The Ledger

Chapter 1 · The Firm

What, how and why — the two questions a CFO ever asks

Think like a CFO. When you are spending ask: invest or divest? tangible or intangible? and what is your cost of capital? When you are raising ask: internal or external? debt or equity? short-term or long-term?

The circuit of cash

Click each numbered flow. This single loop is the whole subject in one picture.

Which wrapper? Forms of business

The choice is a trade-off: limited liability and easy access to outside capital on one side, tax simplicity and control on the other. Size, capital needs and liability exposure decide it.

Whose interests? The goal, and the problem

The goal: maximise market value. But shareholders are not identical — some want cash now, some want wealth later. Does that wreck the objective? No, as long as the financial market works. Meet the Ant (saver) and the Grasshopper (spender): a well-functioning capital market lets each convert value across time however they like, so both agree the firm should simply make the pie as big as possible.

The agency problem. Shareholders want market value maximised — but managers run the firm. That is the separation of ownership and control: shareholders are principals, managers are agents, and their interests can drift apart. Two consequences you will meet all term: incentives matter (compensation must be designed so managers' decisions aren't distorted), and some inefficiency is unavoidable because managers always know more than investors do.

The opportunity cost of capital

F&H Corp's CFO defends heavy investment in a declining business: "we are confident of returns around 8% on investment. That's a far better return than F&H earns on its cash holdings" — which sit in near risk-free government securities yielding 4%.

Is 8% better than 4%? Not necessarily. The cost of capital is not what your own cash currently earns. It is what investors could earn elsewhere in the market on an investment of the same risk. A risky 8% encabulator project must be judged against the return available on comparable-risk securities — which may be well above 8%. The 4% T-bill rate is only the right hurdle for a risk-free project.

Chapter 2 · The Reports

Three statements, one story about cash

The three activities

A real statement of cash flows just adds the three up, adjusts for FX, and reconciles opening to closing cash. Nothing more mysterious than that:

Read it as a sentence: this company burned cash on investment, and funded it by raising far more from investors than its operations produced. That is the signature of a fast-growing firm — and a fragile one if markets close.

The balance sheet (Home Depot, fiscal 2017, $ millions)

Notice the equity line: only $1,454 million. Home Depot bought back so much of its own stock (treasury stock −$48,762m) that book equity is nearly wiped out. Remember that number — in Chapter 3 it makes ROE and the debt ratios look spectacular and terrifying at the same time. Book equity is an accounting residue, not a market value.

The income statement — walking down to net income

Two lines matter more than the rest. EBIT ($14,755m) is what the assets earned before anyone argues about financing — it belongs to debt and equity together. Net income ($8,630m) is what is left for shareholders after the lenders and the tax authority are paid.

Chapter 3 · Value Created

Did we actually make our investors richer?

Here is the map of every ratio in this course. Click a box to jump to the chapter that covers it.

Market measures

Market capitalisation is the total market value of equity. Home Depot at the close of fiscal 2017: 1,170 million shares × $204.92 = $239,756 million.

An alternative MVA definition uses the whole firm: market value of debt plus equity, minus the book value of total capital. And note how the buyback-shrunken book equity inflates that 164.9 — a warning that ratios built on book values can be almost meaningless.

Economic value added — profit after all costs

Ordinary profit deducts operating costs. It forgets the most expensive input of all: the capital itself. EVA (also called residual income) fixes that.

Return on capital says the same thing as a rate: ROC = NOPAT ÷ total capital = 9,317 ÷ 26,682 = 34.9%. Which lets you rewrite EVA as a spread:

EVA lab

Drag the three levers. Watch how a perfectly profitable-looking firm destroys value the moment its cost of capital rises above its return.

Accounting rates of return — and their traps

Why ROE is the least trustworthy of the three. It is measured against book equity, so a firm can inflate it almost at will by borrowing and buying back shares — exactly what makes Home Depot's 199% meaningless as a measure of skill. ROA and ROC put debt and equity investors on the same footing and are far harder to game.

Three problems that apply to EVA and every accounting return:

Chapter 4 · The Du Pont Lens

Where does a return actually come from?

Efficiency: how hard are the assets working?

Use the average whenever assets moved a lot during the year — a mid-point avoids flattering a firm that grew its balance sheet late in the period. Be consistent, and say which you used.

Turnover and period are the same fact told two ways: period ≈ 365 ÷ turnover. Home Depot collects in a week because most customers pay at the till — a supplier selling on 60-day terms would look completely different, and neither is "better" outside its industry.

Profitability: how much sticks per dollar of sales?

