Every chapter, readable.

What a business is, in money

Before any technique, one picture: a company is a machine that takes money in, turns it into things that produce, and gives money back. Everything you will learn is a way of measuring one part of that loop.

Start where you already are

You already run a business. Before any of the vocabulary, look at what actually happens in it.

A client pays you 3 000 for a campaign. That money does not appear the day you agree the job. First you spend: hours, render credits, a subscription, maybe a freelancer. Weeks later you deliver. Perhaps thirty days after that, the money arrives. In between, you were paying for a job that had not paid you yet, out of money that came from somewhere: a previous client, your savings, an overdraft.

That is a complete business in one paragraph, and it contains every problem in finance:

• You put money in before you got money out. Someone had to fund that gap.
• The money you put in came from somewhere, and that somewhere expected something back.
• Whether the job was worth doing depends on what you got out compared with what you put in, and when.
• The profit you booked the day you delivered is not the same thing as the money in your account.

Every technique in this book is a precise way of answering one of those four. Nothing more mystical than that is going on. The reason finance feels like a foreign language is that it has a specific word for each of these, and everyone uses the words as if you already knew them. So we will earn the words one at a time, and no word will be used here before it has been explained or defined on the spot.

A company is a loop, and it has four moves

Scale that campaign up to a company with ten thousand employees and nothing changes structurally. Money goes round a loop, and management makes four decisions about that loop. These four are the whole of corporate finance, and every course you take at emlyon sits inside one of them.

Move 1 · Raise the money. A business needs money before it can produce anything. It gets it from owners, who buy a share of it and get whatever is left at the end, or from lenders, who are paid an agreed amount first and must be repaid regardless. That money is capital. Deciding how much comes from each source is the financing decision.

Move 2 · Buy things that produce. Factories, machines, software, inventory, people, an acquisition. In your case, a camera, a rig, a subscription, a freelancer's week. This is the investment decision, and it is where value is actually created or destroyed.

Move 3 · Sell, and collect. The things you bought produce something customers pay for. Notice the two verbs: selling and collecting are different events, often separated by months, and the gap between them has to be funded. That is operations, and it is where most of a business's daily life happens.

Move 4 · Give back what is left. After paying suppliers, staff, lenders and the state, whatever remains belongs to the owners. Management either hands it over, or keeps it to reinvest in move 2. That is the payout decision.

Then the loop runs again, and again. A good business is one where each turn of the loop leaves more than it consumed. That sentence is the whole subject, and the rest of this book is about how to know whether it is true for a given company.

The first real idea: what a return is, and why money costs something

Take move 2 on its own. You spend 1 000 on a camera. It brings in an extra 400 of profit a year. The return is 400 divided by 1 000, so 40% a year. Simple, and it is the number everyone quotes.

Now the question almost nobody asks first: where did the 1 000 come from, and what did it want?

Three possibilities, and they are not the same:

• You borrowed it at 8% a year. Then the money has an explicit price: 80 a year, payable whether the camera works or not.
• You used your own savings, which were sitting in a fund earning 5%. Nobody sends you a bill, but you gave up 50 a year to do this. That forgone 50 is an opportunity cost, and it is every bit as real as the bank's 80.
• An investor put it in, expecting the kind of return people expect from a small creative business, which is a lot more than 5% because they might lose the lot. Call it 20%.

In all three cases the money had a price. In the third case the price is high precisely because the outcome is uncertain. This is the single most important idea in the chapter: capital is never free, and the riskier the use, the more it costs. The name for that price is the cost of capital.

And now the decision rule that governs everything a company does:

> Do it if the return is bigger than what the money costs. Do not do it if it is not.

The camera at 40% against money costing 8%, 5% or even 20% is an easy yes. But swap the numbers. A project returning 6% funded with capital costing 9% destroys value every year it runs, and it will still look like a success in a press release, because revenue went up, profit went up, and the business got bigger. Growth and value creation are different things, and confusing them is the most common and most expensive error in business.

The second real idea: time has a price too

So far everything happened in the same year. Real businesses do not work like that. You spend now and collect later, sometimes years later. So we need to compare money that arrives at different times, and that requires one more idea.

Would you rather have 100 today or 100 in a year? Today, obviously. But why exactly, because the reasons matter:

1. You can put it to work. 100 today, invested at 8%, is 108 in a year. So today's 100 is genuinely worth more than a future 100, and the gap is the return you could have earned.

2. Prices rise. In a year, 100 buys less than it does today.

3. The future one might not arrive. A promise is not cash. The less certain the promise, the less you should pay for it now.

Now flip it round, because this is the move the whole discipline is built on. If money earns 8% a year, how much do you need today to have 100 in a year? You need the amount that grows into 100:

amount × 1.08 = 100 so amount = 100 / 1.08 = 92.59

So a promise of 100 in one year is worth 92.59 today, at an 8% rate. Two years out, you divide twice: 100 / 1.08 / 1.08 = 85.73. Ten years out you divide ten times and get 46.32. That arithmetic, dividing by (1 + rate) once per year of waiting, is called discounting, and the answer is called the present value.

present value = future amount / (1 + rate) ^ number of years

That is the entire mechanism. There is nothing else hiding in it. The rate you divide by is the discount rate, and choosing it is where all the argument lives, because it carries both what the money could otherwise earn and how risky the promise is. A safe promise from a government gets a low rate and loses little value. A risky promise from a startup gets a high rate and loses most of it.

Put the two ideas together and you have valuation

You now have everything you need to say what a business is worth, and you have not been asked to accept a single thing on faith.

A business is a machine that produces cash flow in future years. Each of those future amounts is worth less than its face value today, and how much less depends on how far away it is and how risky it is. So:

> The value of a business is all the cash it will ever produce, with each year's amount pulled back to today.

Written down, that sentence is the equation everything else in this book serves:

Value = CF₁/(1+r) + CF₂/(1+r)² + CF₃/(1+r)³ + …

Two inputs. That is all. And each is a genuine fight:

• Which cash flow? Not profit, which is an accounting judgement about which period a sale belongs to. Cash. Getting from published accounts to real cash is chapters 3 to 5, and it is where most beginners go wrong.
• Which rate? The cost of capital, which depends on how risky this particular business is and on how it is funded. That is chapters 20 to 22.

A shortcut worth deriving, because you will use it constantly. Suppose a business produces the same amount forever: 150 a year, no growth, no end. Adding up infinitely many discounted amounts sounds hard. It is not, and here is why in one line.

If the rate is 10%, then any pot of money earns 10% a year. So what pot would throw off exactly 150 a year, forever? A pot of 1 500, because 10% of 1 500 is 150. A stream of 150 a year forever and a pot of 1 500 are the same thing. Therefore:

Value of a constant stream forever = annual amount / rate

Test it: 150 / 0.10 = 1 500. Now raise the required rate to 15%, because you decide the business is riskier. A pot throwing off 150 a year at 15% only needs to be 1 000. The business just lost a third of its value and nothing about the business changed. Only your view of its risk did.

That is the most important thing in this chapter after the loop. The number at the bottom of a valuation is not a fact about a company. It is a fact about a company and an opinion about risk, and the opinion is doing a great deal of the work.

Value and price are two different questions

Here is a distinction that separates people who understand finance from people who have memorised it, and it is Damodaran's central point.

Value is what a business is worth, given the cash it will produce, how fast that grows, and how risky it is. You estimate it with the equation above. It is an act of judgement about a business.

Price is what somebody will pay for it today. It is set by supply and demand, by mood, by how much money is looking for a home in that sector this year. You estimate it by looking at what similar businesses are changing hands for, which is called using a multiple.

Both are legitimate. Professionals do both. What is not legitimate is using the tools of one to answer the question of the other, and the classic version of that error is running a valuation, not liking the answer because it disagrees with the market, and quietly adjusting assumptions until it agrees. That is not valuation, it is reverse-engineering with extra steps.

The useful habit, and it is a habit you can start this week: when price and your value disagree, do not conclude that the market is stupid. Work out what the market must be assuming. If a company trades at a price that only makes sense if it grows 6% a year forever, and its market grows at 2%, you have converted a vague disagreement into a specific, checkable claim about market share. That move is worth more than any formula in this book, and it has a name you will meet in chapter 18.

Ten words you will meet everywhere, defined now

The complaint people have about finance is that everyone throws terms around as if they were obvious. So here they are, in plain language, before you need them. You are not expected to be able to use them yet. You are expected never to be ambushed by one again. Each has a chapter that teaches it properly, and clicking any dotted word tells you which.

• revenue · what the company sold. The top line. Neither cash nor profit.
• margin · how much of each euro of sales survives to a given line. A 40% gross margin means 40 cents of every euro is left after making the thing.
• cash flow · money actually moving in or out, as opposed to profit, which is an accounting judgement.
• equity and debt · the two kinds of money a business runs on. Lenders get paid first at an agreed rate; owners get whatever is left, which may be nothing or may be everything.
• cost of capital and WACC · what the money costs. WACC is just the blend of the two, weighted by how much of each the company uses.
• NPV · the value a project creates after paying for it. Positive, do it.
• IRR · the same decision expressed as a percentage return rather than an amount of money. Intuitive, and it has traps.
• ROIC · the return the business earns on the money tied up in it. Compare it with the cost of capital and you know, in one comparison, whether the business deserves to exist.
• reinvestment · cash put back in rather than paid out. Growth is bought with it, which is why growth is never free.
• terminal value · in a valuation, everything that happens after the years you forecast in detail. Usually most of the answer, which is why people argue about it.

Notice how many of these you have already used in this chapter without the label. That is the point. The ideas are not hard. The vocabulary is unfamiliar, and unfamiliar is a problem that reps solve.

Companies to know, and to actually go and look at

Finance is learned on real companies, not on symbols. Pick a handful now and follow them all year. When a concept arrives, ask what it looks like at these names. Everything below is public and free to read.

Pick one as your running company today and do not change it. Chapters 12, 19, 24 and 44 all build on the same company, and the whole point is that your understanding of it compounds. Choose something you can name a product of and would enjoy reading about. Avoid banks and insurers for now: their accounts are a different discipline.

Where to look: for a French listed company, the document d'enregistrement universel on its investor relations page. For a US one, the 10-K on sec.gov/edgar. Both are free, and the second half of both is where the real information is.

Why your background makes this easier than it looks

One last thing, because it changes how you should spend your hours.

Three years of engineering means the mathematics ahead of you is not the obstacle. Discounting is a geometric series. Portfolio theory, in chapter 38, is a constrained quadratic optimisation. Black-Scholes, in chapter 42, reduces to the heat equation. You have solved harder things than any of these under exam conditions.

Your actual gap is three specific things, and none of them is intelligence:

1. Vocabulary. Several hundred terms that everyone uses without defining. Pure memory, solved by reps and by the card deck in this app.

2. Accounting. A set of conventions decided by committees, not derived from anything. It has to be learned rather than worked out, which is a different and more irritating kind of effort.

3. Institutional knowledge. Who the players are, what a rating agency does, why a covenant matters. It accumulates from reading real filings, which is exactly why you pick a company today.

So do not spend your time on the maths. Spend it on the words, the accounts and the reading. And every time a chapter ends, do the three things that actually build memory rather than the feeling of it: retrieve it from a blank page, say it out loud, and build it in a spreadsheet.

What a company owns, and who has a claim on it

The balance sheet is a photograph taken at one instant: everything the business uses on one side, everyone who paid for it on the other. It balances by construction, and once you see why, half of accounting stops being arbitrary.

The one sentence that never breaks

Take your own business again. Write down everything it controls: the laptop, the camera, the money three clients owe you, whatever is in the bank. Now write down everything it owes: an unpaid supplier invoice, the balance on a loan, tax you have collected and not yet handed over.

The difference between those two lists is yours. If you sold everything for exactly what the books say it is worth and paid off everyone you owe, what is left is the owners' share. Which gives:

what you control − what you owe = what is yours

and rearranged, the sentence every accountant on earth writes first:

Assets = Liabilities + Equity

This is not a rule someone imposed. It is an identity, and here is the reason it cannot break: every euro of stuff the business has was paid for by somebody. Either a lender or supplier funded it, in which case it sits under liabilities, or an owner did, in which case it sits under equity. There is no third source of money. So the two sides are the same pile counted twice: once by what it became, once by who provided it.

Once you hold that, the balance sheet stops being a list to memorise. Every time you are unsure which side something goes on, ask: is this a thing the business uses, or is it a claim someone has on the business?

A photograph, not a film

The balance sheet is dated. It says, in effect, 31 December, 23:59. It is a still image of a moving thing.

That matters more than it sounds. A retailer's balance sheet on 31 December, just after Christmas, looks nothing like the same retailer on 30 September, when the warehouses are full of stock bought for the season and not yet sold. Neither picture is wrong; both are one frame from a film. When you compare two companies, check they closed their books at similar points in their own cycle, and when a number looks strange, ask whether you are looking at the year's most flattering day. Companies choose their year end, and they do not choose it at random.

The next chapter covers the income statement, which is the film: what happened over a period rather than what is true at an instant. Holding that difference is most of what beginners are missing when accounting feels confusing.

The left side: what the business uses

Assets are listed by how quickly they turn into cash. Two blocks.

current assets, meaning within a year:

• Cash and short-term deposits. What it says.
• receivables · money customers owe you for work already delivered. You made the sale, you have not been paid. Very common, entirely normal, and the cause of more small-company deaths than any other single line.
• inventory · goods bought or made and not yet sold. For your studio, near zero. For a supermarket, enormous.
• Prepaid expenses · things paid for in advance, like a year of software billed up front. You have paid, and you are owed the service.

Non-current assets, meaning the long-lived stuff:

• PP&E · buildings, machines, vehicles, fit-out. Shown at what they cost minus the wear charged so far, which is called depreciation and gets its own treatment in chapter 3.
• intangible assets · software, licences, patents, and brands acquired in a deal. Note that word. Under normal accounting, a brand a company built itself does not appear on its own balance sheet at all. LVMH's own Louis Vuitton brand is largely invisible in its accounts; brands it bought are not. That single quirk explains a lot of apparently strange balance sheets.
• goodwill · what a buyer paid above the fair value of the identifiable things it bought. A receipt for a past acquisition. You cannot sell it, and when the acquisition disappoints, it gets written off in one large non-cash hit.
• Investments in other companies, and deferred tax assets, which we will leave for later.

The right side: who has a claim

The same split, by when it is due.

current liabilities:

• payables · what you owe suppliers for things already delivered. Look at it properly for a second: your supplier has funded your business, interest-free, for however long the terms run. Payables are a genuine source of financing, and chapter 9 shows how much.
• Short-term debt and the current portion of long-term loans.
• Accrued expenses · costs incurred but not yet invoiced or paid, such as salaries earned this month and paid next.
• Deferred revenue · a strange and important one. A customer paid you up front for something you have not delivered. You have the cash and you owe them the work, so it is a liability, not revenue. Any subscription business carries a lot of it.

Non-current liabilities: long-term borrowings, pension obligations, and provisions for things likely to cost money later.

Equity, which is the residual:

• share capital and share premium · what owners paid in when shares were issued.
• retained earnings · every profit ever made, minus every dividend ever paid.
• Other reserves, including currency translation and revaluations.

And now the most common misconception in beginner accounting, so read this twice. Retained earnings is not money in the bank. A company can show 4bn of retained earnings and 30m of cash. The 4bn describes profits it earned and did not distribute; those profits were long ago converted into machines, stock, acquisitions and receivables. Retained earnings tells you the history of the owners' claim, cash tells you what is in the account this morning, and confusing them is the single most reliable way to get an exam question wrong.

Book value and market value are different things

Here is a fact that confuses people for years, so let us kill it now.

The balance sheet records what things cost, less wear, not what they are worth. A building bought in 1994 sits at its 1994 price minus thirty years of depreciation, even if it is now in the middle of Paris and worth twenty times that. A brand built over decades is not there at all. Research that produced a drug is usually expensed as it happens, so it leaves no asset behind.

So the book value of equity, meaning assets minus liabilities as the accounts state them, is a historical record. The market value of equity, meaning the share price times the number of shares, is what investors will pay today for the future the business will produce.

They are almost never the same, and the gap tells you what kind of business you are looking at:

• A bank trades near book value, because its assets are mostly financial instruments carried at something close to market prices. Book value is meaningful there, which is why bank analysts use it.
• A luxury house or a software company trades at a large multiple of book value, because the things that make it valuable, brands, customer relationships, code, are barely on the balance sheet.
• A heavy industrial sits somewhere in between: real assets, recorded at cost, that genuinely do produce the cash.

The practical rule: do not use book value to judge whether a company is cheap unless you are looking at a financial institution. Chapter 17 gives you the multiples that are actually used, and it explains this properly. For now, know that when a company says its equity is 2bn and the market says it is 40bn, nobody is lying: they are answering different questions.

How an analyst re-cuts it, and why emlyon will assume you can

Accountants sort a balance sheet by liquidity. Analysts re-sort it by economic function, and this reorganisation is the signature of the French school. Vernimmen opens with it and your professors will treat it as known.

The question the re-cut answers is simple and better: how much capital does this business actually tie up to operate, and who funded it?

Two moves.

One · gather what the business needs to run. It needs its long-lived assets. It also needs to fund the gap between paying suppliers and being paid by customers, which is receivables plus inventory minus payables, called the working capital requirement and the whole subject of chapter 9.

capital employed = fixed assets + working capital

Two · see who funded it. Not the accountant's split, but the economic one: lenders, net of any cash the company is sitting on, and owners.

financed by = net debt + equity where net debt = financial debt − cash

And the two are equal, because they must be: it is the same identity, rearranged.

Why bother? Because it isolates the operating business from how it was funded, and every serious tool later depends on that separation. The return on capital in chapter 8, the cost of capital in chapter 21, the enterprise value in chapter 18: all of them assume you can look at a balance sheet and see capital employed on one side and its funding on the other. Get comfortable with this now and four later chapters become easy.

What you can see in sixty seconds

With nothing but a balance sheet, you can already say useful things. Get into the habit of asking these four in order.

1 · How is it funded? Compare net debt with equity. A company with 110 of net debt against 170 of equity is moderately geared. One with 800 against 170 is a different animal, and everything about its risk follows from that.

2 · What could go wrong in the next twelve months? Compare current assets with current liabilities. If short-term obligations exceed the things turning into cash within the year, the company depends on refinancing or on the bank staying friendly. That dependence is fine until the day it is not.

3 · What kind of business is this? A balance sheet dominated by PP&E is a heavy industrial: it needs a lot of capital to produce a euro of sales. One dominated by receivables and inventory is a trading or manufacturing business where the working capital cycle is the thing to watch. One that is mostly goodwill has grown by acquisition, and you should ask how well those acquisitions have gone.

