The Discounted Cash Flow (DCF) method values an asset by summing up all its expected future cash flows, but adjusted for the time value of money. This means a dollar received in the future is worth less than a dollar received today.

The core formula for DCF is $V_a = \sum_{t=1}^{T} \frac{CF_t}{(1+k)^t}$, where $V_a$ is the value of the asset, $CF_t$ is the cash flow in period $t$, and $k$ is the relevant discount rate that reflects the risk associated with those cash flows.

The first step in applying DCF is to determine the specific cash flow measure you will use in the numerator of the formula. This choice is critical because it dictates what aspect of the firm's value you are trying to calculate.

The second step, which must be consistent with your cash flow choice, is to select the corresponding discount rate for the denominator. The discount rate should always match the risk profile of the cash flows being discounted.

One cash flow measure is Dividends, often used in models like the Gordon Growth Model (GGM) to estimate the cost of common stock and value equity based on future dividend payments.

Free Cash Flow to the Firm (FCFF) represents the cash flow available to all capital providers—both creditors and stockholders—after all operating expenses and necessary investments have been covered. It is calculated as $FCFF = EBIT - \text{Cash Tax Payments} + \text{Depreciation} - \text{CAPEX} - \text{Increases in NWC}$.

When using FCFF as the numerator, the appropriate discount rate is the Weighted Average Cost of Capital (WACC), which reflects the average cost of financing for the entire firm. The formula for firm value becomes $V_{firm} = \sum \frac{FCFF}{(1+WACC)^t}$, valuing the entire firm.

Free Cash Flow to the Equity (FCFE) represents the cash flow available only to equity holders after all operating expenses, debt payments, and necessary investments have been made. It is calculated as $FCFE = NI + \text{Depreciation} - \text{CAPEX} - \text{Increases in NWC} + \text{Increases in Net Long-Term Debt}$.

When using FCFE as the numerator, the appropriate discount rate is $k_e$, the cost of equity, as these cash flows belong solely to equity holders. The formula for equity value becomes $V_{equity} = \sum \frac{FCFE}{(1+k_e)^t}$, valuing only the equity portion of the firm.

If you calculate $V_{equity}$ using FCFE, you can then find the total firm value by adding the market value of debt: $V_{firm} = V_{equity} + V_{debt}$. If the market value of debt is unavailable, the book value of total debt can be used as an approximation.

The first step is to forecast the firm's financial performance as far into the future as is reasonably possible, typically three to five years. This involves creating pro forma financial statements, including an income statement and balance sheet, to project future revenues, expenses, and investments.

Next, you compute the free cash flow for each forecasted year, using either the FCFF or FCFE formulas, depending on whether you aim to value the entire firm or just its equity.

The third step involves calculating the Terminal Value (TV), which represents the value of all cash flows beyond your explicit forecast horizon. This can be done using a constant growth model, $V_t = \frac{CF_t(1+g)}{k_{cf} - g}$, assuming cash flows grow at a constant rate $g$ indefinitely, or a no-growth model, $V_t = \frac{CF_t}{k_{cf}}$, if cash flows are expected to remain constant. Here, $CF_t$ is the cash flow for the last forecast year, and $k_{cf}$ is the appropriate cost of capital.

The fourth step is to compute the appropriate discount rate, which will be either the WACC for FCFF or the cost of equity ($k_e$) for FCFE, ensuring consistency with your chosen cash flow measure.

Finally, you discount all projected future cash flows (including the terminal value) back to the present using the calculated discount rate. The sum of these present values yields the intrinsic value of the firm or its equity.

The Comparables Method values firms by comparing them to similar companies that have recently been involved in M&A activities or are publicly traded. It assumes that similar businesses should have similar valuations.

A key strength of this method is its practicality when detailed data for a DCF model is difficult to obtain. However, a limitation is that it may not be as applicable for firms that are not profitable, as many common multiples rely on earnings.

The first step is to identify comparable firms—companies that are similar to the target company in terms of industry, size, growth prospects, and risk.

Once comparable firms are identified, valuation multiples are used to estimate the target firm's value. These multiples can be derived from public market data or M&A transactions involving the comparable companies.

The Price-to-Earnings (P/E) ratio is a widely used multiple that indicates how many dollars investors are willing to pay for every dollar of a company's earnings. It can be calculated as $\frac{\text{Price per 1 share}}{\text{Earnings per 1 share (EPS)}}$ or $\frac{\text{Market value of equity}}{\text{Net income}}$.

To calculate a target firm's value using the P/E ratio, you multiply the comparable company's P/E ratio by the target company's earnings. Some analysts may use the inverse, Earnings/Price, to work with smaller numbers.

The Price-to-Sales (P/S) ratio is particularly useful for valuing companies where earnings are negative or non-existent, as it does not require profitability. It is calculated as $\frac{\text{Market Cap}}{\text{Total Sales}}$ or $\frac{\text{Price of 1 share}}{\text{Sales per Share}}$, where Sales per Share is $\frac{\text{Total sales}}{\text{Shares outstanding}}$.

While P/S is valuable for non-profitable firms, a limitation is that sales alone do not always reflect a company's profitability or efficiency.

Creative multiples can also be used, such as 'number of clicks' for internet companies, demonstrating that any relevant metric can form the basis of a comparison.

The Price/EBITDA ratio is another important multiple, often used for early-stage companies where cash flow generation is a key indicator of value. EBITDA stands for Earnings Before Interest, Taxes, Depreciation, and Amortization, providing a measure of operational cash flow. Sometimes, if EBITDA is close to zero, the inverse EBITDA/Price might be used.

The 'Unpaid Salary Issue' arises in private firms when an owner does not officially pay themselves a salary, instead taking distributions as dividends. This understates the firm's true operating expenses, making its reported earnings appear higher than they would be under standard compensation practices.

To address this, appraisers insert a hypothetical expense representing what it would cost to hire someone to perform the owner's role, providing a more accurate picture of the firm's profitability.

Private firm shares typically face a 'Liquidity Discount' because they are more difficult to sell quickly compared to liquid, transparent, and credible public shares. This illiquidity means private shares are generally valued 40-50% less than their public counterparts.

Conversely, a 'Control Premium' is often paid when an entity seeks to obtain a majority share in a company. This premium, typically 30-35% above the per-share value, compensates existing shareholders for losing control over the firm's operations and strategic direction.

One common real estate appraisal method is the Replacement Cost approach, which estimates a property's value by calculating how much it would cost to replace all of its components. This includes the cost to construct the house itself, as well as additional features like landscaping and fences.

The Comparables Approach is favored by mortgage brokers and relies on market data from similar properties. This method is analogous to the Comparables Method for firm valuation.

In the Comparables Approach, an appraiser selects three to six similar houses, known as 'comps,' that have recently sold in the same area.

Adjustments are then made to account for differences between the subject property and the comps, such as variations in square footage, the presence of air conditioning, or other features.

After making these adjustments, a final market value for the property is calculated based on the adjusted prices of the comparable homes.