narrative-to-numbers

name

narrative-to-numbers

description

Builds the business story behind a valuation and connects it to the drivers that carry value — market size, growth, margin, reinvestment efficiency and risk. Tests a narrative as possible, plausible and probable, and keeps the feedback loop open. Use when starting a valuation, writing the story behind a company, setting growth or margin assumptions, sanity-checking a story against its numbers, choosing a target margin or sales-to-capital ratio, or when a valuation needs a defensible reason for its inputs.

Narrative to numbers

A story without numbers is a fairy tale. It cannot be wrong, so it cannot be tested, and it never tells you what price to pay. Numbers without a story are a spreadsheet nobody believes. Every input came from somewhere, but nobody can say where, so any reader who disagrees has nothing to argue with except the answer.

The bridge between them is a mapping rule, and it runs both ways:

• Every claim in the story moves exactly one driver in the model.
• Every input in the model carries one sentence of story.

Two counts prove the bridge holds. Model inputs with no story sentence: zero. Story claims with no driver: zero. Both counts are mechanical, and the second one is where most valuations fail — a claim that moves no driver is decoration, and a claim that moves two is double counted.

This skill owns stages S1, S2, S11 (the driver choices) and S18 of knowledge/frameworks/intrinsic-valuation-playbook.md. It produces 03-narrative/narrative.md and 03-narrative/drivers.json.

The sequence

1. Survey the landscape     business map + base-year numbers + benchmarks
2. Write the narrative      prose, spreadsheet closed
3. Test it                  possible / plausible / probable, then the three screens
4. Connect to drivers       each claim -> one payload field
5. Value it                 dcf-valuation-engine, then the consistency validator
6. Keep the loop open       counter-narratives now, break/shift/change later

The order is binding. Starting at step 4 with a template of inputs and inventing a story afterwards produces a rationalisation, not a valuation. No downstream check can detect it, because the numbers will be internally consistent with each other and with nothing else.

Before step 1, run the bias audit. Name who pays for this valuation, what answer they want, what public position you already hold, and whether you have seen the market price. Do the qualitative work before looking at price. If you have already seen it, treat it as an anchor to argue against, never toward.

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Step 1 — Survey the landscape

The output is not numbers. It is a business-model map plus the benchmarks that tell you what is normal in this business. Those benchmarks are what stop the story from drifting.

Map the business as a loop in about six boxes: suppliers, customers, who sets price, what slice the firm keeps, what it must invest in to grow, what it spends to get there. For Uber in 2014 those six boxes were drivers, riders, surge pricing, payment through the app, the 20% slice, and technology as the only real reinvestment. Each box became a driver.

The numeric half belongs to other skills. financial-statement-normalization produces trailing-twelve-month revenue and EBIT, capitalizes leases and R&D, and rebuilds invested capital. Read its output, not the raw filing. A base year with R&D still expensed understates both EBIT and invested capital, so the margin and the ROIC you benchmark against the industry are both wrong.

Benchmark three things against the industry and against the largest incumbents: revenue growth, pre-tax operating margin, and sales-to-capital or ROIC. For a company claiming it will become the largest player in its business, look at what the largest players actually earn. Global automakers earn 0.3% to 8.5% operating margins. A 16% target margin for a car company is a claim about the world, not a rounding of the industry median.

Read the quarterly trend as evidence that a claimed inflection has started. Do not extrapolate it. Momentum is not a narrative.

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Step 2 — Write the narrative

Write it in prose with the spreadsheet closed. Three rules: keep it simple, keep it focused, stay grounded in reality. If it does not fit in a paragraph, you do not have a narrative yet.

A narrative has to constrain something. "Uber is a technology company" rules nothing out and sets no driver. Compare it with this. Uber is an urban car-service company. It expands the car-service market moderately, holds a 20% slice against competition, benefits from local rather than global network effects, and owns no cars. That version fixes five drivers and can be shown wrong on any of them.

Give the narrative a title that states the bet. Damodaran's Tesla story is titled "The Payoff to Flexibility — A Plausible Path to Auto Dominance", and the word plausible in that title is doing real work. It says which grade the story earns before anyone reads it.

Then break the prose into discrete claims. One market, one capability, one margin path per claim. The claim list is the input to step 3.

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Step 3 — Test it

Two tests run here, and they catch different things.

The grading ladder sorts each claim by how confidently you can assign a probability, and routes it to the matching device.

Grade	Definition	Where it goes	What promotes it
Probable	expected, with evidence — product success, financial results	base-year numbers and expected cash flows	—
Plausible	a reasoned argument, no tangible evidence yet	a higher expected growth rate inside the DCF	product success, financial results
Possible	the probability cannot be assessed at all	option value, added on top of the DCF, once	market-potential evidence, product testing

"Possible" does not mean unlikely. It means unassessable, which is why it gets a different tool. A claim is routed exactly once. A market counted in revenues may not also be counted as option value.

Write down the promotion trigger for every claim now. Step 6 has nothing to watch for otherwise.

