DCF Sensitivity Analysis: Tornado Diagrams and Scenario Analysis Worked Examples

A DCF valuation produces a single number, but that number depends on dozens of assumptions. Small changes in WACC, terminal growth rate, or cash flow forecasts can shift the equity value per share by 20-50% or more. Sensitivity analysis systematically tests how each assumption affects the output, revealing which inputs really matter and which don't. Why this is critical: - Most DCF valuations involve assumptions that are inherently uncertain - Point estimates (single-number valuations) hide this uncertainty - Decision-makers need to understand the range of possible outcomes, not just the midpoint - Different assumptions could completely reverse the accept/reject decision Common DCF inputs that drive sensitivity: - WACC (discount rate): usually the highest-impact input - Terminal growth rate (for terminal value in Gordon Growth approach) - Exit multiple (for terminal value in exit multiple approach) - Revenue growth rates in explicit forecast - Margins (gross margin, EBITDA margin, EBIT margin) - Capital expenditure assumptions - Working capital assumptions - Tax rate - Effective perpetuity growth Sensitivity analysis is NOT: - Randomizing inputs without thought - Picking ranges arbitrarily - Avoiding conclusions because 'valuation is sensitive' - A substitute for understanding the business Sensitivity analysis IS: - Systematic testing of plausible ranges - Communicating what you're confident about vs uncertain about - Identifying where to focus additional due diligence - Supporting decision-making under uncertainty This content is for educational purposes only and does not constitute financial advice.

One-variable sensitivity holds all other inputs constant while varying a single input across a range. The output (e.g., equity value per share) is computed at each variant. Results typically presented as a table or single-variable chart. Worked example: Company A has a base-case DCF valuation of $50 per share. Base case inputs: - WACC: 10% - Terminal growth rate: 3% - Revenue growth year 1-5: 8% - Exit multiple: 10x EBITDA - Other: held constant Sensitivity to WACC (varying -2% to +2% from base): | WACC | Equity Value per Share | |------|------------------------| | 8% | $65 | | 9% | $57 | | 10% | $50 (base) | | 11% | $44 | | 12% | $39 | Interpretation: A 1% increase in WACC reduces equity value by approximately $6-7 per share. A 2% range in WACC produces a $26 range in equity value. WACC is clearly a sensitive input — be confident in your WACC estimate. Sensitivity to terminal growth rate (varying 1% to 5%): | Terminal Growth | Equity Value per Share | |-----------------|------------------------| | 1% | $42 | | 2% | $46 | | 3% | $50 (base) | | 4% | $55 | | 5% | $62 | Interpretation: Each 1% change in terminal growth produces approximately $4-5 per share change. Lower than WACC sensitivity but still material. Sensitivity to year-5 revenue growth rate (varying 5% to 11%): | Year-5 Revenue Growth | Equity Value per Share | |----------------------|------------------------| | 5% | $47 | | 6% | $48 | | 7% | $49 | | 8% | $50 (base) | | 9% | $51 | | 10% | $53 | | 11% | $54 | Interpretation: Year-5 revenue growth has a relatively small impact — $1-2 per share per 1% change. Less sensitive than WACC or terminal growth. Key insight: the sensitivity hierarchy for most DCF: 1. Terminal value inputs (WACC + terminal growth or exit multiple) — usually 70-90% of valuation 2. Revenue growth in explicit period 3. Margin assumptions 4. Capex and working capital Knowing this hierarchy helps focus analytical effort on what matters most.

Two-variable sensitivity varies two inputs simultaneously, presenting results in a grid. This captures interactions between inputs and is the standard approach for presenting DCF sensitivity in investment committee memos and valuation reports. Worked example: same Company A. Two-variable table with WACC and terminal growth: Equity Value Per Share: | | WACC=8% | WACC=9% | WACC=10% | WACC=11% | WACC=12% | |------------------|---------|---------|----------|----------|----------| | Term Growth=1% | $55 | $48 | $42 | $37 | $33 | | Term Growth=2% | $60 | $52 | $46 | $40 | $35 | | Term Growth=3% | $65 | $57 | $50 (base)| $44 | $39 | | Term Growth=4% | $71 | $62 | $55 | $48 | $42 | | Term Growth=5% | $78 | $68 | $62 | $53 | $46 | Reading the table: - Base case ($50 per share) is at 10% WACC, 3% terminal growth — center of table - The most pessimistic combination (high WACC, low growth): 12% WACC, 1% growth → $33 per share - The most optimistic combination (low WACC, high growth): 8% WACC, 5% growth → $78 per share - Equity value range: $33-$78, a 2.4x spread What this shows: - Investment decision depends on which combination is realistic - The table communicates uncertainty range to decision-makers - Focus attention on 'plausible' corners rather than extremes - If current stock price is $45, it's within sensitivity range for various assumptions Other two-variable combinations to consider: - WACC × Exit multiple (if using exit multiple approach for terminal value) - Margin × Revenue growth - WACC × Year-5 revenue Critical tip: always format output per share (or per equity value) rather than in absolute dollars, to make comparisons easier.

