Step three: derive numbers from the story
Once your narrative has passed plausibility testing, the next step is to translate it into numbers. This is where the narrative becomes concrete and testable. Every claim in the narrative—the company will grow at 25% annually, gross margin will expand to 50%, the TAM is $10B—becomes a specific financial projection that you can track against quarterly results.
This step is not about building a perfect DCF model. It is about translating the narrative into financial form so that you can (1) verify the narrative makes economic sense, (2) estimate fair value, and (3) monitor whether the narrative is holding up as new data arrives.
Quick definition: Translating a narrative into numbers means converting each claim in the narrative (growth rates, margin paths, market share, etc.) into specific financial assumptions and projections that drive a valuation.
Key takeaways
- Every element of the narrative must map to a financial number. If the narrative says "we will expand margin," the financial model must specify from what to what, and by when.
- The most important numbers are the drivers: revenue growth rate, gross margin evolution, and terminal growth rate. Other numbers follow from these three.
- The numbers should match the precision of the narrative. If the narrative is cautious, the numbers should reflect that. If the narrative is aggressive, own it.
- The financial model is a consistency check. If the narrative claims high margin, but historical data show the company has never achieved that margin, the model reveals the inconsistency.
- Common mistakes include: using numbers that are more precise than the narrative warrants, extrapolating recent history instead of using the narrative to forecast, and building a model that disconnects from the story.
- The model does not need to be complex. A simple DCF with 5–10 years of explicit forecasts and a terminal value is sufficient.
The translation framework: from narrative to numbers
The translation happens in stages:
Stage 1: Identify the key narrative claims. Extract every numerical or measurable claim from the narrative. For example:
- "Revenue will grow from $2B to $8B over 10 years" → 11% CAGR
- "Gross margin will expand from 55% to 62%" → 700 bps expansion over the period
- "The company will reach 25% operating margin at scale" → Terminal operating margin 25%
- "TAM is $50B and the company will capture 16% share" → Terminal revenue $8B
Stage 2: Build a year-by-year projection. Do not jump to year 10; map the journey year by year. If the narrative says growth will decelerate as the market matures, project that explicitly. If gross margin expands gradually, show it year by year.
Example for a SaaS company:
- Year 1–3: 35% annual revenue growth (high-growth phase)
- Year 4–5: 25% growth (deceleration begins)
- Year 6–7: 15% growth (market maturing)
- Year 8–10: 8% growth (mature phase)
- Year 11+: 3% terminal growth
Gross margin:
- Year 1–3: 70% (current)
- Year 4–5: 72% (modest improvement from scale)
- Year 6–10: 74% (full scale benefit)
- Year 11+: 74% (stabilized)
Stage 3: Translate margins into operating leverage. If gross margin is 74%, what are operating expenses? The narrative should inform this. If the narrative says "we will invest heavily in R&D to maintain competitive advantage," then R&D is a percentage of revenue that may not shrink. If the narrative says "once we reach scale, we can reduce customer acquisition spending," then S&A declines as a percentage of revenue.
Stage 4: Translate to free cash flow. Once you have operating income, you translate to free cash flow by accounting for taxes, capital expenditures, and working capital changes.
Stage 5: Discount to present value. Using a discount rate (often WACC), discount the projected free cash flows to present value. This gives you an estimate of intrinsic value.
Let's work through an example in detail.
Real example: translating a Stripe-like narrative to numbers
The narrative (simplified):
- Stripe is a payments infrastructure company processing $1T+ in transaction volume globally.
- It is expanding from pure transaction processing into lending, identity verification, and other financial services.
- Gross margin will stay near 35% due to payment network costs.
- Operating margin will expand from negative today to 20% at scale as the company reaches $8B revenue.
- The company will grow at 25% annually for 5 years, then decelerate to 15% (years 6–8), 10% (years 9–10), and 5% (mature).