Prefer the operating profit margin. Plain profit margin subtracts interest, so it punishes a firm merely for financing itself with debt — two identical businesses would score differently purely because of their capital structure. Adding back after-tax interest measures the business, not the balance sheet.

The Du Pont formula

Every firm would love a high ROA, and competition stops them. The two levers trade off against each other: fast-food chains have high asset turnover and thin margins; classy hotels have low turnover and fat margins. Move along the curve — but you rarely move the curve itself.

Du Pont explorer

Move the sliders. The dot is your firm; the curves are constant-ROA contours. Notice you can reach 20% ROA from opposite corners of the map.

The merger trap

Firms often buy a supplier hoping to capture the supplier's profit as well as their own. The margin duly rises — and, unless the buyer has genuine skill in running the new business, the extra assets drag turnover down by exactly as much:

Margin 20% → 30% looks like a triumph. Turnover 0.50 → 0.33 quietly cancels it. ROA is unchanged at 10%. Vertical integration moves profit between line items; it does not, by itself, create value.

Chapter 5 · Leverage, Liquidity & Growth

Can they pay next decade's debts — and next month's bills?

Leverage: how much of the firm belongs to lenders?

Use the total versions when a firm is a regular short-term borrower. And treat these particular numbers with care: they are extreme only because buybacks gutted book equity. On market values Home Depot is conservatively financed. Some firms genuinely do run this hot on purpose — companies taken private in a leveraged buyout (LBO) typically issue enormous amounts of debt.

Coverage ratios ask the question a lender actually cares about: how many times over could this year's earnings pay this year's interest? Adding depreciation back gets closer to the cash available. Fourteen times over is comfortable — which is why book leverage ratios of "94%" should never be read on their own.

Leverage and ROE: the extended Du Pont

Borrowing does two opposite things to shareholders: interest payments reduce net income, but there are fewer equity holders to share what remains. Which effect wins? Split ROE into four:

The middle two multiply to ROA — unaffected by the financing mix. The outer two both depend on leverage and pull in opposite directions: the leverage ratio rises with debt, the debt burden term falls. The net effect on ROE is ambiguous, which is precisely why ROE is a poor scoreboard and why Modigliani and Miller (Chapter 8) become necessary.

Growth: how fast can we expand on our own money?

If net assets are proportional to sales, then growing sales requires assets in proportion:

So a firm can grow faster without outside capital if it ① ploughs back a high share of earnings, ② earns a high ROE, and ③ carries a low debt-to-asset ratio. In practice both rates are slightly circular — ROE itself depends on the growth rate — so you solve for the pair that leaves leverage unchanged.

Liquidity: can we pay this month?

Net working capital = current assets − current liabilities = 18,933 − 16,194 = $2,739 m, which is 6.2% of total assets.

The ladder strips out progressively less liquid assets. The gap between 1.17 and 0.34 is inventory: Home Depot's ability to pay depends on selling 69 days of timber and paint.

Two health warnings. ① Changes in the current ratio mislead: borrow a large sum from the bank and park it in marketable securities, and both current assets and current liabilities rise — net working capital is unchanged but the ratio moves. (Hence the practice of netting short-term investments against short-term debt.) ② The cash ratio ignores reserve borrowing power — a firm's ability to borrow on short notice, which is real liquidity even though no ratio shows it.

Reading ratios like an analyst

Home Depot's own history tells a story in three acts: 1999–2007, a steady decline in the ability to generate sales from assets, largely offset for a while by a rising profit margin; 2008, a sharp fall in margin and a collapse in ROA; 2009–2017, both turnover and margin rising every single year.

And the golden rule: every ratio must be read against industry norms. Median asset turnover runs about 1.96 in retail but 0.26 in oil and 0.28 in utilities; median market-to-book is 3.55 for beer and liquor but 1.17 for steel. A "bad" number in one industry is an excellent one in another.

Chapter 6 · Efficient Markets

What is already in the price?

Weak form: the analyst versus the coin

Two analysts forecast Microsoft, Marks & Spencer, Philips and Rio Tinto. Analyst 1 has every scrap of historical price data. Analyst 2 tosses a coin. Who wins? Plot each stock's return on day t against its return on day t+1 and you get a shapeless cloud — the correlations are −0.037, −0.020, +0.004, +0.010. Effectively zero.

Why patterns self-destruct. Suppose everyone knew Microsoft would be $80 next month while it trades at $40 today. Nobody would sell at $40. The price would jump to (nearly) $80 now. The moment a cycle becomes apparent to investors, their own trading destroys it. Predictable patterns are self-erasing — which is exactly why the leftover price path looks random.

