A.3 Equity Valuation

Basic Prerequisites: Statistics & Inference and Econometrics & Time Series. (these are the folder-level prerequisites for pages 02–06; page 01 states its own, smaller, entry requirements)

1. Intuition & Practical Objective

Equity valuation answers one question with many dialects: what is a claim on a business worth today? The first-principles answer is blunt and old - the present value of the cash the owner will receive, discounted at a rate that compensates for the risk of not receiving it. Everything else (multiples, “comps”, screen thresholds) is either a shortcut around that computation or a market-based cross-check on it.

This folder is the valuation hub of the Accounting & Finance area. It is a hub: it (a) gives you the fast formula lookup below (the DCF identities every later note cross-references), and (b) routes you to six sub-pages that walk from raw intuition through cash-flow forecasting, the cost of capital, terminal value and the enterprise-to-equity bridge, the failure modes, and the relative-valuation / sensitivity layer.

The one-sentence essence. “Value an asset as the discounted present value of its expected future cash flows, discounted at a rate that reflects their risk; keep cash flows and discount rates consistent (equity flows at the cost of equity, firm flows at the cost of capital), and never let a perpetuity assumption hide inside a spreadsheet.”

2. Mathematical Ground Truth & Derivations

Quick-Reference Lookup (job #1). All formulas below are transcribed from Damodaran, Investment Valuation (2002/3rd ed.) and cross-checked against Koller (McKinsey) and Pinto (CFA); the numbers in the check column were re-executed and reproduced from the verified corpus (see §3).

Notation: $\text{EBIT}$ operating income, $t$ tax rate, $\text{Dep}$ depreciation, $\text{CapEx}$ capital expenditure, $\Delta \text{NWC}$ change in non-cash working capital, $NI$ net income, $\delta$ the debt fraction of net reinvestment, $k_e$ cost of equity, $k_d$ pre-tax cost of debt, $r_f$ risk-free rate, $\beta$ equity beta, $\text{ERP}$ equity risk premium, $g$ growth, $K_c=\text{WACC}$ cost of capital.

Cash-flow definitions (the two rivers).

Critical consistency caveat (Damodaran §2.1). Cash flows after interest are equity flows and must be discounted at $k_e$; cash flows before interest are firm flows and must be discounted at $K_c=\text{WACC}$. Mismatching them is the single most common valuation error and shifts value by 10–20% (see the verified error table below).

3. Computational Implementation - the DCF consistency engine

This runs on the standard library only. It reproduces Damodaran’s Illustration 2.1 - the proof that equity-DCF and firm-DCF give the same equity value, and that the wrong discount rate does not.

Both routes give equity $\approx$ $1073 (Damodaran rounds to $1073 and $1873; the residual $0.54$ is his rounding of $\text{WACC}=9.94\%$). Discount equity flows at the cost of capital and you over-value equity by $175; discount firm flows at the cost of equity and you under-value by $261. Consistency is not a convention - it is the model.

4. Failure Modes & First-Principles Breakdowns

Hub signposts - the folder’s failure-mode analysis lives in 05 · Failure Modes & Practice. In one line each:

1. GIGO forecasts - a DCF is an arithmetic engine on inputs; garbage revenue margins and reinvestment assumptions dominate the output no matter how elegant the discounting.
2. Terminal-value dominance - in a typical two-stage model the perpetuity term is 70–80% of value, so the model’s accuracy is really the accuracy of $g_n$ and $K_c$ (a $1\%$ move in either swings value by 20%+ once $g\to K_c$).
3. Wrong cost of capital / mismatched discounting - using WACC for equity flows (or a “cost of equity” for firm flows) silently shifts value by double digits; so does a beta or ERP that is not comparable to the cash-flow definition.

5. References

• Damodaran, Aswath: Investment Valuation: Tools and Techniques for Determining the Value of Any Asset (Wiley, 2nd/3rd ed.). The valuation canon.
• Koller, Goedhart & Wessels (McKinsey): Valuation: Measuring and Managing the Value of Companies
• Pinto, Henry, Robinson & Stowe (CFA Institute): Equity Asset Valuation
• John Burr Williams: The Theory of Investment Value (1938)

6. Connected Graph Bridges

• Foundational base: Statistics & Inference · Econometrics & Time Series
• Downstream quantitative layer: Fundamental Multi-Factor Models (value/quality factors born from these ratios)
• Risk bridge: Credit Risk & the Merton Model (equity-as-a-call on firm assets) · Stress Testing & Scenario Analysis (valuation sensitivity)
• Sub-pages (in-folder): 01 From Zero · 02 Cash-Flow Forecasting · 03 Cost of Capital · 04 Terminal Value & EV→Equity · 05 Failure Modes · 06 Advanced Extensions

Beginner: start at 01 · Practitioner: start at 05