The three screens test the finished set of claims against arithmetic, economics and business reality. The impossible is never allowed. The implausible needs extraordinary justification. The improbable is the dangerous class: each assumption looks fine alone, and together they contradict how business works.

Full screen list, the aggregation test for a crowded market, and the growth/risk/ reinvestment triangle: resources/narrative-tests.md.

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Step 4 — Connect the narrative to the drivers

This is the bridge itself. The value chain is fixed:

total market x market share = revenues
revenues - operating expenses  = operating income
             - taxes           = after-tax operating income
             - reinvestment    = free cash flow to the firm

Those cash flows are then adjusted for time and operating risk through the discount rate, and for survival through a probability of failure.

Each claim maps to exactly one field in the dcf-valuation-engine payload. This table is the working core of the skill.

Narrative claim is about	Driver	Payload field
Market definition, market size, how fast that market grows	Total market	base_revenue plus revenue_growth (see the conversion below)
Competitive position, network effects, the share the firm attains	Market share	revenue_growth
The slice of the transaction the firm keeps	Revenue slice	revenue_growth (it scales the revenue path)
Pricing power, cost structure, scale economies	Operating margin	operating_margin, as a glide to the target
How long until the target margin is reached	Margin convergence	operating_margin.converge_by
Capital intensity: asset-light or asset-heavy	Reinvestment efficiency	sales_to_capital
Tax domicile, tax migration, accumulated losses	Tax	tax_rate, net_operating_loss_carryforward
Business maturity, operating risk, country exposure	Discount rate	cost_of_capital, terminal.cost_of_capital
How long the moat holds off competition	Length of the growth phase	forecast_years, and each converge_by
Whether excess returns survive in perpetuity	Terminal excess return	terminal.return_on_capital
The economy-wide ceiling on perpetual growth	Terminal growth	terminal.growth_rate
Whether the business can fail outright	Survival	failure.probability, failure.proceeds_basis, failure.proceeds_percent
Debt, cash, minorities, holdings, options, share count	Bridge	bridge.debt, bridge.cash, bridge.minority_interests, bridge.non_operating_assets, ,

The market-and-share conversion. The engine takes a revenue path, not a market and a share. Do the multiplication yourself, then hand over the growth rate:

target revenue_N = total market_N x market share_N x revenue slice
revenue_growth   = (target revenue_N / base_revenue)^(1/N) - 1

Keep the market, the share and the slice in drivers.json as the story record, because they are the numbers a reader will argue with. The growth rate is what the engine consumes. Set the growth lever from an end-state revenue level, never from a rate you like the look of. That forces you to look at absolute dollars in year N and ask who loses that revenue.

Every lever gets a reference class. A target margin picked against the auto industry median of 3.01%, the technology median of 10.25% and the software median of 21.24% is a choice you have to defend. A target margin picked from nowhere is a number nobody can argue with. The lever menus Damodaran uses, and the terminal defaults with the argument each override requires: resources/driver-mapping.md.

Write the story link on every row. A row with no link is deleted, or the missing claim is found. That single discipline is what the whole skill exists to enforce.

The artifact

drivers.json carries the dcf-valuation-engine payload, plus two blocks that keep the bridge auditable:

{
  "base_revenue": 46848, "base_ebit": 5650.4, "base_invested_capital": 27818.4,
  "forecast_years": 10,
  "revenue_growth": {"start": 0.35, "end": 0.0156, "converge_by": 10},
  "operating_margin": {"start": 0.1206, "end": 0.16, "converge_by": 5},
  "sales_to_capital": 4.0,
  "tax_rate": {"start": 0.1199,    
        
      
                
    
        
              
   

   
     
     
     
     
  
   
         
      
  

currency must match the cost-of-capital artifact. The validator checks it, and a currency mismatch is the most common silent error in DCF work.

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Step 5 — Value it

The arithmetic belongs to the engine. Hand it the payload:

python3 <skills>/dcf-valuation-engine/resources/dcf.py value --in drivers.json > dcf-result.json

Then run valuation-consistency-checks before reading the answer. It re-runs the impossible screens mechanically on the finished model, checks that the terminal reinvestment rate equals g / ROC, and flags a terminal return on capital above the terminal cost of capital. Fix the offending input, not the output, and re-run.

Two diagnostics decide whether the story survived contact with the arithmetic:

• Marginal ROIC over the forecast. Tesla's 4.00 sales-to-capital against an auto median of 1.37 implies a marginal ROIC of 51.66%. That is a claim about a permanent advantage, and it has to be argued in the prose or the ratio has to come down.
• Terminal excess return, terminal.return_on_capital minus terminal.cost_of_capital. Anything above zero claims a moat that survives forever. Name the moat or set them equal.

Then convert the point estimate into a range. Use a scenario grid when the doubt is about which story, and monte-carlo-valuation when it is about how much. Label every row possible, plausible or probable, and name the cell you actually believe. A range with no chosen cell is an abdication. A range with no likelihood labels is a wish list.

