A.3.5 Failure Modes & Real-World Practice

Basic Prerequisites: 04 · Terminal Value & EV→Equity.

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1. Intuition & Practical Objective

A DCF is arithmetic; its accuracy is entirely the accuracy of its inputs. This page names the failure modes precisely so a practitioner knows where to distrust the model and how the errors show up in money terms - and it ends with the decision rule that turns a valuation into an investment: the margin of safety.

The three failures, in one line each:

1. GIGO forecasts - revenue, margin and reinvestment assumptions are guesses, and they dominate the output.
2. Terminal-value dominance - $70$–$80\%$ of value is the perpetuity, so $g_n$ and $K_c$ are the valuation.
3. Wrong cost of capital / mismatched discounting - a rate error silently moves value by $14$–$16\%$ before you notice.

And the practice discipline: buy well below intrinsic value, because intrinsic value is an estimate, not a fact.

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2. Mathematical Ground Truth & Derivations

Where the errors enter. Value is a ratio-like function of its drivers, so small input errors compound:

$$V_0=\frac{{\text{FCFF}}_1}{K_c-g},{\text{FCFF}}_1=\text{Revenue}\times \text{Margin}\times (1-t)\times (1-\text{RR}).$$

Two structural facts:

• The denominator amplifies. $\frac{\partial V}{\partial g}=\frac{{\text{FCFF}}_1}{(K_c-g{)}^2}$ and $\frac{\partial V}{\partial K_c}=-\frac{{\text{FCFF}}_1}{(K_c-g{)}^2}$. A $1\%$ change in either moves value by roughly $\frac{0.01}{K_c-g}\approx 9\%$ at $K_c-g=0.106$ - and non-linearly as $g\to K_c$.
• Terminal share. For an explicit window $n$ and perpetuity,

$$\text{TV share}=\frac{\text{PV}(\text{TV})}{\text{PV}(\text{explicit})+\text{PV}(\text{TV})},$$

which for a growing firm approaches $1$ quickly. The model is mostly a statement about the stable state.

The margin of safety (Graham). If intrinsic value $\hat{V}$ is an estimate, the rational response is to require a buffer before buying:

$$\text{buy if }P\le (1-m)\hat{V},m\in [20\%,40\%].$$

The margin converts valuation uncertainty into a decision rule: you are paid for being approximately right and protected against being precisely wrong.

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3. Computational Implementation - the failures in numbers

Stdlib only. It measures GIGO sensitivity, terminal dominance via the denominator, the wrong-rate error, and converts value into a buy rule.

Read the numbers: a $2$-point margin swing ($18\%\to 22\%$) moves the value $+28.5\%$ to $+33.0\%$ depending on the reinvestment rate (e.g. $12.47\to 16.02$ at $rr=0.40$), a $0.40\to 0.60$ reinvestment-rate swing at fixed $20\%$ margin spans $\pm 26\%$ ($8.33\to 14.24$), and a $1$-point move in $g$ moves the single-stage value $10$–$18\%$ (e.g. $2002\to 2210$). One wrong discount rate moves equity $+16.4\%$. No spreadsheet can out-precision its assumptions - which is why the practitioner’s answer is a range plus a margin of safety, not a point estimate.

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4. Failure Modes & First-Principles Breakdowns

1. GIGO forecasts. Revenue growth, margins, and reinvestment are the model’s real inputs. Sensitivity tables (above) should accompany every DCF; a single point estimate is dishonest about how little is known.
2. Terminal-value dominance. $70$–$80\%$ of value is the perpetuity; the five-year detail is largely theatre. Test $g_n$ and $K_c$ specifically, cap $g_n$ at $r_f$, and never let $g_n\to K_c$.
3. Wrong cost of capital. Using WACC for equity flows (or a beta/ERP not matched to the cash flow) shifts value $13$–$16\%$ with no visible sign in the model. Match cash flow to discount rate mechanically.
4. Precision illusion. Reporting $11.29 to the cent implies accuracy that the inputs do not support. Report a range; the margin of safety is the engineered response to that uncertainty.
5. Anchoring to price. The most common real-world failure is not mathematical but psychological: reverse-engineering assumptions until the model “confirms” the current market price. Intrinsic value must be estimated independently of price.
6. Ignoring the decision rule. A valuation with no buy rule is trivia. The output of the exercise is “buy below $9.03”, not “fair value is $11.29”.

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5. References

• Damodaran, Investment Valuation
• Graham, The Intelligent Investor
• Graham & Dodd, Security Analysis
• Koller et al. (McKinsey), Valuation
• Fridson & Alvarez, Financial Statement Analysis: A Practitioner’s Guide

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6. Connected Graph Bridges

• Back: 04 · Terminal Value & EV→Equity · Index Hub
• Forward: 06 · Relative Valuation & Advanced Extensions
• Risk: Stress Testing & Scenario Analysis · VaR & Expected Shortfall
• Research: Backtesting Hygiene & Deflated Sharpe (overfitting the forecast to the past)