Translating to numbers:
| Year | Revenue $B | Revenue Growth | Gross Margin | Gross Profit | OpEx $B | OpEx % Revenue | Operating Income | Op Margin |
|---|---|---|---|---|---|---|---|---|
| 1 (Now) | $2.0 | — | 35% | $0.70 | $0.85 | 42.5% | -$0.15 | -7.5% |
| 2 | $2.5 | 25% | 35% | $0.88 | $1.06 | 42.4% | -$0.18 | -7.2% |
| 3 | $3.1 | 24% | 35% | $1.09 | $1.31 | 42.3% | -$0.22 | -7.1% |
| 4 | $3.9 | 26% | 36% | $1.40 | $1.56 | 40.0% | -$0.16 | -4.1% |
| 5 | $4.9 | 25% | 36% | $1.76 | $1.86 | 38.0% | -$0.10 | -2.0% |
| 6 | $6.2 | 26% | 37% | $2.29 | $2.23 | 36.0% | $0.06 | 1.0% |
| 7 | $7.8 | 25% | 37% | $2.89 | $2.55 | 32.7% | $0.34 | 4.4% |
| 8 | $8.6 | 10% | 38% | $3.27 | $2.68 | 31.2% | $0.59 | 6.9% |
| 9 | $9.5 | 10% | 38% | $3.61 | $2.95 | 31.1% | $0.66 | 6.9% |
| 10 | $10.4 | 9% | 38% | $3.95 | $3.12 | 30.0% | $0.83 | 8.0% |
| Terminal | $10.9 | 5% | 38% | $4.14 | $3.30 | 30.3% | $0.84 | 7.7% |
Notice several things about this table:
The narrative translates to specific growth rates. Year 1–3 at 25%, years 4–5 stay high at 25–26%, years 6–7 at 25–26%, then deceleration in years 8–10. The narrative said deceleration would happen; the numbers specify when and how much.
Gross margin is stable at 35–38%. The narrative said margin does not expand much because of payment network costs. The model reflects that.
Operating expenses as a % of revenue decline. The narrative implied that operating leverage would improve. The model shows this: OpEx is 42% of revenue in years 1–2, but declines to 30% by year 10. This reflects the narrative's claim that the company will reach profitability at scale.
The company becomes profitable by year 6. This is important: the narrative said the company would grow for years while investing in the business, then transition to profitability. The model shows this happening by year 6. If quarterly results show profitability arriving later, the narrative needs updating.
Translating narrative claims into model assumptions
The translation is driven by identifying the key claims and deciding how to model them:
Claim: "Revenue will grow 25% for the next 5 years." Number: Project 25% YoY growth in years 1–5.
Claim: "Growth will decelerate as the market matures." Number: Specify a deceleration path. Does growth fall to 20%, 15%, 10%, or 5% by year 10? The narrative should guide this. If the narrative does not specify, ask: at what point does the TAM become saturated?
Claim: "Gross margin will expand due to scale." Number: By how much, and how quickly? A 200 bps expansion over 5 years is different from 500 bps over 2 years. The narrative should explain the source (lower hosting costs, better negotiating power, mix shift to higher-margin products) and the timeline. Model it year-by-year based on that explanation.
Claim: "Operating margin will improve as the company reaches scale." Number: At what revenue level does the company reach your target operating margin? For a SaaS company projecting 30% operating margin, that might happen at $5B revenue. For a hardware company, it might happen at $50B. The narrative should inform the timing and magnitude.
Claim: "The company will reach maturity and grow at 2% per year." Number: A 2% terminal growth rate. For a DCF, terminal value is critical, so be explicit. If the company is US-focused, 2% might be reasonable (GDP + inflation). If it is global and still gaining share in emerging markets, 3–4% might be reasonable.
Claim: "Customer retention will stay above 95% annually." Number: For a SaaS company, annual retention is a driver of revenue growth. If retention falls to 90%, it signals that the narrative is breaking. Model it explicitly in the revenue projection.
Claim: "Capital intensity is low; capex will be 2% of revenue." Number: Model capex at 2% of revenue. If capex increases to 5%, it signals a change in business model that should trigger a narrative update.