4 · Is anything odd? Goodwill larger than equity means one big write-down away from wiping out the owners' stake. Inventory growing much faster than the business means product nobody wanted. A pension deficit sitting quietly in non-current liabilities is a real claim on future cash.

None of this needs a formula. It is reading, and it comes from doing it twenty times rather than from a technique.

How profit is manufactured

The income statement is the film the balance sheet is a still of: what the company earned over a period and what it consumed to earn it. Each line belongs to a different set of people, and knowing which is what makes half of valuation obvious later.

The film, not the photograph

Chapter 2 gave you a still image: what the company controls and who has a claim, at one instant. The income statement covers what happened between two of those instants. It answers: over this year, what did we earn, what did it cost us, and what was left?

It has one structure and you should be able to write it from memory tonight, because every model you will ever build is this cascade with forecasts in it:

Revenue

− Cost of goods sold

= Gross profit

− Operating expenses (SG&A, R&D, other)

− Depreciation and amortisation

= EBIT, also called operating profit

− Interest

= Pre-tax profit

− Tax

= Net income

Read down it once and notice the shape: you start with everything the customer paid, and you subtract, in order, the people who have a claim on it. First the cost of making the thing. Then the cost of running the company. Then the wear on the assets. What is left at EBIT is the profit the business produced. Then lenders take their interest, then the state takes its tax, and whatever survives belongs to the owners.

That order is not arbitrary and it is not just accounting convention. It is a queue of claimants, and it explains something you will otherwise have to memorise later.

Each line belongs to different people

This is the idea to take from the chapter, and it is worth more than the definitions.

gross profit belongs to the product. Revenue minus what it cost to make the thing sold. It tells you about pricing power and unit economics. A luxury house runs a gross margin around 65-70%; a supermarket around 20-25%. Neither is better, they are different machines.

EBIT belongs to everyone who funded the business, lenders and owners together, because it is measured before any of them has been paid. That is exactly why, in chapter 17, the valuation multiples that use EBIT and EBITDA are paired with the value of the whole business rather than the value of the shares.

net income belongs to owners alone, because interest has gone to lenders and tax to the state. Which is exactly why the price-to-earnings ratio, the most quoted number in markets, is a shareholder measure.

So the income statement is a ladder from everybody's money down to the owners' money. Hold that, and the enterprise-versus-equity distinction that trips up most candidates in interviews becomes something you can derive rather than recall.

EBITDA: the most used and most abused number in finance

EBITDA = EBIT + depreciation + amortisation

Why anyone bothers: depreciation and amortisation are accounting allocations of money spent in earlier years, not cash leaving this year. Adding them back gives a rough measure of what the operations generated, and it makes two companies comparable even when one has new machines and the other old ones, or when they depreciate over different lives. That is genuinely useful, and it is why bankers speak in EBITDA all day.

Now the three specific ways it lies, and you should be able to recite them:

One · it ignores capital spending. The machines really do wear out and really do have to be replaced. A business with EBITDA of 100 that must spend 90 a year on equipment is nothing like a business with EBITDA of 100 that spends 10. EBITDA says they are identical.

Two · it ignores working capital. A fast-growing company can produce plenty of EBITDA while every euro of it is absorbed by rising receivables and stock. Chapter 9 shows this happening.

Three · it ignores interest and tax, which are real cash costs, especially for a company carrying debt.

And a fourth, subtler point: EBITDA is not defined by any accounting standard. Companies choose their own adjustments, so "adjusted EBITDA" can quietly exclude share-based pay, restructuring that happens every year, and start-up costs for projects that never start. Chapter 11 teaches you to read that bridge line by line. Charlie Munger called it "bullshit earnings", which is too strong, but the instinct behind it is right: use EBITDA for comparison, never as a measure of what a business actually generates.

Accrual accounting, and why profit is not cash

Everything above rests on one convention, and it is the source of nearly all beginner confusion.

Revenue is recorded when it is earned, meaning when the goods are delivered or the service performed, not when the customer pays. Costs are recorded when they are incurred and matched against the revenue they helped produce, not when the invoice clears the bank. That is accrual accounting, and it exists for a good reason: it tells you what a period actually achieved, rather than what happened to land in the bank account during it.

Three consequences you should be able to state instantly:

• You deliver a job in March and are paid in May. Revenue and profit belong to March. Cash arrives in May. In between, the balance sheet carries a receivable.
• A customer pays in January for a year of service. Cash arrives in January, revenue is recognised month by month across the year, and the unearned part sits as a liability.
• You buy a 120 machine with a four-year life. Cash out 120 today, and the income statement is charged 30 a year for four years as depreciation.

In every case the timing of profit and the timing of cash are different. That is not a defect. It is the entire reason a third statement exists, and chapter 4 is that statement.

The move an interviewer makes: change one thing

Once you have the cascade, the standard test is to change one item and ask what happens all the way down. It looks like a trick and it is really a check that you understand the queue.

Depreciation rises by 10, tax rate 25%.

• EBIT falls by 10, because depreciation sits above it.
• Pre-tax profit falls by 10.
• Tax falls by 2.5, because you are taxed on a smaller profit.
• Net income falls by 7.5, not by 10.

That last step is the one that separates people. Any deductible cost of X reduces profit after tax by X × (1 − tax rate), because the state shares the pain. The saving, X times the tax rate, is called the tax shield, and it comes back with force in chapter 26 when you learn why debt is attractive: interest is deductible and dividends are not.

And EBITDA? Unchanged at its old level, because depreciation is added straight back. Which tells you something about human nature: a management team that wants a bad year to look better will talk about EBITDA.

Practise the pattern with other items until it is reflex:

• Interest rises by 40. EBIT unchanged, EBITDA unchanged, net income down 30 at a 25% rate. Anything below EBIT never touches operating profit, which is exactly why leverage changes P/E and does not change EV/EBITDA.
• A supplier price rise of 60 in COGS. Gross profit −60, EBIT −60, EBITDA −60, net income −45. It hits everything, because it is above every line.

Below EBIT: the tail where the truth gets muddy

Between EBIT and net income sits a stretch that distorts reported profit constantly, and where analysts do most of their adjusting.

• Interest, and interest income if the company holds cash.
• Restructuring charges · redundancy and site closure costs. Legitimately one-off, unless they appear every year, in which case they are an operating cost with better branding.
• impairments · writing down goodwill or an asset that is no longer worth its carrying value. Large, non-cash, and usually an admission that an acquisition disappointed.
• Gains or losses on disposals · selling a building at a profit is not a sign the core business improved.
• Discontinued operations · a business being sold, reported separately so the continuing business is comparable.

The professional habit is normalisation: strip out what will not repeat and say clearly what you stripped and why. Chapter 11 gives you the discipline properly, but start the habit now, and be even-handed about it. Removing one-off costs while keeping one-off gains is how you flatter a company by accident, and it is a real and common failure of junior analysis.

FR ↔ EN, because your professors will switch mid-sentence

compte de résultat = income statement · chiffre d'affaires = revenue · marge brute = gross profit · résultat d'exploitation = EBIT · excédent brut d'exploitation (EBE) ≈ EBITDA · dotations aux amortissements = depreciation and amortisation · charges financières = interest expense · résultat net = net income.

Where the money actually went

Profit is an opinion formed by accounting rules. Cash is a fact you can check at the bank. This statement is the reconciliation between the two, and it is where companies get caught.

Why this statement has to exist

Chapter 3 ended on a problem. Because of accrual accounting, profit is recorded when a sale is earned and costs when they are incurred, regardless of when money moves. So the profit figure and the bank balance are answering different questions, and both are legitimate.

Which means a company can be:

• Profitable and out of money. It sold plenty on credit, customers have not paid, and the wages are due on Friday. This is the most common way a healthy-looking small business dies, and it kills good businesses more often than bad ones, because growth makes it worse.
• Loss-making and awash with cash. It took a large non-cash write-down this year while customers keep paying on time.

Neither statement is lying. They measure different things. The cash flow statement exists to reconcile them, and it is the one a serious investor reads first, because profit involves judgement at a dozen points and cash mostly does not.

Three sections, three questions

1 · Cash from operations · does the core business actually generate money?

This is the important one. In real filings it is almost always built the indirect method way, which starts from profit and works towards cash:

Net income

+ depreciation, amortisation and other non-cash charges

− increase in working capital (or + a decrease)

= cash from operations

The logic in one sentence: start with accounting profit, add back everything you subtracted that never actually left, then correct for the timing gap between profit and cash, which lives entirely in receivables, inventory and payables.

2 · Cash from investing · what did we spend to stay alive and to grow?

Mostly capex, plus acquisitions and purchases or sales of investments. Nearly always negative for a healthy growing company: a business that is not spending on its asset base is either capital-light or quietly shrinking.

3 · Cash from financing · who funded us, and who got paid?

Debt drawn and repaid, shares issued or bought back, dividends paid.

CFO + CFI + CFF = the change in cash

And that change must tie to the movement in the cash line on the balance sheet. That tie is not a formality: it is the first check you will build into every model you ever make, and if it does not hold, the model is wrong somewhere.

The sign rule, and the intuition behind it

This is where marks are lost, so get the intuition rather than memorising a table.

An increase in an operating asset uses cash.

Receivables up means you sold and were not paid: the sale is in profit, the money is not in the bank, so you must subtract the difference. Inventory up means you spent money on stock that is sitting in a warehouse: cash out, no profit yet.

An increase in an operating liability provides cash.

Payables up means you received goods and have not paid for them yet: the cost is in profit, the money is still in your account.

The mnemonic if you want one: asset up, cash down. Liability up, cash up. But the sentence to actually hold is: working capital is the gap between the profit story and the cash story, so the cash statement corrects for the change in that gap.

Note the word change. It is not the level of receivables that appears here, it is the movement over the year. A company with enormous but stable receivables has no cash effect at all.

Free cash flow: the number that actually matters

free cash flow = cash from operations − capital expenditure

That is what remains after the business has generated cash and spent what it needed to keep running. It is what can be used to repay debt, pay dividends, buy back shares or make acquisitions. free cash flow is, in a real sense, the point of the whole exercise: chapter 13 defines it with more precision and then discounts it, and that is a valuation.

Two warnings, both practical.

Capex is not one thing. Maintenance capex keeps capacity where it is; growth capex adds to it. Companies rarely split them and the split matters enormously, because a business spending heavily to grow is in a different position from one spending heavily to stand still. A rough test: compare capex with depreciation. Around 1.0 suggests steady state. Well above 1.0 suggests growth investment. Persistently well below 1.0 suggests a company harvesting its asset base, which flatters profit today and produces a cliff later.

"Free cash flow" is used loosely. Some people mean CFO minus capex, some subtract dividends, some mean something else entirely. When someone quotes it, ask which. That question alone marks you out as someone who has built a model rather than read about one.

What this statement lets you catch

Four patterns. Learn them now and you will use them for the rest of your career, because they are how earnings quality is judged in practice.

1 · Profit rising while cash from operations falls. The most important red flag there is. It usually means receivables are ballooning: revenue is being booked to customers who are slow, or unwilling, or in the worst case not real. Chapter 11 gives you the full checklist.

2 · Cash from operations propped up by stretching payables. Delaying supplier payment produces cash this year and reverses next. A rising payables balance alongside a fully drawn credit facility is not clever working capital management, it is a company that cannot pay.

3 · A persistent gap between EBITDA and cash from operations. Compute cash conversion, CFO over EBITDA, for five years. A mature business should convert roughly 70 to 95 percent. A falling trend means profit is not becoming money, and there is always a reason.

4 · Capex well below depreciation for years. The asset base is being run down. Reported profit looks fine because the depreciation charge is based on old, cheap assets, and the catch-up spending arrives later, usually at the worst moment.

None of these require a model. They require reading three numbers over five years, which takes ten minutes and is the single highest-return habit in this entire book.

The three statements are one machine

You have met three documents. They are three views of one system, wired together by three connections. Once you can trace a change through all three and watch the balance sheet still balance, you have the foundation the whole rest of the book stands on.

Three documents, one system

Everything so far has been preparation for this chapter. The balance sheet, the income statement and the cash flow statement are not three separate reports that happen to be published together. They are three views of the same machine, and they are wired together by exactly three connections.

Wire 1 · net income flows into equity.

closing retained earnings = opening retained earnings + net income − dividends

The bottom of the income statement lands on the balance sheet. This is what makes profit accumulate into the owners' claim.

Wire 2 · net income starts the cash flow statement.

The indirect method begins at net income and adjusts its way to cash. So the same number enters two statements, doing two different jobs.

Wire 3 · the change in cash lands on the balance sheet.

closing cash = opening cash + net change in cash

That is the whole wiring. Three connections, and once they are made and every other line has something driving it, the system is live: change one assumption anywhere and everything updates, and the balance sheet still balances. When it stops balancing, one of the wires is cut, and chapter 40 turns that into a modelling discipline.

The second-order wiring, which matters just as much

Below the three main wires, the same items appear in more than one place, and the pattern is always the same: one economic event, several accounting consequences.

• Depreciation · an expense on the income statement, an add-back on the cash flow statement, and a reduction in net PP&E on the balance sheet. One event, three appearances.
• Capex · cash out in investing, an increase in PP&E on the balance sheet, and nothing at all on the income statement today. It reaches profit later, as depreciation.
• Working capital · the balance sheet holds the levels of receivables, inventory and payables; the cash flow statement carries the change in those levels.
• Debt · interest on the income statement, principal movements in financing, and the outstanding balance on the balance sheet.
• Dividends · out through financing on the cash flow statement, and out of retained earnings on the balance sheet. Never on the income statement, because a dividend is not a cost of doing business, it is a distribution of what is left.

That last one catches people constantly, so say it once out loud: a dividend never appears on the income statement.

The question you will be asked, and the format that answers it

"Depreciation increases by ten. Walk me through the three statements." It is the most asked technical question in finance, in every interview, at every firm, every year. It is asked because it cannot be bluffed: either you understand the wiring or you do not.

The format never changes, and the order is the answer:

> Income statement first. What happens to operating profit, then to net income, remembering the tax effect.

> Cash flow statement second. Start at net income, add back anything non-cash, state the actual movement in cash.

> Balance sheet third. The asset side, then the liabilities and equity side, and then say the words "and it balances."

Say the three statements in that order every time, even when the change is trivial. It signals that you are following a system rather than reasoning from scratch, and it stops you from forgetting the tax effect, which is where most candidates fall over.

Debugging: when it does not balance

You will spend real hours of your life on a model whose balance sheet is out by some number. There is a shortcut, and almost nobody teaches it.

Look at the size of the gap first. The magnitude usually names the culprit.

• Out by exactly the dividend? The dividend was taken out of cash in financing but never deducted from retained earnings, or the reverse.
• Out by exactly the depreciation? It was charged on the income statement but not deducted from PP&E, or it was added back on the cash flow and also removed somewhere else.
• Out by exactly net income? Wire 1 is broken: profit is not flowing into retained earnings at all.
• Out by twice something? It is being counted twice, somewhere.
• Out by a growing amount each year? The error is in a flow that accumulates, so look at the roll-forward schedules rather than at a single year.

The three usual suspects, in order of frequency: net income not flowing into retained earnings · depreciation double-counted · dividends recorded on only one of the two statements.

That habit, reading the size of the difference before hunting through formulas, turns a two-hour debugging session into a two-minute one, and it is the reason models keep a visible check row rather than a hidden one.

Why this chapter is the foundation of everything after it

It would be reasonable to think of this as an accounting technicality. It is not, for three reasons.

One · every valuation is a forecast of these three statements. In chapter 19 you will project revenue, margins, capital spending and working capital, and pull free cash flow out of the result. If the wiring in your head is loose, you will build a model that runs but whose numbers do not describe a coherent company, and you will not know which assumption is lying to you.

Two · the balance check is your only honest test. A model that balances is not necessarily right, but a model that does not balance is definitely wrong. It is the only automatic verification you get, which is why professionals leave it visible and conditionally formatted, in red, forever.

Three · it is the entry ticket. Fluency here is the thing every technical interview screens for first, because it takes months to fake and minutes to test. Get it now, keep it warm by re-deriving case 1 once a week, and that screen stops being something you worry about.

The grammar you write all of it in

In finance a spreadsheet is not a tool, it is the language you are read in. The logic will be easy for you. The conventions are unwritten, strictly enforced, and they are what a model is judged on before anyone looks at your answer.

Why the conventions matter more than the formulas

Everything you produce for the next year comes out in a spreadsheet: your valuation, your model, your assessment-centre test. Your engineering background means the logic is not where you will struggle. What you need is the convention, and the reason is not aesthetic.

A model is a document that other people have to argue with. A managing director opening your file at eleven at night wants to find your revenue growth assumption in five seconds, change it, and see the answer update everywhere. If they cannot, they do not trust the file, and a file that is not trusted is worthless no matter how correct it is.

So the standard to build to is not "it works". It is: can a stranger audit this in five minutes without asking me anything? Everything below follows from that single question.

The five laws

One · colour code by input type. This is not optional.

• Blue · a hardcoded input. A number you typed, an assumption.
• Black · a formula calculated on this sheet.
• Green · a link to another sheet in the same workbook.
• Red · a link to another file. Avoid entirely if you can.

Anyone opening your model scans for blue, because blue is the list of things to argue with. A file where assumptions hide inside black formulas is considered untrustworthy, and rightly, because it is.

Two · never hardcode a number inside a formula. =B12*1.08 is the crime. The 8% belongs in its own labelled cell. If a number could ever change, it lives somewhere with a label next to it.

Three · one row, one formula, dragged across. Every column in a row should be structurally identical, so the whole row can be checked at a glance. Inconsistent formulas within a row are the most common source of genuine errors in real models, because the eye cannot see them.

Four · build checks and leave them visible. The balance sheet tie, the cash flow tie, a sum-of-parts tie. Format them to turn red when they break. Hiding a check to make the model look clean is how a broken model reaches a client.

Five · structure it: assumptions, then calculations, then outputs. Clearly banded or on separate named sheets. Someone should never have to hunt.

These five are not a house style. They are the industry's, and following them is the fastest way to look like you have done this before.

The functions that actually get used

The list is short on purpose. Ninety percent of financial modelling uses about fifteen functions.

Arithmetic and logic · SUM, SUMPRODUCT, IF, AND, OR, IFERROR, MIN, MAX, ROUND.

MIN and MAX matter more than they look: they are how you build a debt sweep that never repays more than is outstanding, and a cash balance that never goes negative.

Lookups · INDEX combined with MATCH, or XLOOKUP if your version has it.