Semistrong form: measuring the reaction

Cumulative abnormal returns for 8,668 US takeover targets, 1975–2016. The target's price jumps on the announcement — and then nothing.

Two lessons live in that chart. The jump is enormous and instantaneous — about +25% on the day after announcement. And the line is flat afterwards: by the time you read the news, the opportunity is gone. (The gentle drift before day zero is the uncomfortable part — some information leaks.)

How long do you really have? Trump announced "reciprocal tariffs" at about 4:20 p.m. EST on 2 April 2025. Suppose you were standing next to him. E-mini S&P 500 futures spiked, then collapsed roughly 3% within minutes of the boards being shown. The window between hearing news and it being in the price is measured in seconds, not days.

Strong form: can the professionals beat it?

Most studies find that mutual funds earn less than their benchmark portfolios after expenses, and roughly match them before expenses. Diversified equity funds underperformed the Wilshire 5000 in about 60% of the years from 1971 to 2017. And you cannot solve it by picking the smart ones: a top-quartile fund in one year has no more than an average chance of being top-quartile the next.

Where the hypothesis cracks: bubbles

Efficiency is supported by mounting evidence — and it still fails from time to time. The strongest challenge is the observation of bubbles.

Neither episode looks like a market calmly discounting information. Which raises the question Chapter 7 answers: if prices are set by people, and people are not always rational, what happens then?

Chapter 7 · The Human Factor

Four questions about your own head

Chapter 8 · Modigliani–Miller

You cannot make a pie bigger by slicing it differently

The arbitrage: four strategies

Firm U is unlevered, so E_U = V_U. Firm L is levered, so E_L = V_L − D_L. Both generate the same operating profits. Buy 1% of each and compare.

Strategies 1 and 2 give an identical return, so they must cost the same: V_U = V_L. Strategies 3 and 4 also give identical returns, so again V_U = V_L. If the two firms ever traded at different prices you could buy one, short the other, and pocket the difference for zero risk. Investors would do exactly that until the gap closed.

The same proof without any hand-waving about risk

Let firm L have a random cash flow R and a debt repayment obligation D, and set the risk-free rate to zero so the discount factor is 1. Debt holders are paid first and capped; equity holders get whatever is left over.

Because min(R,D) + max(0, R−D) = R for every outcome, the two claims always add back up to the whole cash flow. Debt and equity are just two ways of cutting one random variable in half.

The case of Macbeth Spot Removers

Macbeth has no leverage, pays out all operating income, and faces no taxes. It has 1,000 shares at $10 = $10,000 of equity, and expects income of $1,500 a year in perpetuity — though that income is not certain. The board is considering issuing $5,000 of debt at 10% and using the proceeds to repurchase 500 shares.

The argument — and the flaw

Supporters of the repurchase say: "If income exceeds $1,000, leverage increases the return to equity holders. If it is below $1,000, leverage reduces it. Since we expect income above the $1,000 break-even, we can best help shareholders by going ahead with the $5,000 debt issue." Expected EPS does rise from $1.50 to $2.00. So what is wrong?

Shareholders can borrow on their own account. Suppose an investor puts up $10 of their own money, borrows a further $10 at the same 10%, and buys two unlevered Macbeth shares:

That is exactly the payoff of one share in the levered company — 0/10/20/30%. If investors can manufacture leverage themselves at the same rate, they will not pay a premium for a firm that does it for them. So the share price stays at $10 either way, and the firm's total value is unchanged. Homemade leverage is the whole argument.

Proposition 2: what leverage does change

Proposition 2: the expected return on the common stock of a levered firm increases in proportion to the debt–equity ratio, measured in market values; and the rate of increase depends on the spread between the expected return on a portfolio of all the firm's securities and the expected return on the debt.

Is that 20% a free lunch? No — it is compensation for risk. Watch what a $1,000 fall in operating income does:

Leverage doubles the sensitivity of shareholder returns to business fortunes. Higher expected return, proportionally higher risk, same value. Shareholders are indifferent.

Watch out for hidden leverage

Debt does not always announce itself. Reeby Sports is considering a carbon-fibre Bocce shoe: $500,000 of up-front marketing plus $500,000 of equipment, with a company cost of capital of 10%.

The CEO calls to cancel the equipment order. The salesperson, anxious to keep the sale, offers: buy now, pay later — five fixed payments of $122,000 a year instead of $500,000 today.

