150M

We repeat this calculation for each forecast year.

#### Step 2: Terminal Value Calculation

At the end of Year 5, we calculate the terminal value:

- Terminal Value = FCFF_5 × (1 + g) / (WACC - g)

- Assume FCFF in Year 5 = $180M, Growth rate (g) = 3%, WACC = 10%

TV = $180M × (1 + 0.03) / (0.10 - 0.03)

TV = $180M × 1.03 / 0.07

TV = $2,646M

#### Step 3: Discount Cash Flows and Terminal Value

Discount the FCFF and Terminal Value to present value using the WACC of 10%:

- PV(FCFF_1) = $150M / (1 + 0.10)^1 = $136.4M

- PV(FCFF_2) = $160M / (1 + 0.10)^2 = $132.2M

- … repeat for each year.

Finally, for the terminal value:

PV(Terminal Value) = $2,646M / (1 + 0.10)^5 = $1,644.6M

#### Step 4: Sum the Present Values

- Sum of discounted FCFF for 5 years = $662M

- PV of Terminal Value = $1,644.6M

- Enterprise Value = $662M + $1,644.6M = $2,306.6M

#### Step 5: Calculate Equity Value and Share Price

Assume the company has $300M in debt and $50M in cash (Net Debt = $250M):

- Equity Value = $2,306.6M - $250M = $2,056.6M

Assume the company has 50 million shares outstanding:

- Share Price = $2,056.6M / 50M = $41.13 per share

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### Conclusion

By following these steps and calculations, you can build a robust DCF model to estimate the value of a firm. Valuation models are vital for understanding a company’s intrinsic value and guiding investment or business decisions. The accuracy of the model heavily depends on the quality of the input assumptions (WACC, growth rates, etc.) and the ability to accurately forecast future free cash flows.