Learn INDEX/MATCH rather than VLOOKUP, and know why: it can look to the left, it does not break when someone inserts a column, it is faster on large sets, and it separates where to look from what to find. Using it in a modelling test is a small but real competence signal.

Finance · NPV, IRR, XNPV, XIRR, PMT, RATE.

Note XNPV and XIRR take actual dates rather than assuming even periods, which is what you want whenever cash flows are irregular, which is most of the time in the real world.

Dates · EOMONTH, EDATE, YEARFRAC.

Tools rather than functions · data table for sensitivities, goal seek for solving backwards, and CHOOSE for scenario switching.

That is the whole toolkit for a valuation model. If you find yourself reaching for something exotic, stop and ask whether you are being clever at the expense of being auditable.

Keyboard, because speed is graded

In a modelling test, mouse use is a tell. It is not that speed matters for its own sake; it is that people who have built many models do not reach for the mouse, and assessors know it.

The core set, and it is small:

• F2 edit the cell · F4 toggle absolute and relative references, the most-pressed key in modelling · Alt = autosum
• Ctrl + arrow jump to the edge of a block · Ctrl + Shift + arrow select to the edge
• Ctrl + 1 format cells · Alt H O I autofit column width
• Ctrl + [ trace precedents, meaning jump to the cells feeding this one, which is how you audit someone else's file
• F9 recalculate · Alt A S S sort · Alt + N + V pivot table

Twenty minutes a day for a week with the mouse physically unplugged and these become permanent. It is one of the few things in this book where mechanical practice, rather than understanding, is the whole method.

Sensitivity is the deliverable, not the answer

This is a habit rather than a technique, and it separates analysis from arithmetic.

No single-point answer is ever the deliverable. A valuation ships with a grid of value against the two assumptions that actually move it. A project appraisal ships with the break-even level of the input you are least sure about. A budget ships with a downside case.

The reason is not modesty. It is that a number without a range implies a precision you do not have, and everyone senior enough to matter knows it. Presenting "the value is 47.3" invites the question "how confident are you?", to which there is no good answer. Presenting "41 to 58, driven mainly by the discount rate, and here is the grid" answers it before it is asked.

Mechanically, a two-variable data table takes about fifteen seconds once your model is built properly, which is one more reason for the five laws: a model with buried hardcodes cannot be sensitised at all without surgery.

The other half of the habit is anti-fragile structure. Before you finish, ask: if my boss changes revenue growth by two points at ten at night, does the whole model update, or do I have to hunt? Build for the change you know is coming.

Making statements comparable

Absolute numbers tell you nothing. Common-size and trend analysis turn a pile of euros into a shape you can compare across years and across companies.

A company reports revenue of 4.2bn. Is that good? The question is meaningless. Analysis begins the moment you convert absolute numbers into ratios, percentages and trends, because only then can you compare: against last year, against a competitor, against the sector.

The three lenses, applied in this order

1 · Vertical analysis (common-size). Restate every income statement line as a percentage of revenue, and every balance sheet line as a percentage of total assets. Suddenly a 4.2bn company and a 380m company are directly comparable. What you are looking at is shape: a 70% gross margin software business and a 22% gross margin distributor are different animals, and the common-size statement says so immediately.

2 · Horizontal analysis (trend). Track each line over 3 to 5 years, indexed to 100 in the first year, and compute the growth rate of each. What matters is not any single level but the divergence between lines. Revenue +9% while receivables +34%: that gap is the story. Revenue +9% while SG&A +21%: that is operating leverage going the wrong way.

3 · Cross-sectional (peers). The same ratios for 4 to 6 comparable companies. This is where you learn what "normal" is in this industry, and normal is the only benchmark that means anything. A 4% net margin is catastrophic in software and excellent in grocery retail.

The discipline that separates analysis from arithmetic

Ratios do not produce conclusions. They produce questions. The workflow is always:

> observe a number → compare it to the right benchmark → notice a divergence → form a hypothesis → go find the evidence in the notes to the accounts.

The notes are where the answers live, and almost nobody reads them. That is your edge.

The starter set of ratios (each gets its own lesson, this is the map)

• Profitability: gross margin, EBITDA margin, EBIT margin, net margin, ROE, ROCE/ROIC.
• Efficiency: asset turnover, DSO, DIO, DPO, cash conversion cycle.
• Leverage/solvency: net debt/EBITDA, gearing, interest coverage, debt/capital.
• Liquidity: current ratio, quick ratio.
• Cash quality: CFO/EBITDA, FCF conversion, capex/D&A.

Two traps that catch students every single time

1. Comparing across accounting standards. IFRS versus US GAAP differ on inventory (LIFO exists in the US, is banned under IFRS), on development-cost capitalisation, on revaluation of fixed assets. Since IFRS 16 (2019) all leases sit on the balance sheet, which inflated debt and EBITDA everywhere at once: comparing a pre- and post-IFRS 16 year without adjusting is a false conclusion, and it still catches people.

2. Averaging stocks against flows. ROE uses net income (a flow, over the year) over equity (a stock, at a point in time). Use average equity when the balance sheet moved a lot, and say that you did.

FR ↔ EN

analyse financière = financial analysis · en pourcentage du chiffre d'affaires = common-size · rentabilité économique = ROCE · rentabilité financière = ROE · seuil de rentabilité = break-even point.

Profitability: ROE, ROCE and DuPont

Margin tells you how profitable a sale is. Return on capital tells you whether the business deserves to exist. Only one of them drives value.

There are two families of profitability metric and confusing them is expensive.

Margins measure profit per euro of sales: gross, EBITDA, EBIT, net. They tell you about pricing power and cost structure.

Returns on capital measure profit per euro of capital invested: ROE, ROCE, ROIC. They tell you whether the business creates value. This is the family that matters, because value creation has exactly one definition:

Value is created when ROIC > WACC

A business can have a wonderful margin and destroy value, if it needs an enormous asset base to produce it. And a thin-margin business can be a superb one if it turns its capital over fast enough. That is the whole insight, and it is what the DuPont decomposition makes visible.

The definitions, precisely (interviewers test the precision, not the concept)

ROE = Net income / Shareholders' equity

ROCE = EBIT / Capital employed (capital employed = fixed assets + working capital)

ROIC = NOPAT / Invested capital (NOPAT = EBIT × (1 − tax rate))

ROE is an equity return: it is after interest, so it is contaminated by leverage. ROCE and ROIC are whole-firm returns: pre-financing, so they measure the operating business itself. When you want to judge the quality of a business, use ROIC. When you want to judge the return to a shareholder, use ROE. Never use ROE to compare two companies with different capital structures without decomposing it first.

The DuPont decomposition (this is the tool)

Three-step:

ROE = Net margin × Asset turnover × Financial leverage

= (NI/Revenue) × (Revenue/Assets) × (Assets/Equity)

Five-step, which is what you actually want because it separates operations from financing and tax:

ROE = Operating margin × Asset turnover × Interest burden × Tax burden × Leverage

= (EBIT/Rev) × (Rev/Assets) × (EBT/EBIT) × (NI/EBT) × (Assets/Equity)

Now a 20% ROE has an anatomy. Company A: 15% margin × 0.9 turnover × 1.5 leverage. Company B: 3% margin × 2.5 turnover × 2.7 leverage. Same ROE, wildly different risk. B's return depends on both high turnover and high leverage; a small demand shock and it collapses. DuPont turns one number into a diagnosis.

ROIC and growth: the equation you will use all summer

Growth in operating income = ROIC × Reinvestment rate

This is the single most useful identity in valuation. Growth is not free and it is not an assumption you get to make: it is bought with reinvested capital, at the efficiency your ROIC allows. A company wanting 9% growth with a 15% ROIC must reinvest 60% of its NOPAT. If your DCF assumes 9% growth and 20% reinvestment, your model is internally inconsistent and any decent interviewer will find it in ten seconds.

A warning about ROE

ROE can be raised by buying back stock (equity shrinks), by taking on debt, or by writing down assets. None of those create value. This is why ROE is the favourite metric of managements with bad businesses, and why ROIC is the one to lead with.

FR ↔ EN

rentabilité économique (ROCE) = return on capital employed · rentabilité financière (ROE) = return on equity · effet de levier = leverage effect · résultat opérationnel après impôt = NOPAT · taux de réinvestissement = reinvestment rate.

Working capital and the cash cycle

The most common way a growing, profitable company dies. And the lever you can actually pull as an operator.

Working capital is the cash trapped in the gap between paying for things and getting paid for them. It is the most operational subject in finance and the one that will matter most to you as someone who runs a business.

Working capital requirement (BFR) = Receivables + Inventory − Payables

The cash conversion cycle, in days

DSO = Receivables / Revenue × 365 days to get paid by customers

DIO = Inventory / COGS × 365 days stock sits before it sells

DPO = Payables / COGS × 365 days you take to pay suppliers

Cash conversion cycle (CCC) = DSO + DIO − DPO

That number is how many days of operating cash the business must finance itself. A CCC of 60 days means every euro of revenue growth requires roughly 60 days of that revenue in additional funding. Grow fast enough and you run out of money while reporting record profits. This is exactly how healthy-looking companies die, and it is the reason "profitable" and "solvent" are different words.

Negative working capital: the best business model quirk in finance

Some businesses collect before they pay: supermarkets (customers pay instantly, suppliers wait 60 days), subscription software (annual prepayment), Amazon in its retail years. Their CCC is negative, which means growth generates cash instead of consuming it. They are self-funding growth machines. When you see negative working capital, stop and understand why: it is usually the most durable advantage on the balance sheet.

How it enters valuation

In a DCF, free cash flow subtracts the change in working capital. Model it as days (DSO, DIO, DPO) driven off revenue and COGS, never as a flat percentage plugged in, because the whole point is that it scales with activity. In an LBO, working capital release is one of the first sources of cash a sponsor engineers in year one.

The operator's levers, in order of how quickly they work

1. DSO down: invoice on the day of delivery, deposits up front, automated chasing, penalty terms that are actually enforced. Fastest and cheapest lever there is.

2. DPO up: negotiate longer terms. Free financing, but stretch too far and you are financing yourself off suppliers who will eventually reprice you.

3. DIO down: better forecasting, fewer SKUs, drop-shipping. Slowest but structurally the most valuable.

The trap in reading DPO

A rising DPO looks like great cash management and is sometimes a liquidity crisis in disguise: a company that cannot pay simply does not pay. Always read DPO next to the cash balance, the revolver draw, and the trend. Rising DPO plus a drawn revolver is a red flag, not an achievement.

FR ↔ EN

BFR (besoin en fonds de roulement) = working capital requirement · délai clients = DSO · délai fournisseurs = DPO · rotation des stocks = inventory turnover · fonds de roulement = net working capital in the French balance sheet sense.

Leverage, coverage and credit

How much debt is too much. The lender's view of your company, which is also the view that decides whether it survives a bad year.

Debt magnifies. It raises returns when things go well and it is the mechanism through which companies die when they do not. Credit analysis asks one question in several ways: can this company service its debt through a downturn?

The ratios, and what each one is really asking

Stock ratios (how much debt relative to size)

Net debt / EBITDA the market's shorthand for leverage

Gearing = Net debt / Equity

Debt / (Debt + Equity) capital structure weight, the one used in WACC

Flow ratios (can the cash service it)

Interest coverage = EBIT / Interest expense

EBITDA / (Interest + scheduled repayments)

DSCR = Cash available for debt service / Total debt service (used in project and real-estate finance)

FFO / Net debt (used by the rating agencies)

Rough calibration for a normal industrial company (memorise the bands, they come up constantly)

• Net debt/EBITDA below 1.0x: conservative, arguably under-levered.
• 1.5x to 2.5x: normal, comfortable, typical investment-grade territory.
• 3.0x to 4.0x: aggressive. Where a leveraged buyout usually sits after the deal, and where covenants start to bite.
• Above 5.0x: distressed unless the cash flows are contractual and extremely stable (utilities, towers, some infrastructure).
• Interest coverage below 2.0x: fragile. Below 1.0x the company is not earning its interest.

Those bands shift by sector. A utility with regulated revenues can carry 5x. A cyclical capital-goods maker cannot carry 3x. Stability of cash flow determines debt capacity, not size.

Covenants: where theory meets the contract

Loan agreements contain maintenance covenants (tested quarterly: leverage below X, coverage above Y) and incurrence covenants (tested only when you do something: raise more debt, pay a dividend). Breaching a maintenance covenant is a default event even if you have paid every euro on time. That is why a company can be perfectly liquid and still be handed to its lenders. When you analyse a levered company, find the covenants and calculate the headroom. Analysts who quote leverage without quoting covenant headroom are doing half the job.

The leverage effect (the French formulation, and the most elegant statement of the trade-off)

ROE = ROCE + (ROCE − i) × D/E × (1 − t)

Read it: shareholders earn the operating return, plus the spread between the operating return and the interest rate, amplified by the debt-to-equity ratio. If ROCE > i, leverage lifts ROE. If ROCE < i, leverage accelerates the destruction. One formula containing the entire promise and the entire danger of debt. This is core Vernimmen and it will be assumed at emlyon.

Liquidity vs solvency, which are not the same failure

• Liquidity: can it pay next month? (current ratio, quick ratio, cash, undrawn revolver)
• Solvency: are assets worth more than liabilities over the long run? (leverage, equity)

A solvent company can die of illiquidity in a week. That is what a credit crunch is.

FR ↔ EN

endettement net = net debt · levier financier = financial leverage · capacité d'endettement = debt capacity · couverture des intérêts = interest coverage · clauses / covenants = covenants · solvabilité = solvency · liquidité = liquidity.

Earnings quality: EBITDA is not cash

Where companies are caught. The gap between reported profit and real cash is the most information-dense number in the accounts.

Accounting gives management genuine discretion: when to recognise revenue, how fast to depreciate, what to capitalise, how large a provision to book. Most use it reasonably. Some use it to manage the number. Earnings quality analysis is how you tell the difference, and it is the most valuable diagnostic skill in this level.

The master test

Cash conversion = CFO / EBITDA

A healthy mature business converts roughly 70% to 95%. Persistently below that, and something is absorbing the profit: working capital, or the profit was never real. One weak year is noise. Three is a pattern.

The specific red flags, in the order you should check them

1. Receivables growing faster than revenue. Sales booked to customers who are slow or unable to pay. Check DSO trend and the bad-debt provision.

2. Inventory growing faster than COGS. Demand missed the plan. A write-down is queued.

3. Capitalising what should be expensed. Development costs, software, customer acquisition. Capitalised spending skips the P&L today and drips through as amortisation later, so today's margin is flattered. IFRS permits development capitalisation; US GAAP is stricter, which is one more comparability trap.

4. Depreciation lives lengthened. A quiet change in useful life raises reported profit with zero economic change. It is disclosed in the notes, always in the driest possible language.

5. Serial "one-off" charges. Restructuring every year for four years is not one-off. It is a cost of doing business that management has excluded from its adjusted numbers.

6. The adjusted-EBITDA bridge growing. When the gap between reported EBIT and "adjusted EBITDA" widens each year, read every single add-back. This is where stock compensation gets excluded as if it were free.

7. Provisions released into profit. Booking a large provision in a bad year and releasing it in a weak one smooths earnings. Look at movements in the provisions note, not just the balance.

8. Revenue recognised early. Bill-and-hold, percentage-of-completion aggression, channel stuffing at quarter end. Look for a receivables spike in Q4 with a Q1 reversal.

Stock-based compensation, the modern argument

Companies present "adjusted EBITDA excluding SBC" because it is non-cash. It is also a real transfer of ownership from you to employees, and if the company buys back shares to offset dilution, it becomes cash. Damodaran's position, which is correct and worth being able to argue: SBC is an expense, treat it as one, and if you add it back you must then model the dilution. Being able to argue both sides is a genuine interview differentiator.

The one-sentence method

> Compare the growth rate of net income, of operating cash flow, and of free cash flow over five years. If they diverge, the divergence is the story, and the notes contain the reason.

FR ↔ EN

qualité des résultats = earnings quality · provisions = provisions · dotations = charges/allowances · retraitements = adjustments/restatements · éléments non récurrents = non-recurring items.

The teardown: reading a real annual report

Everything so far, applied to one real document, ending in a one-page brief you could hand to a partner.

This lesson is the level's capstone. You take one real company and produce a one-page brief. Everything in levels 2 to 6 will be built on this company, so choose one you actually find interesting: a French listed name whose document d'enregistrement universel you can read, or a US filer with a 10-K. Something with a real product. Avoid banks and insurers for now, their accounts are a different discipline.

The document, and where the value is hidden

A 10-K (US) or URD (France) has a predictable structure:

• Business description · what they sell, to whom, through what channels.
• Risk factors · legally defensive and mostly boilerplate, but the ordering is informative and any newly added risk this year is worth reading closely.
• MD&A (management discussion) · management's own explanation of the year. Read it, then check it against the numbers.
• The financial statements · what you have been learning.
• The notes · where the real information is. Segment reporting, revenue recognition policy, leases, debt maturities and covenants, provisions, share-based payment, related parties, subsequent events.

Amateurs read the press release. Analysts read the notes. The gap between the two is where most of the edge lives.

The order of attack (roughly 2 hours the first time, 30 minutes once you are fluent)

1. Business model, in your own words, in five lines. What is sold, to whom, at what price, how often, and what would make a customer leave. If you cannot write this, stop: no amount of ratio work will save you.

2. Segments. Revenue and operating profit by segment and by geography. Most companies are two or three businesses stapled together and the consolidated margin is a blend that describes none of them.

3. Three years of the three statements, into Excel, by hand. Yes, by hand: typing them is how you notice things.

4. The ratio set from lessons 1.1-1.5.

5. Cash quality: CFO/EBITDA, FCF, capex/D&A.

6. Capital structure: net debt, maturity ladder, fixed vs floating, covenants, and headroom.

7. The notes, hunting specifically for: revenue recognition policy, capitalisation policy, lease obligations, provisions and their movements, share-based payment, related-party transactions.

8. Two or three peers, the same ratios, so "good" and "bad" have a reference.

The one-page brief (the deliverable, and the format you will reuse for the rest of your career)

> What it is · one paragraph on the business model.

> How it makes money · segment mix, margin structure, the unit economics.

> Is it a good business · ROIC vs an estimated cost of capital, the trend, and why.

> Is it safe · leverage, coverage, covenant headroom, downside case.

> Are the numbers honest · cash conversion, the adjusted-EBITDA bridge, anything found in the notes.

> The three questions I would ask management · the sharpest thing in the whole document, because it shows you know what you do not know.

That last section is what a partner reads first. Good questions are more impressive than any conclusion.