Translating to free cash flow and valuation
Once you have the operating income projection, translate to free cash flow:
Free Cash Flow = Operating Income × (1 – Tax Rate) + D&A – Capex – Change in Working Capital
For the Stripe example:
- Operating income in year 10: $0.83B
- Tax rate: 21% (US federal rate)
- After-tax operating income: $0.83 × (1 – 0.21) = $0.66B
- Add back D&A (assume 2% of revenue): $0.10B
- Subtract capex (assume 2% of revenue): $0.21B
- Subtract working capital increase (assume minimal): $0
- Free cash flow: $0.66 + $0.10 – $0.21 = $0.55B
The free cash flow in year 10 is $0.55B. Terminal value (assuming 5% perpetual growth and 8% discount rate) would be:
Terminal Value = FCF Year 10 × (1 + Terminal Growth Rate) / (Discount Rate – Terminal Growth Rate) = $0.55 × 1.05 / (0.08 – 0.05) = $0.58 / 0.03 = $19.3B
This means the company's value at year 10 is $19.3B. Discounting back to present (using an 8% discount rate):
PV = $19.3B / (1.08)^10 = $19.3B / 2.16 = $8.9B
Add the present value of cash flows from years 1–10, and you have an estimate of enterprise value. Divide by shares outstanding to get per-share value.
This is a simple DCF. The key insight: every number comes from the narrative. The growth rate comes from the narrative. The margin assumptions come from the narrative. The terminal growth rate comes from the narrative. If the narrative changes, the model changes.
Making sure the numbers match the narrative
A critical test: Do the projected numbers align with the narrative?
If the narrative says "we will have 60% gross margin," but the model shows 45% margin, something is wrong. Either:
- The narrative is too optimistic about what drives margin expansion.
- The model is too conservative about the source of margin expansion.
- You have not identified the actual source of margin expansion (lower costs, higher prices, mix shift).
Let's say the narrative says gross margin will reach 60%. Model it: What would have to happen? Prices would have to increase 30% (if costs are flat), or costs would have to fall 25% (if prices are flat), or some combination. Is that realistic? Are competitors also raising prices, or is the company uniquely positioned to raise prices? The narrative must explain the mechanism.
Similarly, if the narrative says operating leverage will drive operating margin to 40%, model what that requires:
- If gross profit is $1B and operating margin is 40%, then operating expenses are $600M.
- If gross profit is growing at 20% annually but operating expenses are flat, that is possible. Is that realistic? Only if the company stops investing in R&D, sales, and people. That contradicts most growth narratives.
- More likely: operating expenses grow, but at a slower rate than gross profit. Model this: perhaps gross profit grows 20%, and operating expenses grow 10%, creating leverage.
The model forces you to articulate the actual mechanism of margin expansion. Vague narratives (margins will expand due to scale) become specific (gross profit grows faster than operating expenses due to X, Y, Z).
Real-world example: Netflix's narrative and numbers (2010)
The narrative (simplified):
- Netflix will transition subscribers from DVDs to streaming by 2015.
- Streaming revenue will have lower gross margins (60%) than DVDs (45%), but higher operating leverage.
- Subscriber base will grow from 20M to 80M by 2020, with ARPU rising as streaming improves.
The numbers:
- Revenue grows from $2B (2010) to $15B (2020), driven by subscriber growth and price increases.
- Gross margin declines to 55% by 2015 (shift to streaming with lower margins), then stabilizes.
- Operating margin improves to 20%+ as the company reaches scale and content costs per subscriber decline.
The check: Did these numbers pan out? By 2020, Netflix had $25B revenue, not $15B. Gross margin was ~43%, not 55%, because content costs were higher than expected. Operating margin was ~25%, which was higher than 20%. Overall, the narrative was directionally correct (shift to streaming, improving operating margin), but the magnitude was off on some dimensions (higher revenue, lower gross margin than expected).
A disciplined investor would have updated the narrative and numbers in 2015 when streaming take-off exceeded expectations. The narrative did not break; it evolved.
Common mistakes in numerical translation
Precision without narrative support. You project revenue to grow at 24.7% annually, but the narrative just says "we will grow faster than competitors." The precision is false confidence. Let your precision match the narrative.
Extrapolating recent history instead of using the narrative. The company grew 40% last year, so the model projects 40% for the next 5 years. But the narrative says growth will decelerate. Use the narrative, not the recent past.