A rejected project became profitable without a single operating number changing. Is the deal acceptable now? Still no. The mistake is the discount rate. Those five $122,000 payments are not risky project cash flows — they are debt service, a fixed contractual obligation. Discounting them at the project's 10% risky rate understates what they really cost. Value the loan separately at Reeby's actual borrowing rate: at 5%, the payments are worth 122 × 4.33 = $528k in present value for $500k of equipment. That $28k of hidden financing cost more than wipes out the apparent $23k gain, and the project is negative-NPV again — exactly as it was before.

Hidden leverage is everywhere: long-term leases, long-term contracts with suppliers, pension liabilities, and liabilities for employees' post-retirement health care. Each is a stream of fixed obligations that behaves exactly like debt — and each will flatter a project or a balance sheet if you forget to treat it as such.

So why does corporate finance exist at all?

MM says firm value is determined on the left-hand side of the balance sheet by real assets — not by the proportions of debt and equity issued to buy them. If that is literally true, financing decisions are irrelevant and this course could stop here. It does not stop here, because MM's assumptions are what break in reality: no taxes (Chapter 10 kills that one), no costs of financial distress, no information asymmetry, no agency conflicts, and investors who borrow on exactly the firm's terms. MM is not a description of the world — it is a checklist of the only things that can possibly make financing matter.

Chapter 9 · Cost of Capital

The hurdle rate — and where beta comes from

Weighting it up

Estimating the cost of equity

The cost of debt is usually easy — look at the yield. Equity has no promised return, so we need a model. The capital asset pricing model:

Beta is the slope of a regression of the stock's returns on the market's. Two things to keep your eye on: the standard error (how much the estimate could be off) and R² (how much of the stock's total risk is market-driven at all).

The ranking is stable and intuitive — a cyclical steelmaker at the top, a regulated utility at the bottom. But look at U.S. Steel's 2013–17 estimate: 3.01 with a standard error of 0.93, so the true beta is plausibly anywhere from about 1.2 to 4.8. Never treat a single regression beta as a fact. Industry averages are usually more reliable than one company's.

Leverage and the cost of equity

Toggle between MM's clean case and reality. In both, the flat line is what matters: the return on the package of debt and equity does not move.

How risky are the assets themselves?

Equity beta mixes business risk with financial risk. Strip the leverage out and you get the beta of the underlying business — the number you actually need when you are valuing a project or a differently-financed comparable. Two things drive it:

The derivation is worth seeing once. Start from the identity PV(asset) = PV(revenue) − PV(fixed cost) − PV(variable cost). The beta of PV(revenue) is the weighted average of its parts:

So for a given cyclicality of revenue, asset beta is proportional to the ratio of the present value of fixed costs to the present value of the project. A business with heavy fixed costs is riskier even if its sales are no more cyclical than anyone else's.

Beta lab

Chapter 10 · WACC in Practice

The government's slice, and the number you use on Monday

The tax shield

Firm U has no debt. Firm L borrowed $1,000 at r_D = 8%. Corporate tax T_c = 21%. Same EBIT, different total pie:

$17 that would have gone to the government goes to investors instead. Assume the debt is fixed and permanent, and that the shield carries the same risk as the interest payments that generate it. Then it is a perpetuity of T_c·r_D·D discounted at r_D:

After-tax WACC

Think of it as the expected rate of return on a portfolio of all the firm's outstanding securities, with the tax subsidy on the debt leg netted off. Many firms set a single company-wide WACC and update it only when risk or interest rates move materially — a common reference point that keeps divisions from arguing their way into favourable discount rates.

So why isn't every firm 100% debt?

Taken literally, the tax shield says: borrow everything. Three escape routes explain why nobody does.

The trade-off theory

Financial distress occurs when promises to creditors are broken, or honoured with difficulty. Investors know levered firms may fall into it, and they worry about it in advance — which shows up in today's price.

Sangria Corporation — the full worked example

Market values: assets $1,250m, debt $500m at r_D = 6%, equity $750m at r_E = 12.5%. Consistently profitable, marginal tax rate 21%. So D/V = 0.4 and E/V = 0.6.

Cross-check it from the equity side. Set the project up as a mini-firm with the same D/E as Sangria: assets 12.5, debt 5.0, equity 7.5.

How to misuse WACC

A manager campaigning for a pet project argues:

The two assumptions behind every WACC

When assumption 2 fails — say Sangria's crusher supports only 20% debt versus 40% for the firm — you cannot just plug the new weights into the old formula, because r_E is not a constant. You must unlever and relever.

WACC lab · unlever and relever

Set a target debt ratio for the project and watch the three steps recompute. Notice the WACC barely moves — and the cost of equity moves a lot.

Four questions people always ask