FR ↔ EN

document d'enregistrement universel (URD) = the French equivalent of the 10-K · annexes = notes to the accounts · rapport de gestion = MD&A · comptes consolidés = consolidated accounts · commissaire aux comptes = statutory auditor.

Time value of money

One euro today beats one euro next year. Every valuation technique in finance is a consequence of that sentence.

Money has a time dimension because capital can be put to work. A euro today can be invested; a euro next year cannot be invested this year. The exchange rate between the two is the discount rate.

The four formulas that carry almost everything

Present value PV = FV / (1 + r)^n

Future value FV = PV × (1 + r)^n

Perpetuity PV = CF / r

Growing perpetuity PV = CF₁ / (r − g) requires r > g

Annuity (n periods) PV = CF × [1 − (1+r)^-n] / r

The growing perpetuity is the Gordon growth model, and it is what a terminal value is. Note the subscript: CF₁ is next year's cash flow, not this year's. Using CF₀ is the single most common terminal-value error, and it understates value by exactly (1+g).

Compounding conventions, which cost real marks

• Annual: FV = PV(1+r)^n
• m times per year: FV = PV(1 + r/m)^(mn)
• Continuous: FV = PV·e^(rn), the convention in derivatives pricing, so you will meet it again in level 5.
• Effective annual rate: EAR = (1 + r/m)^m − 1. A 12% nominal rate compounded monthly is 12.68% effective. Bond and loan quotes are nominal; comparisons must be effective.

Real versus nominal, the consistency rule

(1 + nominal) = (1 + real) × (1 + inflation)

The rule that matters: discount nominal cash flows at a nominal rate, real cash flows at a real rate. Mixing them is a classic error, and it is the reason valuations of high-inflation-country assets go wrong. If you value a Lebanese or Turkish asset, either build in local inflation and discount at a local nominal rate, or build real cash flows and discount at a real rate. Never one of each.

Mid-year convention

Standard DCFs discount as if all cash arrives on 31 December. Cash actually arrives through the year, so practitioners often discount at t − 0.5. It raises value by roughly (1+r)^0.5, about 4% at a 9% discount rate. Not a rounding error. State which convention you used.

Why your engineering background helps here

A perpetuity is the limit of a geometric series: Σ CF/(1+r)^t = CF/r. A growing perpetuity is the same series with ratio (1+g)/(1+r), which converges only if g < r. That convergence condition is not a technicality: it is why no company can grow forever faster than the economy, and it is the hard constraint on every terminal value you will ever build.

FR ↔ EN

valeur actuelle = present value · actualisation = discounting · capitalisation = compounding · taux d'actualisation = discount rate · annuité = annuity · rente perpétuelle = perpetuity.

Risk, return and beta

Why the discount rate exists, and how the market prices risk. The most contested number in finance.

The discount rate is not a technical parameter, it is a price: the return investors demand for bearing this particular risk. To estimate it you need a theory of which risk is compensated.

The central insight: only non-diversifiable risk is paid for

Total risk splits in two. Specific risk (this company's factory burns, its CEO leaves) can be diversified away by holding many assets, so the market does not compensate you for bearing it: you chose to. Systematic risk (recession, rates, energy prices) hits everything at once and cannot be diversified away. Only that gets a premium. This is the foundation of everything in this lesson and of level 5.

CAPM

Cost of equity E(R) = Rf + β × ERP (+ country risk premium where relevant)

• Rf · risk-free rate: a long-dated government bond in the currency of the cash flows. Euro cash flows → German Bund. Dollar cash flows → US Treasury. The maturity should roughly match the horizon, so 10-year is the convention.
• β · how much this asset moves with the market. β = Cov(Ri,Rm)/Var(Rm). β = 1 moves with the market; β = 1.6 amplifies it; β = 0.5 dampens it.
• ERP · the equity risk premium: the extra return demanded for holding equities over the risk-free asset. Historically ~4-6% for developed markets. Damodaran publishes an implied ERP monthly, derived from current index prices and expected cash flows, which is more defensible than a historical average and is free.

Estimating beta properly (this is where the practical marks are)

A regression beta off five years of weekly returns is noisy, backward-looking, and contaminated by the company's current leverage. The professional method is the bottom-up beta:

1. Take the businesses the company operates in and find the sector's average levered beta from peers.

2. Unlever each: βu = βL / [1 + (1 − t)(D/E)]. This strips out financing risk, leaving pure business risk.

3. Average the unlevered betas, weighting by the revenue or EBIT contribution of each business.

4. Relever at the company's own target capital structure: βL = βu × [1 + (1 − t)(D/E)].

This produces a beta that reflects the businesses the firm is actually in and the leverage it intends to run, rather than the noise of a share-price regression. It is Damodaran's method, it is standard in banks, and using it in an interview is a strong signal.

Country risk

For a company operating in Lebanon, Turkey or Brazil, the ERP is not the mature-market ERP. Damodaran's approach: mature ERP + a country risk premium derived from the sovereign default spread, scaled up by the relative volatility of equity to bonds. Then weight by where the company's revenues come from, not where it is listed. A French luxury group selling 40% into Asia carries Asian risk regardless of the Paris listing.

The honest caveat you should be able to state

CAPM is empirically weak. Beta explains little of the cross-section of returns; the size and value factors (Fama-French) do better, and momentum better still. Finance uses CAPM anyway because it is simple, transparent, and internally consistent, and because the alternatives introduce more estimation error than they remove. The professional position: use CAPM, know its weaknesses, and always sensitise your value to the discount rate rather than defending a single point estimate.

FR ↔ EN

prime de risque = risk premium · taux sans risque = risk-free rate · risque systématique = systematic risk · risque spécifique = idiosyncratic/specific risk · bêta désendetté = unlevered beta.

WACC

The single number that decides whether a project, a company or a deal is worth doing. Get its construction exactly right.

A company is funded by debt and equity, each demanding a different return. The weighted average cost of capital is the blended hurdle rate the business must clear.

WACC = (E/V) × Ke + (D/V) × Kd × (1 − t)

where V = D + E, Ke is the cost of equity from lesson 2.2, Kd is the pre-tax cost of debt, and t is the marginal tax rate.

Every component, with the mistake to avoid

Cost of equity (Ke) · CAPM, bottom-up beta. Covered.

Cost of debt (Kd) · the rate the company would pay to borrow today, not the historical average rate on its existing debt. Three ways to get it, in order of preference: the yield to maturity on its traded bonds; the risk-free rate plus a credit spread implied by its rating; or, if unrated, the risk-free rate plus a synthetic spread from its interest coverage ratio (Damodaran publishes the coverage-to-spread table free). Never use interest expense divided by debt. That is the historical cost of old borrowing and it can be years out of date.

The tax shield (1 − t) · interest is tax-deductible, so the true cost to the company is after tax. Use the marginal rate that applies to the next euro of profit, not the effective rate distorted by one-off items. And note: if the company is loss-making, there is no shield, because there is no tax to shield.

The weights · market values, always, never book values. Equity weight = share price × shares outstanding. Debt weight = market value of debt, or book value as an acceptable proxy for bank debt at floating rates. Using book equity is the single most common WACC error, and it is why students produce WACCs of 6% for companies that trade at four times book.

Which capital structure? Current or target? The convention: use the company's target structure, which for a stable business is its current structure, and for an LBO is the structure it will move toward. Otherwise you get the absurdity of a company temporarily at 90% debt showing a WACC lower than its own cost of debt.

What WACC is actually for, and what it is not

It is the discount rate for free cash flow to the firm, because FCFF belongs to both debt and equity holders, so it must be discounted at the blended cost of both. That pairing is a rule, not a preference:

FCFF → discount at WACC → gives Enterprise Value

FCFE → discount at Ke → gives Equity Value

Mismatching them is the most punished error in the entire valuation section of any interview.

It is not a universal corporate hurdle rate. A company with two divisions of different risk should use two different discount rates. Using a single company WACC systematically overinvests in the risky division and underinvests in the safe one, which is a documented and expensive corporate pathology.

The order of magnitude to carry in your head

Most large developed-market companies land between 7% and 10%. Below 6% or above 13%, check your inputs before you check your thesis. That instinct catches errors faster than any formula.

FR ↔ EN

coût moyen pondéré du capital (CMPC) = WACC · coût de la dette = cost of debt · économie d'impôt / bouclier fiscal = tax shield · valeur de marché = market value.

Free cash flow: FCFF and FCFE

The numerator. Get this definition wrong and every downstream number is wrong, however good your discount rate is.

"Free cash flow" means at least three different things depending on who is speaking. In valuation there are exactly two definitions that matter, and they must be paired with the right discount rate.

Free cash flow to the firm (FCFF) · cash available to all capital providers, before any financing.

FCFF = EBIT × (1 − t) ← NOPAT

+ D&A ← non-cash, add back

− Capex

− Increase in working capital

Note there is no interest anywhere. That is deliberate: interest is a payment to a capital provider, and FCFF is measured before paying any of them. The financing effect enters through the discount rate (WACC), not through the cash flow. Putting interest in FCFF double-counts the financing cost, and it is the single most common valuation error made by students.

Free cash flow to equity (FCFE) · what is left for shareholders after everyone else is paid.

FCFE = Net income

+ D&A

− Capex

− Increase in working capital

+ Net borrowing (new debt − repayments)

Here interest is already deducted, because it is inside net income.

The pairing rule, again, because it is the whole lesson

FCFF → discount at WACC → Enterprise Value → − net debt → Equity Value

FCFE → discount at Ke → Equity Value directly

Both routes should give the same answer if your assumptions are consistent. In practice FCFF/WACC is used ~90% of the time, because it is insulated from changes in capital structure and therefore more stable. FCFE is used for banks and financial institutions, where debt is raw material rather than financing and where enterprise value is meaningless.

Building it from the cash flow statement instead (faster, and what you will actually do)

FCFF = CFO + interest expense × (1 − t) − capex

CFO already has D&A added back and working capital adjusted, but it is after interest, so you add interest back on an after-tax basis to get to the pre-financing figure.

The four mistakes that get caught in interviews

1. Interest in FCFF. Double-counts financing. The most common.

2. Using EBITDA instead of EBIT × (1−t) + D&A. These are not the same: EBITDA is taxed as if D&A did not exist, which overstates the tax bill's shield. Always tax EBIT, then add back D&A.

3. Forgetting the working capital change, or getting the sign backwards. An increase in working capital uses cash: subtract it.

4. Capex below depreciation in perpetuity. In the terminal year, a business growing at g must reinvest enough to sustain g. Capex permanently below D&A implies a shrinking asset base growing forever, which is impossible. Tie terminal reinvestment to the growth rate: reinvestment rate = g / ROIC.

Normalising the starting point

The first forecast year is the foundation of everything. If the last reported year contained a strike, a disposal gain, or a pandemic, normalise it and say so. A DCF built off an abnormal base year is wrong from cell one, and no amount of careful discounting fixes it.

FR ↔ EN

flux de trésorerie disponible = free cash flow · flux disponibles pour l'entreprise = FCFF · flux disponibles pour l'actionnaire = FCFE · investissements = capex · variation du BFR = change in working capital.

Growth and reinvestment

Growth is not an assumption you are allowed to make. It is bought with capital, at the efficiency your returns permit.

Most bad valuations are bad because of the growth assumption, and specifically because growth was typed in as a number rather than derived from the business. This lesson makes it impossible for you to do that.

The fundamental growth equation

Expected growth in operating income = Reinvestment rate × ROIC

with

Reinvestment rate = (Capex − D&A + ΔWorking capital) / NOPAT

Read it as an accounting identity, not a theory: the only way a business grows its operating income is by putting capital back in (the reinvestment rate) and earning a return on it (ROIC). A company can outgrow this only by improving efficiency, which is a one-off gain of finite size, not a permanent growth rate.

The immediate consequence, which almost everyone misses

Growth is not automatically good. Reinvesting at a ROIC below WACC destroys value, and growing faster destroys it faster. The value of growth is:

Value added by growth ∝ g × (ROIC − WACC) / (WACC − g)

If ROIC = WACC, growth adds literally nothing: you are converting cash into assets that earn exactly what they cost. This is why mature commodity businesses trade near book value however fast they grow, and why capital-light high-ROIC businesses trade at large multiples on modest growth.

Three sources of growth, and how long each lasts

1. Reinvestment growth · the equation above. Sustainable indefinitely if the returns hold.

2. Efficiency growth · better margins or better capital turns on the existing base. Real but finite: you cannot improve efficiency forever, and models that assume 200bp of margin expansion every year for a decade are fiction.

3. Acquisitive growth · real, but the capital cost must be in the reinvestment rate, and the average acquisition earns roughly its cost of capital, which means it adds size without adding value.

Fading growth: the shape a professional forecast has

No company grows at 20% forever. The standard structure:

• Years 1-5: explicit, company-specific forecast, at whatever the business can justify.
• Years 6-10: fade, both growth and ROIC converging toward the industry and toward the cost of capital, because competition erodes excess returns. This fade is the part amateurs skip and the part that carries the honesty of the model.
• Terminal: growth must be at or below the long-run nominal growth rate of the economy, which in practice means the risk-free rate is a natural ceiling (nominal GDP growth and long government bond yields track each other). If your terminal growth exceeds the risk-free rate, your company eventually becomes larger than the economy.

Constraints to state out loud when you present

• Terminal g ≤ risk-free rate. Non-negotiable.
• Terminal ROIC should approach WACC for most businesses. Sustaining a large excess return forever means claiming a permanent moat, which you must then justify with a mechanism: network effects, switching costs, a licence, a brand.
• The implied market share and margins at the end of the forecast must be physically possible. Always compute them and look. A model implying 130% of the addressable market is not rare.

FR ↔ EN

croissance = growth · taux de réinvestissement = reinvestment rate · rentabilité marginale = marginal return · avantage concurrentiel = competitive advantage · rente économique = economic rent.

Terminal value

Sixty to eighty percent of your DCF's value sits in a number about a year you cannot see. Treat it accordingly.

A DCF forecasts explicitly for 5 to 10 years and then must value everything after that in one number. That number, the terminal value, typically carries 60% to 80% of total enterprise value. Every serious challenge to a DCF starts here.

Method 1 · Perpetuity growth (Gordon growth)

TV(n) = FCFF(n) × (1 + g) / (WACC − g)

The intrinsic method: consistent with the rest of the DCF, defensible from first principles. Its weakness is extreme sensitivity to g and WACC, since the denominator is a difference between two similar numbers. A 50bp move in either changes value by 10% or more, which is why this page always ships with a sensitivity table.

Method 2 · Exit multiple

TV(n) = EBITDA(n) × exit multiple

The market-based method: quick, intuitive, and standard in banking and private equity because it mirrors how a real exit happens. Its weakness is philosophical: you have imported a pricing assumption into a valuation, so the model is no longer purely intrinsic. And the multiple you pick is usually today's trading multiple applied to a year ten years away, which assumes market conditions never change.

Best practice: use both, and cross-check. Compute the terminal value with a multiple, then back out the implied perpetuity growth rate. If your 9x exit multiple implies 5.5% perpetual growth, the multiple is too high and you now know precisely why. Bankers do this in every model, and doing it unprompted marks you out.

Implied g = (WACC × TV − FCFF(n+1)) / (TV + FCFF(n+1))

or simply solve TV = FCFF(n)(1+g)/(WACC−g) for g.

The four disciplines of a defensible terminal value

1. The terminal year must be a steady state. Growth at long-run economy levels, margins at sustainable levels, capex and depreciation in a stable relationship, working capital growing with revenue. If year 10 still has 15% growth and expanding margins, you have not reached the terminal state and you need more explicit years.

2. Terminal reinvestment must equal g/ROIC. You cannot assume 3% perpetual growth with no reinvestment. This single discipline eliminates most terminal value abuse.

3. Terminal g ≤ risk-free rate. Stated in every review.

4. Report the share of value in the terminal. If it exceeds ~80%, the DCF is really a bet on the terminal assumption and you should say so plainly rather than pretending the explicit forecast is doing the work.

Two things people get wrong mechanically

• Discounting the TV by the wrong number of periods. A terminal value calculated at the end of year 5 is discounted by 5 periods, not 6. It is already a year-5 number.
• Forgetting to grow the final cash flow. The formula takes FCFF(n+1) = FCFF(n) × (1+g). Missing this understates value by (1+g).

A note of intellectual honesty

The terminal value is where your professional judgement is most exposed, because it is a claim about a world nobody can observe. This is not a flaw to be embarrassed by, it is the nature of valuation. The correct response is not false precision but transparency: state the assumption, show the sensitivity, and cross-check it against a market multiple. A range with defensible bounds beats a point estimate with none, always.

FR ↔ EN

valeur terminale = terminal value · valeur résiduelle = residual value · croissance à l'infini = perpetual growth · multiple de sortie = exit multiple.

The full DCF, end to end

Everything in this level, assembled into the model you will build in an assessment centre and rebuild for the rest of your career.

Now you assemble it. A DCF is nine steps and there is no step you can skip.

The build

1. Forecast revenue. Drivers, not a growth rate typed into a cell: volume × price, or customers × ARPU, or market size × share. A driver-based forecast can be argued with; a growth-rate forecast cannot.

2. Forecast operating margins down to EBIT, with the reasoning made visible.

3. Tax EBIT at the marginal rate → NOPAT.

4. Add back D&A, forecast as a % of revenue or off a fixed asset roll-forward.

5. Subtract capex, split into maintenance and growth where you can.

6. Subtract the change in working capital, driven off days (DSO/DIO/DPO), never a flat percentage.

7. → FCFF for each forecast year.

8. Discount at WACC. Note the period convention: mid-year (t − 0.5) or year-end. State which.

9. Terminal value, both methods, cross-checked. Discount it.

Enterprise Value = Σ PV(FCFF) + PV(Terminal Value)

The bridge to equity value (this is a separate discipline and it is where marks are lost)

Enterprise Value

− Net debt (total debt − cash and equivalents)

− Minority interests (at market value if you can)

− Preferred stock

− Unfunded pension obligations

− Other debt-like items (litigation provisions, earn-outs)

+ Non-consolidated investments / associates (at market or fair value)

+ Excess cash beyond operating needs, if not already in net debt

= Equity Value

Equity value / diluted shares = value per share

Diluted shares: use the treasury stock method for in-the-money options and warrants, and include convertibles where the conversion is in the money. Using basic shares systematically overstates value per share, and it is a checkable error.

The four checks that separate a real model from a student one

• Sanity band. Compare implied EV/EBITDA and P/E to the trading comps. Being at 22x when the sector trades at 9x is not necessarily wrong, but you must be able to name exactly which assumption produces the gap.
• Terminal share. Report it. Above ~80%, discuss it.
• Implied end-state. Compute the market share and margin your model implies in the final year. Look at it. Ask whether it is physically possible.
• Sensitivity, always. A two-variable table on WACC and g at minimum, and ideally a scenario set (base, bull, bear) with the operating assumptions changed, not just the discount rate.

