Company Valuation: DCF, Multiples, and Intrinsic Value

How do you determine what a company is actually worth? DCF and multiples are the two primary frameworks for estimating intrinsic value, and they underpin all equity investing.

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Before you buy a stock, you want to know if the price is reasonable. Valuation is the discipline of estimating what a company is actually worth.

The core idea: a company is worth the present value of its future cash flows.

The Two Valuation Frameworks

1. Discounted Cash Flow (DCF): Estimate future cash flows, discount them back to today, sum them up.

2. Relative valuation (multiples): Compare the company’s valuation metrics to similar companies or its own historical averages.

Both have strengths and weaknesses. Sophisticated analysts use both.

DCF: The Foundation

A company is worth the cash it will generate in the future, discounted back to today:

V_0 = \sum_{t=1}^{n} \frac{CF_t}{(1+r)^t} + \frac{V_n}{(1+r)^n}

Where:

$CF_t$ = free cash flow in year $t$
$r$ = discount rate (WACC)
$V_n$ = terminal value at year $n$

Free cash flow (FCF): Cash generated by the business after paying all operating expenses and investments needed to maintain/grow the business.

FCF = Operating\ Income \times (1 - tax\ rate) + Depreciation - CapEx - \Delta Working\ Capital

The Discount Rate: WACC

The discount rate should reflect the risk of the cash flows. For a public company, this is typically WACC (Weighted Average Cost of Capital):

WACC = w_e \times r_e + w_d \times r_d \times (1 - t)

Where:

$w_e$ = proportion of equity in capital structure
$w_d$ = proportion of debt
$r_e$ = cost of equity (required return for equity investors)
$r_d$ = cost of debt
$t$ = corporate tax rate

Cost of equity is usually estimated using the Capital Asset Pricing Model (CAPM):

r_e = r_f + \beta \times (r_m - r_f)

Where $\beta$ measures the stock’s sensitivity to market movements.

Terminal Value

The hardest part of DCF is estimating the terminal value: the value beyond your explicit forecast period. Two common methods:

1. Gordon Growth Model (perpetuity):

TV_n = \frac{FCF_{n+1}}{r - g} = \frac{FCF_n(1+g)}{r - g}

Assumes free cash flow grows at a constant rate $g$ forever.

2. Exit multiple:

TV_n = EBITDA_n \times \text{EV/EBITDA multiple}

Assume the company is sold at a typical EV/EBITDA multiple for its industry (e.g., 15x EBITDA), giving an enterprise terminal value that you then discount back to today. Do not multiply FCF by an EV/EBITDA ratio, that mixes an equity-after-capex cash-flow number with an enterprise-value multiple and gives the wrong answer.

Valuation Multiples

Multiples are faster and more intuitive than DCF, but they’re shortcuts, not the full picture.

Price-to-Earnings (P/E):

P/E = \frac{Stock\ Price}{Earnings\ Per\ Share}

Low P/E could mean the stock is cheap, or the market expects earnings to fall.

EV/EBITDA:

EV/EBITDA = \frac{Enterprise\ Value}{EBITDA}

Better than P/E for comparing companies with different capital structures (debt levels).

Price-to-Book (P/B):

P/B = \frac{Stock\ Price}{Book\ Value\ Per\ Share}

Often used for banks, insurers, asset-heavy businesses.

DCF in Python

import numpy as np
import pandas as pd

def dcf_valuation(fcf_forecast, terminal_growth, discount_rate, terminal_multiple=None,
                  forecast_years=5, ebitda_forecast=None):
    """
    Discounted Cash Flow valuation.

    Parameters
    ----------
    fcf_forecast : list of floats
        Free cash flow for each forecast year
    terminal_growth : float
        Terminal growth rate (g) used by the Gordon Growth branch
    discount_rate : float
        WACC (r)
    terminal_multiple : float, optional
        Exit EV/EBITDA multiple (only used if `ebitda_forecast` is supplied)
    forecast_years : int
        Number of explicit forecast years
    ebitda_forecast : list of floats, optional
        EBITDA for each forecast year; required when `terminal_multiple` is given.
        Terminal value is then `terminal_ebitda * terminal_multiple`.

    Returns
    -------
    pv_total : float
        Enterprise value
    """
    # PV of explicit forecast period
    pv_explicit = 0
    for t, fcf in enumerate(fcf_forecast, 1):
        pv_explicit += fcf / (1 + discount_rate) ** t

    # Terminal value
    if terminal_multiple is not None:
        if ebitda_forecast is None or len(ebitda_forecast) != len(fcf_forecast):
            raise ValueError(
                "An EBITDA forecast of the same length as `fcf_forecast` is "
                "required when using an EV/EBITDA exit multiple."
            )
        terminal_ebitda = ebitda_forecast[-1] * (1 + terminal_growth)
        terminal_value = terminal_ebitda * terminal_multiple
    else:
        # Gordon Growth Model: TV = FCF_{n+1} / (r - g)
        terminal_fcf = fcf_forecast[-1] * (1 + terminal_growth)
        terminal_value = terminal_fcf / (discount_rate - terminal_growth)

    # PV of terminal value
    pv_terminal = terminal_value / (1 + discount_rate) ** forecast_years

    return pv_explicit + pv_terminal


def pe_comparable(peer_pe_ratios, earnings):
    """
    Estimate stock value using P/E of comparable companies.
    """
    median_pe = np.median(peer_pe_ratios)
    return earnings * median_pe


def ev_ebitda_comparable(peer_ev_ebitda, ebitda):
    """
    Estimate enterprise value using EV/EBITDA of comparables.
    """
    median_multiple = np.median(peer_ev_ebitda)
    return ebitda * median_multiple

PROMPT

Use numpy to build a basic DCF valuation with Gordon Growth and exit-multiple terminal values, plus helpers for comparable-based stock valuation from P/E and EV/EBITDA.

Key Assumptions Drive the Value

DCF is extremely sensitive to assumptions:

Discount rate: A 1% change in WACC can shift valuation by 20-30%
Terminal growth rate: Even 0.5% matters enormously (this is why the perpetuity formula is so sensitive to $g$ )
Forecast period length: 5 years vs. 10 years changes the result significantly

This is why two analysts can reach very different conclusions with the same publicly available information, they make different assumptions.

Key Takeaways

DCF: A company is worth the PV of its future cash flows
Free cash flow is the gold standard for measuring value generated
Terminal value is usually the largest component of DCF value
Multiples are quick estimates that depend on comparable company selection
Valuation is an art informed by science, all models require judgment

References

Penman, Financial Statement Analysis and Security Valuation. McGraw-Hill, 2019. ISBN: 978-0-07-337966-3.
Damodaran, Investment Valuation. Wiley, 2012. ISBN: 978-1-118-13074-1.
Koller, Goedhart, Wessels, Valuation: Measuring and Managing the Value of Companies. Wiley, 2020. ISBN: 978-1-119-66845-5.