Finally, run implied backwards against the market price. "The stock is worth $571 and trades at $1,200" invites an argument about your assumptions. "At $1,200 the market assumes a margin no firm in this industry has sustained" is a claim about the world, and it is checkable. Ask whether that assumption is probable, not whether it is possible. Some scenario always justifies any price.

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Step 6 — Keep the feedback loop open

A narrative is a working hypothesis, not a position. Two habits keep it honest.

Value the counter-narratives. Ask what would have to be true for a much higher value, and for a much lower one. Then run the alternative story through the same model, changing only the drivers that story changes. Knowing what someone else's story is worth beats knowing that you disagree with it. Damodaran valued Uber at $5.9bn and Bill Gurley at $53.4bn, and the counter-narrative run showed the entire gap living in three drivers: market size, market share and the revenue slice. Nothing else was in dispute.

Classify the news when it arrives. That diagnosis is the only one that matters.

Change	What happened	Response	Tool
Break	events end the story — legal, political, competitive, default	existing cash-flow, growth and risk estimates stop being operative	probability of the break, times its consequences
Shift	the business model improves or deteriorates; market size, share or margin move	revise those drivers and re-run	scenario grid or simulation
Change	unexpected entry into or exit from a market	redo the valuation on new market potential	real options

Treating a break as a shift keeps the model running on a business that no longer exists. Treating a shift as a break abandons a valuation over one bad quarter.

Re-grade the claim ledger against the promotion triggers written at step 3. A promotion from possible to plausible moves a market out of the option layer and into the growth rate, and the value moves with it.

Two disciplines close the loop. Revise on business news, never on price moves — price moving against you is not information about the business. And count your revisions in both directions over time. They should be roughly symmetric. A one-sided revision record is evidence of a biased process, not of bad luck.

Re-enter the pipeline at the stage that owns the change, not at the top. A margin re-estimate re-runs the forecast onward. A classification change re-runs everything.

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The failure gallery

Three ways a narrative goes wrong, each with a different tell and a different defence. Detail, tables and the full cases: resources/failure-gallery.md.

The runaway story. A charismatic narrator, plus a disliked status quo being disrupted, plus a claimed societal benefit. Once all three are present the questions stop, because the answers might put the story at risk. Theranos was valued at $9 billion in October 2015. Its board held two former Secretaries of State, a Senate Majority Leader, two generals and exactly one person with a medical background. Prestigious, and irrelevant to whether a drop of blood can run 200 tests. No discount rate saves you here. The claim was in the impossible class, and the only defence was refusing to let the story stop the questions.

The big market delusion. Every company chasing a huge market can be individually defensible and collectively impossible. Aggregate the revenue each company's price requires, and the total exceeds any plausible size for the market. In 2015 the implied 2025 online-advertising revenue across twenty-one companies came to about $522 billion, against $146.6 billion of actual revenue at the time. Not one of those valuations looked silly alone. This failure is invisible from inside a single valuation, so run the aggregation test whenever your company is one of many chasing one market.

The improbable but not impossible case. A mid-2013 sell-side model took Tesla from 24,298 vehicles to 1,137,780, expanded the EBIT margin from 1.8% to 15.3%, and held capital spending at 3% of sales with negative working-capital changes. Every line is arguable on its own. Together they claim enormous growth, expanding margins and almost no reinvestment at the same time. No screen for the impossible catches it. The triangle does.

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Common failures

Symptom	Cause
The story reads as unarguable	It constrains no driver. Rewrite until a claim can be shown false
Value moves hundreds of dollars a share on one input	Normal for a growth company. Say so, and show the grid
A claim shows up in both growth and option value	Double counted. Route each claim once
Terminal ROC left above terminal cost of capital	A perpetual moat granted by default. State it or set them equal
Sales-to-capital far above the industry	Growth assumed to be nearly free. Check marginal ROIC
The range spans 100x with no chosen cell	A grid without a base case is an abdication
The narrative changed after the price moved	Herding with extra steps. Revise on business news
An input nobody can explain in a sentence	Delete it or find the claim behind it

Reference files

• resources/narrative-tests.md — the grading ladder, the impossible/implausible/improbable screens, the growth/risk/reinvestment triangle, the sector aggregation test.
• resources/driver-mapping.md — every lever with its reference menu, the end-state revenue method, terminal defaults and what overriding each one requires.
• resources/failure-gallery.md — Theranos, the online-advertising aggregation table, the improbable Tesla sell-side model, and the Amazon breakeven grid.
• resources/worked-examples.md — Uber June 2014 and Tesla November 2021, end to end.

Related

company-classification-routing fixes the life-cycle stage and constraint set this skill inherits. financial-statement-normalization produces the base year. dcf-valuation-engine runs the arithmetic. valuation-consistency-checks gates the result. valuation-red-team attacks the finished story. monte-carlo-valuation and option-valuation-toolkit handle the uncertainty and the option layer.

Deeper background: knowledge/concepts/narrative-numbers/ for all nineteen concept notes, and knowledge/frameworks/intrinsic-valuation-playbook.md stages S1, S2, S11, S16 and S18.