How to present it (the part nobody teaches and everybody is judged on)

> "I get a range of €41 to €58 per share, with a base case of €48. The stock is at €39. The value is most sensitive to WACC and to the terminal growth rate: a 50bp move in WACC is roughly €4 per share. My base case assumes margins hold at 14%, which is where they have been for five years, and 2% terminal growth against a 3% risk-free rate, so I am not assuming this business outgrows the economy. The main risk to my case is the customer concentration disclosed in note 24."

Range, sensitivity, the key assumption, the main risk. Four sentences. That is the deliverable, not the spreadsheet.

The honest limits of a DCF, which you should volunteer

It is extraordinarily sensitive to inputs, useless for companies with no reliable path to positive cash flow, and it does not tell you when the market will agree with you. Its value is not the number: it is that it forces every assumption into the open where it can be argued with. That is exactly why it is the spine of the discipline and the spine of your degree.

FR ↔ EN

valeur d'entreprise = enterprise value · valeur des capitaux propres = equity value · dette nette = net debt · intérêts minoritaires = minority interests · titres mis en équivalence = associates/equity-method investments.

Multiples: what each one is for

A multiple is a DCF compressed into one number. Knowing which compression to use, and what it hides, is the skill.

A multiple is a shortcut: instead of forecasting cash flows for ten years, you observe what the market pays for a similar business and apply it. Fast, market-anchored, and structurally dishonest about its assumptions, all at once.

The consistency rule that governs everything

Enterprise value pairs with pre-interest measures: EV/EBITDA · EV/EBIT · EV/Sales · EV/FCF

Equity value pairs with post-interest measures: P/E · P/B · P/FCFE · dividend yield

Why: enterprise value is the value of the whole business, funded by debt and equity together, so its denominator must be a profit measure available to both, i.e. before interest. Equity value is what is left for shareholders, so its denominator must be after interest. P/EBITDA is meaningless and asking a candidate to explain why is a standard screening question.

The main multiples, and when each is right

EV/EBITDA · the workhorse. Neutral to capital structure and to depreciation policy, so it compares companies with different leverage and different asset ages. Use it for most industrials, consumer and healthcare businesses. It fails where capex intensity differs sharply between the companies being compared, because EBITDA pretends capex does not exist: comparing a fabless chip designer with a foundry on EV/EBITDA is nonsense.

EV/EBIT · better where capital intensity differs, because depreciation is a real proxy for the capital consumed. Preferred by many industrial analysts for exactly that reason.

EV/Sales · for companies with no meaningful profit: early-stage, turnarounds, deeply cyclical businesses at the trough. It carries almost no information about profitability, so it is only useful when paired with a margin assumption. "3x sales" means nothing until you say at what margin.

P/E · the most quoted and the most abused. It is affected by leverage (more debt, lower net income, lower price, but the ratio moves unpredictably), by tax rates, by one-offs, and it is meaningless for loss-making companies. Its correct use is comparing similar companies with similar capital structures in the same tax regime.

P/B · for banks and insurers, where assets are marked near market value and book equity is economically meaningful. Almost useless for an asset-light services business whose value is people and brand.

Sector-specific multiples exist because the general ones fail: EV/EBITDAR for retail and airlines (adding back rent), EV/subscriber for telecom, EV/ARR for SaaS, price/AUM for asset managers, price/FFO for real estate. Knowing that a sector has its own multiple and why is a competence signal.

What actually drives a multiple (this is the part that turns a lookup into an argument)

Take the growing perpetuity, divide both sides by earnings, and you get:

P/E ≈ payout ratio × (1 + g) / (Ke − g)

So a multiple is a function of growth, risk and the reinvestment needed to sustain that growth. A company trades at 22x rather than 11x because it grows faster, is less risky, or converts more of its profit into cash. When you see a multiple gap between two peers, that is your list of three explanations, and your job is to determine which one applies.

Forward vs trailing

Trailing uses the last twelve months; forward uses next year's consensus. Markets price the future, so forward multiples are more informative and are what practitioners quote. Always state which you are using: a company at 18x trailing and 12x forward is a very different story from one at 18x both.

FR ↔ EN

multiple = multiple · valeur d'entreprise = enterprise value · capitalisation boursière = market capitalisation · comparables boursiers = trading comps.

Enterprise value vs equity value

The single most-tested concept in finance interviews. Own it completely and you will never be caught.

This is the concept that separates people who have understood finance from people who have memorised it, and it is tested in some form in essentially every technical interview.

The definitions

Enterprise value is the value of the operating business, independent of how it is financed. It is what you would pay for the machine that generates the cash flows, before considering who financed it.

Equity value (market capitalisation, for a listed company) is the value of the shareholders' claim: what is left after all other claims are settled.

The bridge

Equity value

+ Total debt

+ Preferred stock

+ Minority interests

+ Unfunded pension obligations, and other debt-like items

− Cash and cash equivalents

− Non-operating assets (associates, non-consolidated investments)

= Enterprise value

Why cash is subtracted (the follow-up question that trips people)

Because cash is not part of the operating business: it generates no operating profit, so it is not in EBITDA. If you buy a company for €100 of equity and it holds €30 of cash, you effectively paid €70 for the business and got your €30 back. You are buying the operations, not the bank balance. Note the refinement a good candidate volunteers: only excess cash should be stripped, because a business needs some operating cash to function, and stripping it all overstates the discount.

Why minorities are added

Consolidated accounts include 100% of a subsidiary's EBITDA even when you own 70% of it. To keep the multiple consistent, the enterprise value must also reflect 100% of that business, so you add the minority stake you do not own. Numerator and denominator must cover the same perimeter.

Why associates are subtracted

An equity-method associate contributes no revenue or EBITDA to the consolidated accounts (only a single line of post-tax profit). So its value must come out of enterprise value, or you would be paying for something the denominator does not contain.

The classic interview sequence, and the answers

"A company raises €100 of debt. What happens to enterprise value?"

Nothing. Cash rises 100, debt rises 100, and they cancel in the bridge. The operating business is unchanged. This is the whole point of enterprise value.

"It then uses that €100 to buy a machine."

Still nothing changes at the moment of purchase: cash falls 100, PP&E rises 100. Enterprise value changes only when the market revises its view of the cash flows the machine will produce.

"The company pays a €50 dividend."

Cash falls 50, so enterprise value rises by 50 (less cash to subtract), while equity value falls by 50. Both correct, and this is the cleanest demonstration that the two measures answer different questions.

"Can enterprise value be negative?"

Yes: when cash exceeds market cap plus debt. It happens with cash-rich, distressed or heavily loss-making small caps, and it means the market values the operating business at less than nothing, which is a signal that it expects the operations to burn the cash.

The habit that prevents every mistake

Before you compute any multiple, ask: whose money is in the numerator, and whose earnings are in the denominator? If the answer is not the same set of people, the multiple is wrong.

FR ↔ EN

valeur d'entreprise (VE) = enterprise value · capitalisation boursière = market cap · dette nette = net debt · intérêts minoritaires = minority interests · titres mis en équivalence = associates.

Trading comps

Building the peer table properly. Most of the work is in choosing the set and normalising it, not in the arithmetic.

Comparable company analysis values a business by reference to what the public market currently pays for similar businesses. It is the most common valuation output in banking, and it is only as good as the comparability of the set.

The build, in the order it is done

1. Choose the universe. Same industry is not enough: you want similar business model, size, growth, margin structure, geography and end-market. A €40bn global leader is not a comp for a €400m regional player even in the same SIC code. Six to ten names is normal; three is thin and twenty means you have not chosen.

2. Pull the market data. Share price, fully diluted share count (treasury stock method), market cap, then the full bridge to enterprise value.

3. Pull the financials. LTM (last twelve months) and forward consensus for revenue, EBITDA, EBIT and EPS.

4. Normalise, which is where the real work is:

• Calendarise to a common year end. A company with a March year end must be adjusted to be compared with December filers.
• Adjust for non-recurring items so every EBITDA in the table means the same thing.
• Handle IFRS 16 consistently across the set.
• Use the same adjusted-versus-reported convention for everyone.

5. Compute the multiples, then the median and the quartiles. Use the median, not the mean: a single outlier ruins the mean, and comps sets always have an outlier.

6. Apply the range to your company's metric to get an implied value range.

7. Explain where your company sits and why. This last step is the analysis; everything before it is data entry.

Why the median and a range, never the average and a point

Comps produce a range because the market prices a range. The deliverable is "5.5x to 7.0x, implying €780m to €990m enterprise value, and we would sit at the upper end because growth and margins are above the peer median". A single number implies a precision that does not exist.

The football field

The standard output chart: a horizontal bar per methodology, showing the value range from each. Trading comps, precedent transactions, DCF, 52-week trading range, LBO analysis. The overlap between the bars is the defensible zone. It is the single most-used chart in banking and you should be able to build one from memory.

What comps do not tell you

They tell you what the market pays today. If the whole sector is mispriced, comps carry that mispricing into your answer, faithfully. This is the fundamental limitation and the reason a DCF sits next to them: comps give you the market's price, a DCF gives you your own estimate of value, and where they disagree is the interesting conversation.

The tells of a bad comps table (interviewers look for these)

• Companies of wildly different size in the same set.
• No normalisation, so the EBITDAs mean different things.
• Mean instead of median.
• A point estimate rather than a range.
• No sentence explaining where the subject sits in the range and why.

FR ↔ EN

comparables boursiers = trading comps · échantillon = the peer set · médiane = median · retraitements = normalisation adjustments.

Precedent transactions

What acquirers actually paid, control premium included. The M&A cousin of comps, and always the higher number.

Precedent transaction analysis values a company by reference to multiples paid in past acquisitions of similar businesses. It answers a different question from trading comps: not "what does the market pay for a share" but "what does a buyer pay for the whole thing".

Why precedents are almost always higher than trading comps

1. Control premium. A buyer acquiring 100% gains the right to direct the business: change management, alter capital structure, redirect strategy. That right has value, typically 20% to 40% over the undisturbed share price in developed markets.

2. Synergies. Strategic buyers pay part of the expected cost and revenue synergies to the seller. Financial buyers (private equity) do not have operating synergies, which is one reason strategics usually win competitive processes.

3. Auction dynamics. A competitive sale process is designed to extract the highest price a buyer will pay, not the market's consensus view.

Consequently: precedents > trading comps > DCF conservative case, most of the time. When precedents come in below trading comps, something specific happened: the transactions occurred in a worse cycle, or they were distressed sales.

The build

1. Screen transactions: same sector, similar target size, ideally within 3 to 5 years. Older deals happened in a different rate and credit environment, which shows up directly in the multiples paid.

2. Get the deal value: the equity purchase price, plus assumed debt, less cash, to get transaction enterprise value.

3. Get the target's LTM financials at announcement. This is the hard part: the data is in the merger proxy, the offer document, or the press release, and it is often incomplete for private targets.

4. Compute the multiple on LTM EBITDA at the time of announcement.

5. Note the context per deal: strategic or financial buyer, competitive or bilateral process, cash or stock, the announced synergies. Two 11x deals mean different things if one was an auction with three bidders and the other a negotiated deal with none.

The specific difficulties

• Data availability. Private targets disclose little. You often only have the price and a revenue figure.
• Vintage. A 2021 multiple reflects near-zero rates and a wide-open credit market. Using it in 2026 without adjustment overstates value.
• Synergy contamination. The multiple paid embeds the buyer's synergies, which are specific to that buyer. You are borrowing someone else's strategic logic.
• Small samples. Three transactions is not a distribution, and you should say so rather than quoting a median of three.

How it is used in practice

As the upper end of the valuation range, and specifically as the answer to "what could we get if we sold the whole company". In a sell-side pitch, precedents anchor the seller's expectations. In a fairness opinion, they evidence that the price offered is within the range of what comparable buyers have paid.

FR ↔ EN

transactions comparables = precedent transactions · prime de contrôle = control premium · synergies = synergies · offre publique d'achat (OPA) = tender offer/takeover bid.

Value, price, and the narrative

Damodaran's central distinction, and the thing that will make your valuations sound like judgement rather than arithmetic.

Two different games are played with the same numbers, and confusing them is the most common intellectual error in finance.

The value game. You estimate what an asset is intrinsically worth from its cash flows, growth and risk. The tool is a DCF. The question is "what is this business worth?" You win by being right about the fundamentals, eventually.

The pricing game. You estimate what someone will pay for the asset today, based on what similar assets fetch and on mood, flows and momentum. The tool is a multiple. The question is "what will this trade at?" You win by being right about demand and supply, now.

Both are legitimate. Both are practised professionally by serious people. What is not legitimate is using the tools of one to answer the question of the other, which is what happens when someone runs a DCF and then adjusts the assumptions until it matches the market price. That is not valuation, it is reverse-engineering with extra steps.

Narrative and numbers

Damodaran's argument, and the best single idea in modern practical valuation: a valuation is a story about a business, disciplined by numbers. Numbers without a narrative are a spreadsheet nobody believes; a narrative without numbers is a pitch deck. The discipline is that every number in the model must trace back to a claim in the story, and every claim in the story must show up as a number.

The test he proposes for a narrative is three-part:

• Possible? Could it happen at all?
• Plausible? Is there a credible path, with evidence?
• Probable? How likely is it, and what would have to be true?

Most startup valuations pass "possible", many pass "plausible", and very few honestly address "probable". Being explicit about which level your narrative sits at is a mark of seriousness.

The practical technique: the reverse DCF

Instead of computing a value and comparing it to price, take the market price as given and solve for the assumptions that justify it. "At €39 the market is implying 4% revenue growth and 12% margins forever." Now you have converted an opinion about price into a testable statement about the business, and you can go and check it. This is the single most useful analytical habit in this level, and it is what good investors actually do.

When each tool is right

• DCF: mature businesses with forecastable cash flows, long horizons, and where you want to argue with the market.
• Multiples: fast triage, sanity checks, sector-wide comparisons, and any conversation with a market participant.
• Both, always, in a real piece of work. The gap between them is the interesting part: if your DCF says €50 and the market says €39, the productive question is not "who is right" but "what does the market believe that I do not?"

The honest closing position (this is a good thing to be able to say)

> A valuation is an informed opinion with its assumptions made visible. Its value is not the number at the bottom, it is that every disagreement about the number becomes a specific, testable disagreement about the business.

FR ↔ EN

valeur intrinsèque = intrinsic value · prix de marché = market price · efficience des marchés = market efficiency · récit / narratif = narrative.

NPV, IRR and the ranking traps

Two rules that usually agree and occasionally disagree. When they disagree, one of them is right and it is always the same one.

Capital budgeting is the investment decision from lesson 0.1, made operational.

NPV · the present value of future cash flows minus the initial investment.

NPV = Σ CF(t)/(1+r)^t − I₀ Take it if NPV > 0.

NPV is measured in currency and is directly additive: the NPV of a portfolio of projects is the sum of their NPVs. That additivity is the property that makes it the correct rule.

IRR · the discount rate at which NPV equals zero. Take it if IRR > cost of capital. Intuitive, expressed as a percentage, and beloved by practitioners because "23% IRR" communicates instantly while "€4.2m NPV" needs context.

Where IRR breaks, and these are examinable

1. Scale. Project A: invest 100, IRR 50%, NPV 30. Project B: invest 1 000, IRR 20%, NPV 150. IRR prefers A; you should take B. A percentage return on a small base can be worth less than a lower return on a large one.

2. Timing. A project returning cash quickly can have a higher IRR but lower NPV than a long-dated one. IRR implicitly assumes intermediate cash flows are reinvested at the IRR itself, which for a 40% IRR project is a fantasy. MIRR fixes this by assuming reinvestment at the cost of capital.

3. Multiple IRRs. Any cash flow stream that changes sign more than once (a mine with a large closure cost, a project with a mid-life refit) can produce several mathematically valid IRRs. Descartes' rule of signs: as many roots as sign changes.

4. Mutually exclusive projects. When you can only pick one, ranking by IRR can be wrong. Use NPV, or compute the incremental IRR on the difference between the two projects.

The rule to state in an interview: when NPV and IRR disagree, follow NPV, because NPV measures value added in currency and is additive, while IRR is a rate that carries a reinvestment assumption you did not choose.

Payback period · how long to recover the outlay. Ignores everything after payback and ignores the time value of money. It is not a decision rule; it is a crude liquidity screen. Discounted payback is marginally better and still not a decision rule.

Two practical extensions

• Equivalent annual annuity, for comparing projects of different lives: convert each NPV into a per-year equivalent, then compare.
• Capital rationing: when capital is limited, rank by the profitability index (PV of inflows / initial investment) rather than by raw NPV, because you are maximising value per euro of scarce capital.

FR ↔ EN

valeur actuelle nette (VAN) = NPV · taux de rentabilité interne (TRI) = IRR · délai de récupération = payback period · indice de profitabilité = profitability index.

Capital structure

How much debt should a company have? Modigliani-Miller says it does not matter, which is exactly why understanding when it does matter is the whole subject.

Modigliani-Miller, Proposition I (no taxes, no distress, no information asymmetry): capital structure is irrelevant. The value of a firm is set by its assets and their cash flows, not by how the claims on them are sliced. Cutting a pizza into more pieces does not make more pizza.

MM Proposition II follows: as you add cheap debt, the equity that remains becomes riskier and its required return rises exactly enough to offset the saving.

Ke = Ku + (Ku − Kd) × D/E

WACC stays constant. This is not a description of the real world; it is a statement that if capital structure matters, it must be because one of the assumptions fails. That is the intellectual move to appreciate, and it is why MM won a Nobel Prize for a theory whose conclusion is "it does not matter".

Then relax the assumptions, one at a time

1 · Taxes. Interest is deductible, dividends are not. The state subsidises debt.

Value of the levered firm = Value unlevered + PV(tax shield) = Vu + t × D

for permanent debt. Taken alone this implies 100% debt, which is obviously wrong, so something must push back.

2 · Financial distress. As leverage rises, the probability of default rises, and distress is expensive: direct costs (lawyers, advisers, fire-sale asset prices) and, larger, indirect costs (customers leave, suppliers demand prepayment, talent goes, management spends its time with lenders instead of on the business).

The trade-off theory, which is the workable answer:

V(levered) = V(unlevered) + PV(tax shield) − PV(distress costs)

There is an interior optimum. WACC falls, then rises, and the bottom of that U is the target capital structure. In practice you do not solve for it; you triangulate: what leverage do sector peers carry, what does the rating agency grid say for the target rating, and what does the downside case support.