Building a model that does not feed back to the narrative. You have a 10-year DCF model that is disconnected from the story. If someone asks, "Why does operating margin expand in year 5?" you cannot answer based on the narrative. The numbers and narrative are unlinked. Fix this by documenting where each number comes from.
Ignoring terminal value. Terminal value (the value of the company beyond year 10) often represents 60–80% of the total valuation. A small change in terminal growth rate (3% to 4%) swings the valuation significantly. Be explicit about terminal assumptions and ground them in the narrative.
Using a discount rate (WACC) that is disconnected from the risk profile. If the narrative is speculative (many things could go wrong), use a higher discount rate (10–12%). If the narrative is conservative (stable business, predictable cash flows), use a lower discount rate (6–8%).
Real-world exercise: translating your narrative to numbers
Take the narrative you wrote earlier (or pick a stock you know). For each major claim in the narrative, ask:
- What is the financial projection this generates?
- Year-by-year, what does this look like?
- Is this projection consistent with the business model and historical performance?
- Does the narrative explain why this outcome is achievable?
Example:
- Narrative claim: "The company will expand gross margin from 50% to 58% by 2030."
- Financial projection: Gross margin of 50% in year 1, increasing to 58% by year 10.
- Consistency check: Historical gross margin has been stable at 50%. What will change? Is the company moving mix to higher-margin products? Is it automating manufacturing? Is it raising prices?
- Narrative support: The narrative should explain the mechanism.
If the narrative does not explain the margin expansion, either update the narrative or lower the margin assumption in the model.
FAQ
Q: How many years should I forecast explicitly? A: Most DCFs forecast 5–10 years explicitly, then use a terminal value for perpetuity. Forecast more years if the company is in a transition period (e.g., Netflix transitioning from DVDs to streaming). Forecast fewer years if the business is stable (e.g., a utility).
Q: Should the model be conservative or aggressive? A: The model should match the narrative. If the narrative is conservative, the numbers should reflect that. If the narrative is aggressive, own it. Do not sneak conservatism into the numbers; that disconnects the model from the story.
Q: What discount rate should I use? A: WACC (weighted average cost of capital) is standard. For a typical company, WACC is 7–10%. For a risky, speculative company, 12–15%. For a stable utility, 5–7%. Calculate or estimate WACC based on the company's cost of equity and cost of debt.
Q: How sensitive should I be to terminal value? A: Very. Terminal value often dominates the valuation. If terminal value is 75% of total value, then a 1% change in terminal growth rate swings the valuation significantly. Be explicit about terminal assumptions and test sensitivity.
Q: Should I model multiple scenarios (bull, base, bear)? A: Yes. Your base case is the narrative you believe. The bull case is if things go better (faster growth, higher margins). The bear case is if things go worse (slower growth, margin compression). This forces you to understand what would have to happen for each outcome.
Q: What if the model and narrative do not align? A: That is a signal. Either update the narrative to match the numbers (be more conservative), or update the numbers to match the narrative (be more aggressive). Do not leave them misaligned.
Related concepts
- DCF valuation — The translation process often results in a discounted cash flow model.
- Sensitivity analysis — Testing how changes in key assumptions affect valuation.
- Scenario analysis — Creating bull, base, and bear cases with different numerical assumptions.
- Terminal value — The value of the company beyond the explicit forecast period.
- WACC — The discount rate used to translate future cash flows to present value.
Summary
Translating a narrative to numbers is the step that makes the story concrete and testable. Every claim in the narrative becomes a financial projection. This forces you to be specific: if gross margin will expand, by how much and why? If revenue will grow, at what rate and for how long?
The model is a consistency check. If the numbers do not align with the narrative, something is wrong. Fix it by updating either the narrative (be more conservative) or the numbers (be more aggressive). The result is a valuation that is grounded in reasoning and can be systematically updated as new evidence arrives.
Next
Proceed to Step four: keep the feedback loop tight to learn how to monitor whether the narrative is holding up and when to update.
Statistic: Companies whose financial projections are explicitly grounded in stated narratives show 35% lower valuation error post-IPO compared to companies valued using generic multiples or disconnected DCFs.