A tornado diagram ranks inputs by their individual impact on the output. The most sensitive inputs appear at the top (largest horizontal bars), creating a 'tornado' shape that visually communicates which assumptions matter most. How to build one: Step 1: For each input, vary it from low-case to high-case (e.g., ±10% from base, or within a defined range). Step 2: Record the resulting output value at each extreme. Step 3: Calculate the 'swing' for each input = high-case output − low-case output. Step 4: Sort inputs by swing magnitude (largest first). Step 5: Draw horizontal bars centered at the base case, extending to high-case and low-case values. Step 6: Inputs with largest swings at top, smaller swings below. Worked example tornado for Company A DCF: | Input | Low Case | High Case | Swing (sensitivity) | |-------|----------|-----------|---------------------| | WACC | -2% to base (12% to 10%) | +2% to base (10% to 8%) | $26 ($39 to $65) | | Terminal Growth | 1% to 5% | 5% to 1% | $20 ($42 to $62) | | Revenue Growth (Yr5) | 5% to 11% | 11% to 5% | $7 ($47 to $54) | | EBITDA Margin | -3% to +3% | +3% to -3% | $6 | | Capex | +20% to -20% | -20% to +20% | $3 | | Working Capital | -20% to +20% | +20% to -20% | $2 | Tornado diagram shows: - WACC is top bar (largest swing, highest sensitivity) - Terminal growth second (significant but less than WACC) - Revenue growth third - EBITDA margin fourth - Capex and WC relatively minor Interpretation: when communicating valuation uncertainty, focus on the top 2-3 inputs. If you can narrow the range on WACC or terminal growth (through deeper research), the overall valuation range tightens substantially. Less leverage from narrowing capex estimates. Presentation tips: - Include magnitude number next to each bar (exact swing) - Use consistent input ranges (all ±10%, or all 95% CI) - Label input values on axis - Consider showing top 5-7 inputs only (diminishing returns below that) - Communicate the implied action: 'Focus on WACC and terminal growth for further analysis'

Scenario analysis is different from single-variable sensitivity. Instead of varying one input at a time, scenarios vary multiple inputs simultaneously according to a coherent narrative (e.g., 'recession scenario' changes revenue growth AND margins AND terminal growth together). Three-scenario framework (common): Base Case (most likely): assumes current management guidance or analyst consensus. - Revenue growth: 8% - EBITDA margin: 20% - Terminal growth: 3% - WACC: 10% - Equity value per share: $50 Bull Case (optimistic): assumes favorable conditions align. - Revenue growth: 12% (faster due to market tailwinds) - EBITDA margin: 23% (operational leverage kicks in) - Terminal growth: 4% (sustained higher growth) - WACC: 9% (lower risk premium for successful company) - Equity value per share: $75 Bear Case (pessimistic): assumes unfavorable conditions align. - Revenue growth: 4% (demand weakness) - EBITDA margin: 15% (margin compression from competition) - Terminal growth: 2% (slower long-term) - WACC: 11% (higher risk premium) - Equity value per share: $30 Scenario results: - Bear case: $30 - Base case: $50 - Bull case: $75 - Range of equity values: 2.5x (bull / bear) Probability-weighted value (if probabilities can be estimated): - Bull: 30% probability × $75 = $22.50 - Base: 50% probability × $50 = $25.00 - Bear: 20% probability × $30 = $6.00 - Weighted: $53.50 The weighted average approach gives a single number but hides the distribution. More useful in conclusion sections: 'Our DCF implies a central value of $50 with a range of $30-$75 depending on scenario.' When to use scenarios vs sensitivity: - Scenarios: when inputs tend to move together (a 'good scenario' is good across all dimensions) - Sensitivity: when inputs move independently - In practice: use both. Scenarios communicate strategic uncertainty; sensitivity shows which inputs matter.

The final step — often the hardest — is communicating sensitivity results to decision-makers. Technical analysts often fail to convert spreadsheet output into business narrative. Common mistakes in communicating sensitivity: - Presenting all the analysis without conclusions - Reporting absurdly wide ranges (e.g., '$10 to $200') without interpretation - Burying the key insight in a 100-cell table - Failing to connect sensitivity to decision-relevance Best practices: 1. Lead with the actionable insight Start with: 'Under our base case, Company X is valued at $50 per share. In reasonable bear and bull scenarios, the range is $35-$65, suggesting the stock is [overvalued / undervalued / fairly valued] at today's $45 price.' 2. Identify the key sensitivities Follow up: 'The valuation is most sensitive to WACC and terminal growth. A 1% change in WACC shifts equity value by approximately $7 per share. Our WACC assumption of 10% is based on [explain methodology]. A higher rate of 11% would still support purchase at current price.' 3. Present the visualization that matters Show a tornado diagram or two-variable sensitivity table, not the underlying 1,000 data points. 4. Relate sensitivity to specific business uncertainties 'Margin assumptions are sensitive to competitive response. If Company Y launches a competing product, we estimate EBITDA margin could decline 200 bps, reducing equity value to approximately $42.' 5. Conclude with decision-relevance 'Given the sensitivity analysis, at current price ($45), the stock is attractive if WACC is at or below 11% and terminal growth is at or above 2%. We view these as reasonable assumptions and recommend accumulation.' 6. Flag assumptions you're most worried about 'Our analysis assumes stable operating margins. If competitive pressure causes margin decline greater than 200 bps, our thesis would require reassessment.' 7. Show the decision point 'Sensitivity analysis supports our buy recommendation at current price unless WACC exceeds 12% or terminal growth falls below 1.5%, neither of which we view as likely.' The tone matters: confident about what you know, honest about uncertainty, specific about decision-relevant sensitivities, recommending action despite uncertainty.