3 · Information asymmetry: the pecking order. Managers know more than investors. Issuing equity signals the shares are overvalued, so the market marks the stock down on announcement. Hence the observed preference: internal funds first, then debt, then equity last. This explains real corporate behaviour better than the trade-off theory does, and profitable companies being under-levered is its signature prediction.

4 · Agency costs. Debt disciplines: interest payments remove the free cash flow that empire-building consumes (Jensen's free cash flow hypothesis, the intellectual basis of the LBO). Debt also distorts: near default, equity holders have an incentive to gamble, since they own the upside and lenders own the downside, and to refuse good projects whose benefit accrues to lenders (debt overhang).

What actually determines a real company's leverage

Cash flow stability and predictability · asset tangibility (collateral) · growth and reinvestment needs · tax position (a loss-making firm has no shield to buy) · rating targets and covenant capacity · sector convention and market access.

FR ↔ EN

structure financière = capital structure · effet de levier = leverage · coûts de faillite = bankruptcy/distress costs · économie d'impôt = tax shield · théorie du compromis = trade-off theory · financement hiérarchisé = pecking order.

Payout: dividends and buybacks

What to do with cash you cannot reinvest above your cost of capital. The decision that reveals what management actually believes.

The payout decision follows directly from the value creation rule. Cash that can be reinvested at a return above the cost of capital should be reinvested. Cash that cannot belongs to the shareholders, and retaining it destroys value.

Dividend irrelevance (MM again). In a frictionless world, payout policy does not affect value: a shareholder wanting cash can sell shares, and one not wanting cash can reinvest the dividend. Value comes from the investment decisions, not from the packaging of the return. Again, the point is to identify the frictions that make it matter: taxes, signalling, transaction costs, and agency.

Dividends versus buybacks, the real comparison

Dividends: a cash payment per share. Sticky, because cutting one is read as a confession of distress, so it is a strong commitment. Attracts a specific investor base (income funds, retail, insurers). In France, dividends are subject to the PFU flat tax of 30% including social charges, unless the taxpayer elects the progressive scale.

Buybacks: the company repurchases its own shares, raising each remaining holder's proportional ownership. Flexible, can be paused without a signal of distress. Tax-efficient in many regimes because the gain is realised at the shareholder's choosing and taxed as capital gains. But they are only value-accretive if the shares are bought below intrinsic value, and managements have a well-documented record of buying most heavily at peaks, when cash is abundant, and stopping at troughs, when it is not.

Signalling. A dividend initiation or increase signals confidence in sustainable cash flow. A cut signals the opposite and is punished heavily. This is why dividends are smoothed: Lintner's classic finding is that managers target a payout ratio but adjust toward it only partially each year, precisely to avoid ever cutting.

The agency argument. Paying out cash removes the temptation to empire-build. Jensen's free cash flow hypothesis says firms with abundant cash and poor investment opportunities systematically over-invest, and that committing to payout, or to debt service, is a discipline mechanism. This is the intellectual foundation of the leveraged buyout.

What actually matters when you analyse payout

• Is it covered? Payout ratio against net income and, better, dividend against free cash flow. Paying dividends out of debt is a real and common pathology, and it is visible: dividends exceeding FCF for several years with net debt rising.
• What are the alternatives? A company with a 25% ROIC should reinvest, not pay out. A company at 6% ROIC against a 9% WACC should pay out everything.
• What does the buyback price say? Buying back at 25x earnings when your own DCF says 15x is destroying value, however good the EPS optics look.

The EPS illusion, worth being able to dismantle

A buyback mechanically raises EPS by shrinking the share count. That is arithmetic, not value creation. If the company borrows at 5% after tax to buy back stock with an earnings yield of 4%, EPS rises and value falls. Rising EPS from a buyback tells you nothing about whether value was created; only the price paid versus intrinsic value does.

FR ↔ EN

politique de distribution = payout policy · dividende = dividend · rachat d'actions = share buyback · taux de distribution = payout ratio · PFU (prélèvement forfaitaire unique) = the French 30% flat tax on investment income.

M&A and accretion / dilution

Why deals happen, why most fail, and the one calculation every banking interview asks for.

Why companies buy other companies · the honest list, in descending order of how often it actually creates value: cost synergies (real, quantifiable, achievable), acquiring capability faster than building it, consolidating a fragmented market, revenue synergies (frequently claimed, rarely delivered), tax and financial engineering, and finally empire-building by a CEO with cash and an investment bank in the room.

The uncomfortable evidence: the majority of large acquisitions fail to create value for the acquirer's shareholders. Target shareholders capture most of the gain through the control premium. The acquirer bears integration risk and pays up front for synergies that may not arrive.

Synergies

• Cost synergies: overlapping headcount, duplicated facilities, procurement scale. Credible, quantifiable, usually realised at 60-90% of the announced figure but later than promised.
• Revenue synergies: cross-selling, distribution reach. Systematically over-claimed, and a disciplined analyst gives them little or no credit.
• Always net off integration costs, which are real, cash, and front-loaded: typically one to two times the annual run-rate synergy.

Accretion / dilution: the calculation

Pro forma EPS = (Acquirer NI + Target NI + after-tax synergies − after-tax incremental interest) / (Acquirer shares + new shares issued)

Accretive if pro forma EPS > standalone EPS. Dilutive if lower.

The shortcut that gets asked for constantly (cash deal):

> Compare the after-tax cost of the funding with the earnings yield being acquired (the inverse of the P/E paid).

> Cash: after-tax interest rate on the debt used, versus the target's earnings yield.

> Stock: the acquirer's earnings yield (1/its P/E) versus the target's.

>

> Stock deal rule of thumb: if the acquirer's P/E is higher than the target's P/E paid, the deal is accretive.

Example: acquirer at 20x (5% earnings yield) buying a target at 14x (7.1% earnings yield) with stock: accretive, because it is issuing expensive paper to buy cheap earnings.

And the warning to deliver in the same breath: accretion is not value creation. A high-multiple company can buy anything cheaper than itself and show accretion. Whether value was created depends on whether the price paid was below the value received, which is a DCF question, not an EPS question. Being able to give the mechanical answer and then immediately qualify it is exactly what separates a strong candidate.

Cash versus stock

• Cash: certainty for the seller, no dilution for the buyer, uses debt capacity, and signals confidence (you are not paying with paper you think is overvalued).
• Stock: preserves liquidity, shares risk with the seller, but signals the acquirer may consider its own shares expensive. Empirically, stock-financed deals underperform cash-financed ones, which is consistent with that signal.

FR ↔ EN

fusions-acquisitions (F&A) = M&A · relution = accretion · dilution = dilution · synergies de coûts = cost synergies · offre publique = public offer.

The LBO and the paper LBO

The purest expression of financial engineering, and the calculation you will be asked to do on paper, without Excel, in a private equity interview.

A leveraged buyout is the acquisition of a company using a large amount of debt, secured against the target's own assets and repaid from the target's own cash flow. The sponsor puts in a slice of equity and, if it works, multiplies it.

Where the returns come from (be able to decompose any LBO return into these four)

1. Deleveraging. Cash flow pays down debt; every euro of debt repaid becomes a euro of equity value at exit. This is the mechanical core.

2. EBITDA growth. Organic growth, margin improvement, bolt-on acquisitions.

3. Multiple expansion. Selling at a higher multiple than you paid. The least controllable and the least respectable source, and any sponsor underwriting to it is taking a market bet.

4. Cash generation. Dividends taken out along the way, including dividend recapitalisations.

What makes a good LBO candidate

Stable, predictable cash flows (the debt must be serviced through a cycle) · low capex requirements · a defensible market position · tangible assets for security · an under-levered starting balance sheet · identifiable operational improvement · and a credible exit route in three to five years. Cyclical, capex-heavy, technologically volatile businesses make poor candidates.

The structure

Sources Uses

Revolver (undrawn at close) Purchase of target equity

Term Loan A / B Refinancing of existing debt

High yield / mezzanine Transaction fees (advisory, financing)

Sponsor equity Minimum cash to balance sheet

Sources must equal uses. In current markets, sponsor equity is typically 35-50% of the total, higher than the 20-30% of the pre-2008 era.

The paper LBO · you will be asked to do this out loud, with no spreadsheet, in about five minutes. Learn the sequence:

1. Entry. Purchase enterprise value = EBITDA × entry multiple. Split it into debt and equity.

2. Project EBITDA over five years at the stated growth rate.

3. Build free cash flow: EBITDA − capex − change in working capital − cash interest − cash taxes.

4. Sweep the cash against debt: debt at exit = entry debt − cumulative repayment.

5. Exit. Exit enterprise value = exit-year EBITDA × exit multiple. Equity at exit = exit EV − remaining debt.

6. Returns. MOIC = exit equity / entry equity. IRR from MOIC over the holding period.

The IRR shortcut you must know cold (5-year hold): 2.0x ≈ 15% · 2.5x ≈ 20% · 3.0x ≈ 25% · 4.0x ≈ 32%. Over 3 years: 2.0x ≈ 26%. Over 7 years: 2.0x ≈ 10%. Sponsors target roughly 20-25% IRR and 2.0-3.0x MOIC.

Why leverage magnifies returns · the mechanism in one line: you buy the whole enterprise but pay for only a fraction of it, so any increase in enterprise value accrues entirely to that fraction, and any debt repaid converts directly into equity. The same mechanism works in reverse, which is why LBOs of cyclical businesses fail spectacularly rather than gently.

FR ↔ EN

LBO = leveraged buy-out (the term is used in French too) · dette senior = senior debt · dette mezzanine = mezzanine · fonds propres du sponsor = sponsor equity · sortie = exit · TRI = IRR.

The debt stack

Who gets paid first, at what price, and with what strings. The plumbing behind every LBO and every restructuring.

Debt is not one instrument. It is a hierarchy of claims, each priced for its position in the queue, and the queue is the whole subject.

The stack, senior to junior

Revolving credit facility (RCF). Working capital line, drawn and repaid as needed, usually undrawn at closing. Cheapest, most senior, and carries a commitment fee on the undrawn amount.

Term Loan A. Amortising, bank-held, shorter maturity (5-6 years), tighter covenants, cheapest term debt. More common in Europe than the US.

Term Loan B. The workhorse of leveraged finance. Institutional investors (CLOs, credit funds), 6-7 years, minimal amortisation (typically 1% a year) with a bullet at maturity, floating rate quoted as a margin over Euribor or SOFR. Often covenant-lite, meaning no maintenance covenants, only incurrence tests, which shifted enormous power to borrowers over the last decade.

Senior secured notes / high yield bonds. Fixed rate, bullet maturity, 7-8 years, no amortisation, incurrence covenants, non-call periods restricting early repayment. Priced on a yield rather than a margin.

Mezzanine / subordinated debt / PIK. Junior, expensive (10-15%), often with an equity kicker (warrants) or payment-in-kind interest that accrues to principal instead of being paid in cash, preserving cash flow at the cost of compounding the balance.

Preferred equity, then common equity. Last in line, unlimited upside.

The single principle: every step down the stack means a longer wait in a bankruptcy, so every step demands a higher return. Price is the compensation for position.

Key mechanics you should be able to discuss

• Security and guarantees: what assets secure which tranche, and which group entities guarantee. In a default, this determines who actually recovers.
• Intercreditor agreement: the contract between lender classes setting payment order, enforcement rights and standstill periods. In a restructuring it is the document that matters most.
• Cash sweep: a mandatory percentage of excess free cash flow (often 50-75%, stepping down as leverage falls) must repay debt.
• Covenants: maintenance (tested quarterly) versus incurrence (tested only on action). Cov-lite structures have only the latter.
• Call protection: non-call periods and prepayment premiums on bonds; term loans usually carry only a short soft-call period.

Floating versus fixed, which is a live issue

Term loans float, so the borrower carries rate risk; bonds are fixed, so the borrower locks in. In a rising-rate environment, floating-rate LBO debt can consume the cash flow the model assumed was available for the sweep. Interest rate hedging is usually a condition of the credit agreement for exactly this reason.

Why this matters beyond private equity

The stack determines who controls a company in distress. When a business breaks its covenants, the negotiation runs top-down through the stack, and the tranche where value "breaks", the fulcrum security, is the one that converts into equity and ends up owning the company. That is the core of distressed investing, in level 6.

FR ↔ EN

dette senior = senior debt · dette subordonnée = subordinated debt · sûretés = security/collateral · convention entre créanciers = intercreditor agreement · clause de remboursement anticipé = prepayment clause.

How markets actually work

The plumbing: who trades, where, against whom, and why the price on your screen is what it is.

Before the mathematics, the institutions. Most finance students can price an option and cannot explain who is on the other side of the trade.

Primary versus secondary market

The primary market is where securities are created and capital actually reaches the issuer: an IPO, a rights issue, a bond issue. The secondary market is where existing securities change hands between investors, and where no money reaches the company at all. When Apple's shares trade, Apple receives nothing. The secondary market matters to the issuer only because liquidity there determines the price obtainable in the primary market.

The participants

• Asset managers (long-only funds, ETFs, pension and insurance money): the largest pool, mostly benchmarked to an index, generally slow-moving.
• Hedge funds: long/short, event-driven, macro, quantitative. Small in assets, large in turnover, and the marginal price setter in many situations.
• Market makers and high-frequency firms: provide continuous two-way quotes, earn the bid-ask spread, hold inventory only briefly.
• Banks: underwriting, market making, and increasingly agency-only execution post-regulation.
• Retail: small individually, large in aggregate, and the dominant flow in some segments.
• Corporates: buybacks make companies among the largest net buyers of their own equity.

Market microstructure

A limit order book matches buyers and sellers by price and time priority. The bid is the highest price a buyer will pay, the ask the lowest a seller will accept, and the spread between them is the market maker's compensation for providing immediacy and bearing inventory risk. Depth is the volume available near the touch. Liquidity is the ability to trade size without moving the price, and it is not constant: it evaporates precisely when it is needed, which is the mechanism behind most market crises.

Market efficiency, in three forms

• Weak: prices reflect all past prices. Technical analysis cannot systematically work.
• Semi-strong: prices reflect all public information. Fundamental analysis on public data cannot systematically beat the market.
• Strong: prices reflect all information including private. Even insiders cannot beat it.

The evidence supports something between weak and semi-strong: most active managers underperform their benchmark after fees, which is the strongest single argument for efficiency, and yet documented anomalies (value, momentum, quality, low volatility) persist. The professional position: markets are mostly efficient, efficient enough that beating them is hard and getting harder, but not so efficient that analysis is pointless. Grossman and Stiglitz made this rigorous: if prices were perfectly efficient nobody would pay to gather information, so a paradox arises and the equilibrium must contain enough inefficiency to pay for the analysis that creates the efficiency.

Why this matters to you specifically

Levels 2 and 3 taught you to estimate value. This level tells you what you are competing against when you act on that estimate. Being right about value and wrong about the market's willingness to agree is the standard experience of a fundamental investor, and knowing that in advance is what makes the difference between a thesis and a position.

FR ↔ EN

marché primaire = primary market · marché secondaire = secondary market · carnet d'ordres = order book · fourchette = bid-ask spread · efficience des marchés = market efficiency · teneur de marché = market maker.

Portfolio theory

The one genuinely free lunch in finance: diversification. And your quadratic optimisation background makes the mathematics trivial.

Markowitz's insight, which won the 1990 Nobel: an asset should be judged not by its own risk but by its contribution to the risk of the portfolio you hold.

The mathematics (familiar territory for you)

For two assets:

E(Rp) = w₁E(R₁) + w₂E(R₂)

σp² = w₁²σ₁² + w₂²σ₂² + 2w₁w₂ρσ₁σ₂

The whole subject lives in that last term. Expected return is linear in the weights; risk is not, because of ρ, the correlation. Whenever ρ < 1, portfolio volatility is strictly less than the weighted average of the individual volatilities. That gap is the free lunch.

In matrix form, which is how it is actually solved:

E(Rp) = wᵀμ σp² = wᵀΣw

and the optimisation is: minimise wᵀΣw subject to wᵀμ = target and wᵀ1 = 1. A quadratic programme with linear constraints, solvable in closed form with Lagrange multipliers. Your engineering course already covered the hard part.

The efficient frontier

Plot every achievable portfolio in (σ, E(R)) space and the northwest boundary is the efficient frontier: for each level of risk, the maximum achievable return. Everything below it is dominated and nobody rational holds it.

Adding a risk-free asset: the capital market line

With a risk-free asset available, the optimal risky portfolio is the tangency portfolio, where a line from Rf touches the frontier. Every investor then holds some combination of the risk-free asset and that same tangency portfolio, varying only the mix according to risk appetite. This is Tobin's two-fund separation, and it is the theoretical justification for index investing: if everyone holds the same risky portfolio, that portfolio must be the market.

Sharpe ratio = (E(Rp) − Rf) / σp

The tangency portfolio is the one that maximises the Sharpe ratio: excess return per unit of total risk. It is the single most-used performance metric in asset management.

How far diversification goes

Portfolio variance decomposes into specific risk (diversifiable) and systematic risk (not). With n equally weighted assets, specific risk falls roughly as 1/n while the covariance term persists. Empirically, most of the diversification benefit in equities is captured by 20 to 30 well-chosen stocks; beyond that the marginal gain is small. What you cannot diversify away is the market itself, which is exactly why only that risk is compensated (lesson 2.2).

The honest problems with mean-variance optimisation

• It needs expected returns as inputs, and they are estimated with enormous error. The optimiser is exquisitely sensitive to them, so it produces extreme, unstable weights: it is an "error maximiser".
• Correlations rise in crises, exactly when you need diversification, so measured historical correlation understates tail risk.
• Variance treats upside and downside symmetrically, which no investor does.
• Returns are not normally distributed; tails are fatter than the model assumes.

The practical responses: shrinkage estimators (Ledoit-Wolf), the Black-Litterman model (blending market equilibrium with your views), constrained weights, and risk-parity approaches. Knowing that the theory has these specific weaknesses, and naming the specific fixes, is exactly the level of sophistication a good programme expects.

FR ↔ EN

diversification = diversification · frontière efficiente = efficient frontier · portefeuille de marché = market portfolio · ratio de Sharpe = Sharpe ratio · covariance = covariance.

CAPM, factors and the risk premium

The model everyone uses and nobody believes, plus the empirical models that replaced it in practice.

CAPM as an equilibrium result

If everyone optimises mean-variance and holds the tangency portfolio (lesson 5.2), then in equilibrium that portfolio must be the market portfolio, and the expected return on any asset is:

E(Ri) = Rf + βi(E(Rm) − Rf)

with βi = Cov(Ri,Rm)/Var(Rm). The security market line plots expected return against beta, and every asset should sit on it.

The empirical verdict, stated honestly

The relationship between beta and realised return is far weaker than the model predicts: the security market line is too flat, low-beta stocks earn more than CAPM says and high-beta stocks less. Fama and French documented systematic deviations that beta cannot explain.

The factor models that followed

Fama-French three-factor (1993):

E(Ri) − Rf = βm(Rm − Rf) + βs·SMB + βv·HML

adding size (small minus big) and value (high minus low book-to-market). It explains far more of the cross-section of returns than CAPM alone.

Carhart four-factor (1997): adds momentum (past winners keep winning over 3-12 months), which is the most statistically robust anomaly ever documented and the most theoretically embarrassing.

Fama-French five-factor (2015): adds profitability (robust minus weak) and investment (conservative minus aggressive), which subsumes much of the value factor's power.

Are factors risk or mispricing? The unresolved question. The risk story: these are compensations for bearing exposures that hurt in bad states. The behavioural story: they are persistent errors, value from over-extrapolation of bad news, momentum from under-reaction. Both camps have Nobel laureates (Fama and Shiller, sharing the 2013 prize with opposite views, which tells you how open the question is). Being able to state both readings is more valuable than picking a side.

The equity risk premium in practice

Three estimation routes:

1. Historical: the realised excess return of equities over bonds, roughly 4-6% for the US over a century, less elsewhere. Weakness: enormous standard error, and survivorship bias in using the most successful market of the last century.

2. Survey: ask practitioners. Weakness: it tracks recent returns.

3. Implied: solve for the discount rate that equates today's index level with expected future cash flows. Damodaran publishes this monthly. Forward-looking, self-updating, and by far the most defensible. Using the implied ERP and being able to explain why is a real signal of quality.

What this means for your valuations

You will keep using CAPM in your DCFs, because it is transparent, simple, and internally consistent, and because factor models introduce estimation error of their own. What changes is your honesty about it: the discount rate is an estimate with a wide confidence interval, so the output is a range, not a point. That is the same conclusion as level 2, arrived at from the market side.

FR ↔ EN

MEDAF (modèle d'évaluation des actifs financiers) = CAPM · prime de risque du marché = equity risk premium · droite de marché des titres = security market line · facteurs = factors.

Fixed income

The largest asset class in the world, and the one where the mathematics is cleanest. Duration and convexity are a Taylor expansion you already know.

A bond is a contract: pay P today, receive fixed coupons C and the face value F at maturity.

P = Σ C/(1+y)^t + F/(1+y)^n

The yield to maturity y is the internal rate of return that equates the price with the promised cash flows. Note what that means: YTM assumes you hold to maturity and reinvest every coupon at y, which is the same reinvestment fiction as IRR in lesson 4.1.

The price-yield relationship

Price and yield move inversely, and the curve is convex, not linear. Price falls as yields rise, but by less and less: the gain from a yield fall exceeds the loss from an equal yield rise. That asymmetry is convexity and it is valuable to the bondholder.

Duration: the first derivative

Macaulay duration D = Σ [t × PV(CFt)] / P weighted average time to cash flow, in years

Modified duration Dm = D/(1+y) the price sensitivity

ΔP/P ≈ −Dm × Δy

A bond with modified duration 7 loses roughly 7% of its value for a 100bp yield rise. Dollar duration (DV01) is the price change for a 1bp move and is what a trading desk actually manages.

Convexity: the second derivative

ΔP/P ≈ −Dm × Δy + ½ × C × (Δy)²

You will recognise this immediately: it is the second-order Taylor expansion of price in yield. Duration alone systematically overstates the loss from a yield rise and understates the gain from a fall, and convexity corrects it. For large moves the correction is material, which is exactly why traders quote both.

What drives duration

Longer maturity raises it. Higher coupon lowers it (more cash arrives sooner). Higher yield lowers it. A zero-coupon bond's Macaulay duration equals its maturity exactly, which is the cleanest case and the one to hold as a reference point.

The yield curve

Yield plotted against maturity. Normally upward-sloping. An inverted curve, where short rates exceed long rates, has preceded most recessions and is the single most-watched macro signal in markets. Three explanations coexist: expectations (long rates are averages of expected future short rates), liquidity preference (a term premium for locking money up), and market segmentation (different investors dominate different maturities). The truth involves all three.

Credit

Corporate yield = risk-free yield + credit spread

The spread compensates for expected default loss plus a risk premium plus illiquidity. Ratings (AAA down to D, with investment grade ending at BBB−) map roughly onto spreads but move more slowly than markets. Spreads widen sharply in risk-off periods, and high yield spreads are one of the best real-time indicators of financial stress available.

Why this matters even if you never trade a bond

The risk-free rate in every DCF you build comes from this market. Your cost of debt comes from credit spreads here. When rates move 200bp, every valuation in the economy moves, and the mechanism is entirely in this lesson.

FR ↔ EN

obligation = bond · coupon = coupon · taux actuariel = yield to maturity · sensibilité = modified duration · duration = Macaulay duration · courbe des taux = yield curve · spread de crédit = credit spread.

Forwards, futures and swaps

Contracts on the future. The pricing logic is one idea, no-arbitrage, applied three ways.

A derivative derives its value from an underlying asset. The three linear derivatives, forwards, futures and swaps, are all priced by the same principle: no-arbitrage. If two portfolios produce identical cash flows in every state of the world, they must have the same price, or a riskless profit exists.

Forwards

A private agreement to buy or sell an asset at a fixed price on a future date. No money changes hands today.

F₀ = S₀ × e^(r−q)T (continuous compounding, q = dividend or convenience yield)

F₀ = S₀ × (1+r)^T (discrete, no income)

The derivation is the whole method: to deliver the asset at T, buy it today for S₀ and finance the purchase at r. Your cost at T is S₀e^rT, so the fair forward price must equal that or you can arbitrage. This is cost of carry, and once you see it you can price any forward.

Futures

Exchange-traded, standardised forwards, with a clearing house between the parties and daily mark-to-market: gains and losses settle every day through a margin account. Consequences: negligible counterparty risk, but daily cash flows, so a position can be liquidated by margin calls even when the eventual view proves right. Futures and forward prices are equal when interest rates are deterministic and diverge slightly when rates are stochastic and correlated with the underlying.

Contango and backwardation. Futures above spot is contango (normal for storable assets, reflecting storage and financing costs); futures below spot is backwardation (typical when there is a convenience yield to holding the physical asset, as in a supply squeeze). Rolling a long futures position in contango bleeds money, which is why commodity index funds structurally underperform spot.

Swaps

An exchange of cash flow streams. The plain vanilla interest rate swap: one party pays fixed, the other pays floating (Euribor or SOFR) on a notional that is never exchanged.

Why they exist: comparative advantage and risk management. A company with a floating-rate term loan that wants certainty pays fixed and receives floating, converting its exposure synthetically without renegotiating the loan. This is exactly the hedge required by most LBO credit agreements in lesson 4.6.

Valuation: at inception the swap is worth zero, with the fixed rate set so that the present values of the two legs are equal. Afterwards it has a value, positive to one side, as rates move, and it is valued as a long position in one bond and a short position in another.

Other swaps you should know by name: currency swaps (exchange principal and interest in two currencies), credit default swaps (periodic premium in exchange for protection against a credit event, the instrument at the centre of 2008), and total return swaps (synthetic exposure to an asset's full return, widely used by hedge funds for leverage).

FR ↔ EN

contrat à terme = forward · contrat à terme standardisé = future · appel de marge = margin call · swap de taux = interest rate swap · notionnel = notional · couverture = hedge.

Options and Black-Scholes

Non-linear payoffs, and the equation that made modern finance. Your PDE background means the derivation will be easier for you than for anyone else in the room.

An option is a right, not an obligation. That asymmetry is what makes the payoff non-linear and the pricing hard.

The four positions and their payoffs at expiry

Long call: max(S − K, 0) − premium unlimited upside, loss capped at the premium

Short call: premium − max(S − K, 0) capped gain, unlimited loss

Long put: max(K − S, 0) − premium profits as S falls, loss capped at the premium

Short put: premium − max(K − S, 0) capped gain, large loss if S collapses

Draw these four diagrams by hand until you can do it in ten seconds. Every structured payoff you will ever meet is a combination of them.

Put-call parity · the no-arbitrage relationship that must hold:

C − P = S − K·e^(−rT)

A long call plus a short put replicates the underlying with financing. If parity breaks, an arbitrage exists. It also lets you price a put from a call instantly, and it is a standard interview question.

What drives an option's value (six variables, and the sign of each)

Underlying price S call ↑ put ↓

Strike K call ↓ put ↑

Time to expiry T both ↑ (more time, more chance of finishing in the money)

Volatility σ both ↑ ← the important one

Risk-free rate r call ↑ put ↓

Dividends q call ↓ put ↑

Volatility raises the value of both calls and puts, because the payoff is asymmetric: more dispersion increases the upside without increasing the downside, which is capped at the premium. This is the single most important intuition in options, and it is why options are best understood as instruments for trading volatility, not direction.

Black-Scholes

C = S·N(d₁) − K·e^(−rT)·N(d₂)

d₁ = [ln(S/K) + (r + σ²/2)T] / (σ√T) d₂ = d₁ − σ√T

The assumptions: geometric Brownian motion for the underlying, constant volatility and rates, no transaction costs, continuous trading, European exercise. The derivation constructs a delta-hedged portfolio whose value is riskless, which must therefore earn r, giving a PDE that transforms into the heat equation. You have solved the heat equation. The finance is the setup, not the mathematics.

Interpretation worth carrying: N(d₂) is the risk-neutral probability of finishing in the money; S·N(d₁) is the expected value of the asset received, conditional on exercise.

The Greeks

Delta (∂C/∂S) hedge ratio: shares per option to be neutral. 0 to 1 for calls.

Gamma (∂²C/∂S²) how fast delta changes. Highest at the money, near expiry.

Vega (∂C/∂σ) sensitivity to volatility. The reason people say they "trade vol".

Theta (∂C/∂T) time decay. Negative for long options: they bleed every day.

Rho (∂C/∂r) sensitivity to rates. Usually the least important.

The volatility smile: where the model breaks

Black-Scholes assumes constant volatility, so implied volatility should be identical across strikes. It is not: out-of-the-money puts trade at higher implied volatility than at-the-money options, producing a "smile" or "skew". The market is pricing fatter tails than a lognormal distribution allows, particularly on the downside, and it has done so consistently since 1987. The model is used as a quoting convention, a translation between price and implied volatility, rather than as a literal description of reality. That is the sophisticated way to hold it.

FR ↔ EN

option d'achat = call · option de vente = put · prix d'exercice = strike · prime = premium · volatilité implicite = implied volatility · dans la monnaie = in the money.

Private equity: the fund model

How the industry actually makes money, which is not the same as how it says it does.

Understanding a PE fund means understanding two levels: the deal (level 4.5) and the fund that holds the deals.

The structure

Limited partners (LPs: pension funds, sovereign wealth funds, insurers, endowments, family offices) commit capital to a fund managed by the general partner (GP). Commitments are drawn down over an investment period of roughly five years, and returned as investments are exited, over a total life of about ten years plus extensions.

The economics: "2 and 20"

• Management fee: ~2% a year of committed capital during the investment period, stepping down to invested capital afterwards. This pays salaries and keeps the lights on, and on a large fund it is a substantial business in its own right.
• Carried interest: 20% of profits above a hurdle rate (preferred return), usually 8% IRR. This is where the wealth is created.
• Catch-up: after the hurdle is met, the GP takes 100% of profits until it has received 20% of total profits, then the split reverts to 80/20.

The distribution waterfall, in order: (1) return all capital to LPs, (2) pay the 8% preferred return, (3) GP catch-up, (4) 80/20 split thereafter. European ("whole-fund") waterfalls compute this across the entire fund; American ("deal-by-deal") waterfalls compute it per investment, which pays the GP earlier and is why LPs negotiate hard on this point and demand clawback provisions.

The J-curve

Early years show negative returns: fees are charged from day one, investments are held at cost, and nothing has been exited. Returns turn positive as exits arrive, producing the characteristic J shape. A fund reporting a negative IRR in year two is behaving normally; the same in year six is not.

IRR versus MOIC, and why the distinction matters

• MOIC (multiple on invested capital) is absolute: total value / invested capital. Time-blind.
• IRR is time-sensitive and can be manipulated: an early exit, a dividend recapitalisation, or using a subscription line (a credit facility that delays calling LP capital) all raise reported IRR without improving the underlying economics at all.

The sophisticated LP looks at both, plus DPI (distributions to paid-in: cash actually returned, which cannot be manipulated), RVPI (residual value, i.e. the unrealised marks) and TVPI (total value, DPI + RVPI). DPI is the honest number, because unrealised marks are the GP's own opinion of what it owns.

Does PE outperform?

The evidence is contested. Gross returns have historically beaten public equity; net of fees, the average fund roughly matches public markets on a risk- and leverage-adjusted basis (the public market equivalent, or PME, is the right comparison and it accounts for the fact that an LBO is a levered equity position). Top-quartile managers genuinely and persistently outperform; the average does not. So manager selection, and access to the best managers, is the entire game for an LP.

FR ↔ EN

capital-investissement = private equity · société de gestion = the GP/management company · commission de gestion = management fee · carried interest = carried interest (used in French too) · TRI = IRR.

Venture capital and cap tables

How startups are financed and how ownership gets diluted. Directly relevant to your own company, not just to a job.

Venture capital funds companies that cannot service debt, in exchange for equity, accepting that most investments will fail.

The power law

A venture portfolio's return is dominated by a small number of enormous winners. A typical fund: half the investments return nothing, a third return capital or a small multiple, and one or two return 20-50x and carry the entire fund. This shapes every VC behaviour: they optimise for the size of the possible outcome rather than the probability of success, which is why "how big can this get" matters more to them than "how likely is this to work", and why a business with a solid, bounded outcome is unfundable by venture even when it is a good business.

The vocabulary you must own

Pre-money valuation = value agreed before the new money

Post-money = pre-money + investment

Investor ownership = investment / post-money

Instruments

• Priced equity round: preferred shares with a defined valuation, a term sheet and, usually, a 1x non-participating liquidation preference (in a sale, the investor takes the greater of their money back or their pro-rata share).
• SAFE (US) / convertible note: money now, valuation later, converting at the next priced round with a discount (typically 20%) and/or a valuation cap. Fast and cheap, but stacking several SAFEs before a priced round creates dilution founders systematically underestimate.
• BSA AIR is the common French equivalent of a SAFE, and it is what you would actually use here.

Liquidation preference, which decides who gets paid

Non-participating 1x: the investor takes the higher of their investment back or their converted pro-rata share. Founder-friendly and the market standard.

Participating ("double dip"): the investor takes their money back and shares in the remainder. Materially worse for founders and a red flag in a term sheet.

Multiple preferences (2x, 3x): appear in down markets and in rescue rounds. In a modest exit they can leave common shareholders with nothing.

The option pool shuffle, the most common founder mistake

Investors typically require an option pool of 10-15% to be created for future hires from the pre-money valuation, meaning founders bear the entire dilution. On a €5m pre-money with a 15% pool, the effective pre-money is closer to €4.25m. Negotiating whether the pool comes from pre- or post-money is worth real percentage points, and most first-time founders do not know to ask.

Anti-dilution

Protects investors if a later round prices below theirs. Full ratchet reprices all their shares to the new lower price and is brutal. Broad-based weighted average is the market standard and far gentler. In a down round these clauses determine who actually owns the company afterwards.

How VCs value what has no cash flows (level 2's machinery does not apply)

1. The VC method: forecast an exit value (usually an EBITDA or revenue multiple at exit), discount at a target return of 30-60% reflecting the failure rate, then work back to a present value and an ownership requirement.

2. Comparable rounds: what similar companies raised at, which is pure pricing, not valuation.

3. Scorecard / Berkus: qualitative frameworks for pre-revenue companies.

4. Damodaran's approach: a real DCF with an explicit probability of failure applied, which is more honest and almost never used in practice.

FR ↔ EN

capital-risque = venture capital · valorisation pré-monnaie = pre-money valuation · table de capitalisation = cap table · BSA AIR = the French SAFE equivalent · préférence de liquidation = liquidation preference · relution/dilution = accretion/dilution.

Valuing young and high-growth companies

Where the standard machinery breaks, and where Damodaran is most useful. The lane you personally lean toward.

Everything in level 2 assumed a history to extrapolate and positive cash flows to discount. Young companies have neither, and the standard responses (use a multiple, use a comparable round) are pricing, not valuation. Damodaran's method is to keep valuing properly and be explicit about the uncertainty.

The four problems

1. No history, so no base year and no trend.

2. Negative earnings, so multiples on profit are undefined and the tax computation must handle loss carry-forwards.

3. Dependence on survival, since a large fraction of these companies simply fail.

4. Enormous dilution ahead, because reaching the modelled scale requires capital not yet raised.

The method: value the business it will become, then adjust for the chance it does not get there

Step 1 · Start with the story, not the spreadsheet. What market will this serve, how large is it, what share can it plausibly take, and what margin does that business earn at scale? The narrative comes first and the numbers implement it (lesson 3.5).

Step 2 · Work backwards from a terminal year. Rather than growing from a tiny base, define the business in year 10: revenue, operating margin, capital intensity. Then interpolate the path from today to there. This forces the implied market share and margin into the open, where they can be challenged.

Step 3 · Handle the losses properly. No tax while losses accumulate; carry the net operating losses forward and shelter early profits with them. Getting this right is worth real value and most models do it wrong.

Step 4 · Reinvest for growth. Use the sales-to-capital ratio: every euro of new revenue requires a certain amount of invested capital. It is the only sensible way to size reinvestment when there is no capex history.

Step 5 · Discount at a rate that declines over time. A pre-revenue company is riskier than the mature business it may become, so the cost of capital should start high (perhaps 12-15%) and fall toward the sector average as the business matures.

Step 6 · Apply an explicit probability of failure.

Value = (Going-concern DCF value × P(survive)) + (Liquidation value × P(fail))

This is the step that distinguishes a real valuation from a hopeful one, and it is why start-up valuations should be presented as a distribution rather than a number.

Step 7 · Adjust for dilution. Value per share today must account for the shares that will be issued to fund the path to the terminal year.

The pricing reality you must also acknowledge

None of the above determines what a Series B actually prices at. That is set by the last comparable round, by how much capital is chasing the sector, and by competitive dynamics between funds. Both games are being played simultaneously (lesson 3.5), and a professional says which one they are playing.

Applying this to yourself

Your own studio is a young company with real revenue, real clients and no external capital. Valuing it properly, revenue path, sustainable margin, the capital it needs, an appropriate discount rate for a business dependent on a small number of clients, is the single most useful exercise you can do with this lesson, and it doubles as the answer to "tell me about a valuation you have done" in an interview.

FR ↔ EN

jeune entreprise = young company · déficit reportable = loss carry-forward · probabilité de défaillance = probability of failure · dilution future = future dilution.

Advanced modelling craft

Three statements, fully integrated, circularity handled, scenarios switchable. The artefact that proves you can actually do the job.

A three-statement model is the professional deliverable: forecast income statement, balance sheet and cash flow, fully linked, so that changing any assumption updates everything and the balance sheet still ties.

The build order (do it in this sequence or you will chase errors for hours)

1. Assumptions tab, everything hardcoded once, in blue.

2. Revenue build from drivers.

3. Income statement down to EBIT.

4. Supporting schedules: fixed assets (opening PP&E + capex − depreciation = closing), working capital (driven by days), debt (opening + drawings − repayments = closing), equity (opening + net income − dividends = closing).

5. Link the schedules back into the income statement (depreciation, interest) and the balance sheet.

6. Cash flow statement, built from the movements in the schedules, never typed independently.

7. Balance sheet, with cash coming from the cash flow statement.

8. The check row. Assets − liabilities − equity = 0, visible, every period.

Circularity, and how to handle it

Interest depends on the average debt balance; the debt balance depends on how much cash flow is available to repay; available cash flow depends on interest. A genuine circular reference.

Three solutions:

• Iterative calculation (File > Options > Formulas > Enable iterative calculation, 100 iterations). Excel resolves it. Simple, and fragile: one error anywhere propagates into #REF! across the model and it is painful to unwind.
• A circuit breaker: a switch cell that, when set to 0, replaces the circular interest calculation with zero, breaking the loop so you can find the underlying error. Always build one.
• Opening-balance interest: calculate interest on the opening debt balance rather than the average. No circularity at all, slightly less precise, and entirely acceptable in most contexts. Many practitioners prefer it for exactly this reason.

The revolver as the balancing item

The cash sweep and revolver mechanism is what makes a model self-balancing: if the company generates surplus cash it repays the revolver, and if it runs short it draws. Build it with MIN and MAX so it can never draw more than the facility or repay more than is outstanding, and so cash never goes negative.

Scenarios

Use a single scenario switch cell (1 = base, 2 = upside, 3 = downside) and CHOOSE or INDEX to select assumption sets. Never maintain three copies of the model: they diverge within a day. A live scenario switch that changes every driver at once is a strong signal of modelling maturity.

Sensitivity

One and two-variable data tables on the outputs that matter: enterprise value against WACC and growth, IRR against entry and exit multiples, EPS against volume and price. Every model ships with at least one.

The error-checking discipline

• The balance check, visible and conditionally formatted.
• Cash never negative in any period.
• Debt never negative.
• Margins and growth rates within plausible bounds (build a "reasonableness" block that flags anything outside a range).
• The sum of the cash flow statement ties to the change in the balance sheet cash line.

Why this level of care pays

Modelling tests are a standard part of assessment centres, and they are marked on structure and checks as much as on the answer. More importantly, an unchecked model gives you a number you cannot defend, and once you have presented a number you cannot defend, nobody trusts the next one either.

FR ↔ EN

modèle financier = financial model · référence circulaire = circular reference · hypothèses = assumptions · scénarios = scenarios · contrôle d'équilibre = balance check.

Capital allocation in practice

The CFO's job, and the single biggest determinant of long-run shareholder returns after the business itself.

Everything in this curriculum comes together in one recurring executive decision: given the cash we generate, where does it go?

The five uses of cash: reinvest organically, acquire, pay down debt, pay dividends, buy back shares. Over ten years, how a management team allocates between these determines shareholder returns more than almost anything else except the quality of the underlying business. Yet most executives are promoted from operations, marketing or engineering, and have never been trained in it. This is the central argument of The Outsiders, and it is why capital allocation is a competence you can visibly demonstrate.

The decision rule, and the honest complication

Reinvest where the marginal return exceeds the cost of capital, return the rest. The complication is that marginal return is not average ROIC: the tenth store in a city earns far less than the first, so incremental returns decline. Good companies measure the return on the last euro invested, not the average across the portfolio, and that distinction is what separates disciplined allocators from ones who keep expanding because the average still looks fine.

The budgeting process, and its pathologies

Most companies allocate by last year's budget plus or minus a percentage, which entrenches historical decisions. The pathologies: the division that shouts loudest gets the capital; a single corporate hurdle rate is applied across divisions of different risk (lesson 2.3); projects are approved on optimistic forecasts and nobody performs a post-audit. The single highest-value practice is the post-completion audit: compare actual returns to the projections that justified the investment. Almost nobody does it, and the knowledge that it will happen changes forecasting behaviour immediately.

Working capital as a source of capital

Level 1.3 showed that a reduction in days is a permanent release of cash. It is the cheapest capital available to any company: no interest, no dilution, no approval process. It is also usually the most neglected.

Treasury

Managing liquidity, funding and financial risk: cash pooling across entities, maintaining committed but undrawn facilities as insurance, laddering debt maturities so refinancing is never concentrated, and hedging FX and interest rate exposure where it protects covenant compliance and planning certainty rather than as a directional bet.

The metrics that align behaviour

Choosing what to measure decides what people do. ROIC-based incentives drive capital discipline; EPS-based incentives encourage buybacks and acquisitions regardless of price; revenue-based incentives drive growth at any cost. Economic profit (NOPAT − WACC × invested capital) is the metric most aligned with value creation, because it charges divisions for the capital they use, and its absence is why so many businesses grow themselves into value destruction.

How to assess a management team, in four questions

1. What has their incremental ROIC been over five to ten years?

2. Have their acquisitions earned above the cost of capital, on their own original projections?

3. Do they buy back stock counter-cyclically (when it is cheap) or pro-cyclically (when cash is abundant)?

4. Is compensation tied to returns on capital, or to size?

Those four questions, answered with numbers from the filings, constitute a management assessment better than any meeting.

FR ↔ EN

allocation du capital = capital allocation · budget d'investissement = capital budget · trésorerie = treasury · création de valeur = value creation · profit économique / EVA = economic profit.

Distress and restructuring

What happens when the debt from level 4 cannot be paid. Where value moves fastest and where the deepest analysis pays.

When a company cannot service its debt, the capital structure of lesson 4.6 stops being a financing arrangement and becomes a negotiation about ownership.

The two questions in every restructuring

1. Is this a liquidity problem (a viable business with a maturity it cannot refinance) or a solvency problem (the business is worth less than its debt)? Liquidity problems are solved with new money or an extension; solvency problems require debt to be written down or converted.

2. Where does value break? Compute the enterprise value of the restructured business, then walk down the claims in priority order until the value runs out. The tranche where it runs out is the fulcrum security, and it is the one that converts into equity and ends up owning the company.

The routes

• Out-of-court (amend and extend / consensual restructuring): faster, cheaper, preserves the business's relationships, but requires very high consent thresholds (often 90-100% of a bond class) so a single holdout can force a formal process.
• Formal proceedings. In France: procédure de sauvegarde (a debtor-friendly, pre-insolvency protective procedure), redressement judiciaire (reorganisation once payments have ceased) and liquidation judiciaire. In the US: Chapter 11 (reorganisation, debtor in possession, with an automatic stay) and Chapter 7 (liquidation). The US regime is materially more debtor-friendly, which is why large European groups sometimes restructure through English schemes of arrangement or the newer EU restructuring directive frameworks.
• Distressed M&A: a sale of the business or its assets, sometimes pre-packaged so the buyer is lined up before the filing.

Absolute priority

In liquidation, claims are paid in strict order: secured creditors up to their collateral, then administrative and preferential claims, then unsecured, then subordinated, then preferred equity, then common. In a reorganisation, priority is frequently violated in practice, because existing equity or junior creditors have nuisance value and can delay a plan, so they extract something to consent. That gap between theory and negotiated outcome is where distressed investors make money.

The distressed investor's move

Buy the fulcrum security at a discount, convert it into equity through the restructuring, and own the recapitalised business at a low entry price. It requires legal analysis (security packages, intercreditor terms, guarantee structures) as much as financial analysis, which is why distressed teams pair credit analysts with restructuring lawyers.

Early warning signs, in the order they usually appear

Covenant headroom narrowing quarter by quarter · a maturity within 18 months with no refinancing announced · a drawn revolver · rising DPO (stretching suppliers) · asset disposals to fund operations · the auditor's going-concern paragraph · rating downgrades · bonds trading below 70 cents. The bond price is usually the earliest honest signal, well before any of the narrative changes.

Why this matters even if you never work in distressed

It is where the levels connect: the accounting of level 0 tells you the business is failing, the leverage of level 1 tells you it is fragile, the capital structure of level 4 tells you who controls the outcome, and the valuation of level 2 tells you where value breaks. It is the best test of whether you have integrated the curriculum.

FR ↔ EN

difficultés financières = financial distress · procédure de sauvegarde = safeguard proceedings · redressement judiciaire = judicial reorganisation · liquidation judiciaire = judicial liquidation · créancier = creditor · abandon de créance = debt forgiveness.

Ethics, compliance and governance

The emlyon core course, the AMF certification ground, and the thing that ends careers when it is treated as paperwork.

This is a required first-year course at emlyon and the substance of the AMF certification, which the school prepares you for. It is also the part of finance where being merely technically excellent is not sufficient.

Market abuse: the two offences

Insider dealing. Using inside information (precise, non-public, price-sensitive) to trade, to recommend a trade, or to disclose it improperly. Under the EU Market Abuse Regulation (MAR, 596/2014, applicable since 2016) this is a criminal and administrative offence across the EU. Note what "precise" means: information about a process, such as an ongoing negotiation, can be inside information at an intermediate stage, well before any deal is agreed. Note also that the attempt is caught, and that passing the information on (tipping) is an offence even if you never trade.

Market manipulation. Transactions or orders that give false or misleading signals, secure a price at an artificial level, or use fictitious devices. This covers wash trades, spoofing (entering orders with no intention to execute), painting the tape, and the dissemination of false information including through media and social channels.

The market abuse infrastructure you must know by name

• Insider lists: issuers must maintain lists of everyone with access to inside information.
• Wall crossing: the formal process of bringing someone inside, with a record.
• Chinese walls / information barriers: separating advisory (which has inside information) from markets and research.
• Restricted and watch lists: securities on which the firm's staff may not trade.
• Personal account dealing rules: pre-clearance and holding periods for employees' own trades.
• STOR: suspicious transaction and order reports, which firms must file.

MiFID II, the framework governing investment services in the EU: best execution, product governance and target markets, suitability and appropriateness assessments, inducement rules, the unbundling of research from execution, and extensive transaction reporting. If you work in markets in Europe, this is the regime you operate inside daily.

The AMF is the French market regulator. The AMF certification ("certification professionnelle AMF") is a required examination for many market-facing roles in France, covering the regulatory environment, market abuse, client relationships, instruments and compliance. emlyon prepares students for it, alongside Bloomberg certification and CFA Levels I and II.

Governance

The board's role, the separation of chair and chief executive, independent directors, audit and remuneration committees, and the underlying principal-agent problem: managers act on behalf of shareholders but have their own interests, and governance is the set of mechanisms that narrow that gap. In France, the AFEP-MEDEF code applies on a comply-or-explain basis to listed companies, and the two-tier structure (conseil de surveillance and directoire) is an available alternative to the unitary board.

ESG and sustainable finance, which emlyon puts at the centre of its programme: the EU taxonomy defining sustainable activities, the SFDR disclosure regime for financial products, and the CSRD requiring extensive sustainability reporting from large companies. The intellectual content worth having: distinguish values-based exclusion from risk-based integration, since the first is a preference and the second is a claim about returns, and be honest about greenwashing risk and the weak correlation between competing ESG rating providers.

The professional posture, which matters more than the rules

Most career-ending failures in finance are not from misunderstanding a regulation; they are from a small compromise made under pressure that becomes precedent. The practical test is simple and reliable: would you be comfortable if this decision, and your reasoning for it, were published? If the answer requires explanation, escalate it instead.

FR ↔ EN

délit d'initié = insider dealing · manipulation de cours = market manipulation · muraille de Chine = Chinese wall · déontologie = professional ethics/compliance · gouvernance d'entreprise = corporate governance · AMF = the French financial markets regulator.

The interview

The map of what is actually asked, the six questions you must own, and how to answer so it sounds like understanding rather than recall.

Finance interviews are unusually predictable. The technical universe is roughly 200 questions and about 30 of them account for most of what is asked.

The structure of a technical interview

1. Accounting (levels 0-1): walk me through the three statements, the linkage questions, working capital, earnings quality.

2. Valuation (levels 2-3): the three methodologies, DCF mechanics, WACC, terminal value, enterprise versus equity value, multiples.

3. Deals (level 4): accretion/dilution, LBO mechanics, the paper LBO.

4. Markets (level 5), for markets roles: rates, options, portfolio construction, plus "what are you watching right now".

5. Behavioural and fit: why finance, why this firm, walk me through your CV, a time you failed.

6. The market question: a stock you like, a deal you have followed, what you would do with a million euros.

The six you must own completely

1. Walk me through the three financial statements, and depreciation increases by 10.

2. Walk me through a DCF.

3. What is the difference between enterprise value and equity value, and why do we subtract cash?

4. Walk me through an LBO / do a paper LBO.

5. Is this deal accretive or dilutive?

6. Which of the three valuation methodologies gives the highest value, and why?

Answer 6 correctly, because it is a genuine test: precedent transactions are usually highest (control premium and synergies), then a DCF can be highest or lowest depending on assumptions, then trading comps. The good answer says "it depends, and here is what it depends on", then gives the usual ordering with the reason.

How to answer (the delivery matters as much as the content)

• Structure out loud. "Three reasons" then give three. The interviewer is assessing whether you organise your thinking, and this is visible in the first five seconds.
• 60 to 90 seconds. Longer and you are lecturing; shorter and it sounds thin.
• Lead with the mechanism, not the definition. "Enterprise value is financing-independent, which is why..." beats reciting a formula.
• Volunteer the caveat. "That is the mechanical answer, but accretion is not value creation." This single habit is the strongest available differentiator.
• Say "I do not know" cleanly, then reason toward it. Bluffing is transparent and it is the fastest way to lose the room. "I have not seen that, but I would think about it as follows" is a perfectly strong answer.

Your specific profile, and how to frame it

You are an INSA engineer who left engineering, runs a real business, and is entering an MSc in Finance. Every interviewer will probe the pivot. Frame it as accumulation, not abandonment: the quantitative training is why the mathematics of valuation and derivatives is easy for you; running a business is why you understand working capital, client concentration and cash conversion as lived facts rather than definitions; and the MSc is the deliberate acquisition of the vocabulary and institutional knowledge you did not have. Then have one number ready from your own business, a cash conversion cycle you fixed, a margin you improved. Concrete beats narrative every time.

The stock pitch, in 90 seconds

What the company does (1 sentence) · the thesis in one line · three supporting points, each with a number · the valuation and what the market is missing · the main risk and what would prove you wrong. Ending on the risk and the falsifier is what makes it sound like analysis rather than advocacy.

Preparation that actually works

Say the answers out loud, recorded, and listen back. Reading them silently does not build the retrieval path you need under pressure. Do the paper LBO on paper, with a timer. Have your one-page company brief from lesson 1.6 and your DCF from lesson 2.7 ready to discuss in detail, because "tell me about a valuation you have done" is the question your entire summer answers.

FR ↔ EN

entretien technique = technical interview · questions de fit = behavioural questions · pitch d'action = stock pitch.

The capstone: the investment memo

One document that proves everything. This is what you show, and the artefact you defend for the rest of the year.

Everything in this curriculum converges on one deliverable: a full valuation and investment recommendation on a real company, written to a professional standard, that you can defend under challenge.

Why this artefact and not a certificate

Anyone can list courses. Very few candidates can hand over a model and a memo and answer questions about every assumption in them. It is the single most efficient proof of competence available to you, it doubles as the answer to "tell me about a valuation you have done", and building it forces you to discover exactly which parts of the curriculum you only think you know.

The structure (8 to 12 pages, plus the model)

1 · Recommendation and summary (half a page). The conclusion first: buy, sell or hold, the target value, the current price, the upside or downside, and the three reasons. Written so that someone who reads only this page has your entire argument.

2 · The business (1-2 pages). What it sells, to whom, through what channel, at what economics. Segments with revenue and margin. The unit economics. Written in your own words, not the company's.

3 · The industry and competitive position (1-2 pages). Market size and growth, the competitive structure, where the pricing power sits and why, and the specific mechanism of any advantage: switching costs, network effects, scale, brand, regulation. "They have a strong brand" is not an argument; "customers pay a 14% premium and repurchase at 62% versus a 41% category average" is.

4 · The financial analysis (2 pages). Levels 0 and 1 applied: margin structure and trend, ROIC against WACC, working capital and cash conversion, leverage and covenant headroom, and an earnings quality assessment. Charts, not tables of everything.

5 · The valuation (2-3 pages). DCF with explicit assumptions, sensitivity table and the terminal share of value. Trading comps and precedent transactions. A football field. The reverse DCF showing what the market is implying, which is the section that most impresses.

6 · The thesis (1 page). What you believe that the market does not, and why. This is the heart of the memo. "The market is extrapolating a temporary margin compression from a raw material spike that the company's contracts reprice with a two-quarter lag, and the reset happens at the January renewal."

7 · Risks and what would change your mind (half a page). Three to five specific risks, each with the observable event that would falsify your thesis. Ending here, rather than on the recommendation, is what makes it read as analysis.

8 · Appendix. The model, the assumption tables, the peer set.

The standard to hold yourself to

• Every number has a source and every assumption is defended in one sentence.
• No sentence survives that could be written about any company in the sector.
• The thesis is falsifiable, with the falsifier named.
• Someone reading only the first half-page gets the whole argument.
• You can answer "why?" three times on any assumption before running out of reasons.

Then defend it

Give it to someone and ask them to attack it. Every hole they find is a hole an interviewer would have found. Rewrite. This iteration is where most of the learning actually happens, and it is the difference between a document you have written and a position you hold.

After 1 October

The memo is not finished when the intake starts, it is the beginning of the second phase. Update it each quarter as results come out. Was your thesis right? Where were your assumptions wrong, and why were they wrong? A memo with four quarters of tracked, honest revisions is a far more powerful artefact than a fresh one, because it demonstrates the thing employers cannot test for in an interview: that you actually follow through.

FR ↔ EN

note d'investissement = investment memo · thèse d'investissement = investment thesis · recommandation = recommendation · risques = risks.