A.2.1 Core Financial Ratios from Zero

Basic Prerequisites: Financial Statements & Accounting (the three statements, the accounting equation). No prior ratio knowledge needed.

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1. Intuition & Practical Objective

This page builds the why of financial ratios with no prior knowledge needed. The objective is one idea: every financial statement is a pile of flows and stocks, and a ratio is simply a flow divided by the stock that earned it - a question of “how hard did the money work?” Learn to frame every ratio as that one question and the whole catalog stops being a list of formulas and becomes a single, repeatable thought.

Start with the dumbest question: why do we need ratios at all? A $1Mprofittellsyounothingbyitself.Isitagoodresult?Itdepends-profitagainstwhatbase?Against$5M of invested capital it is superb; against $1B it is a rounding error. The statements answer “how much,” the ratio answers “how well” - and “how well” is what separates a great business from a busy one.

Three steps:

1. Every ratio is a flow over a stock. Profit (a flow, earned over the period) ÷ book equity (a stock, the capital at a point in time) = ROE. Sales ÷ total assets = asset turnover. Debt ÷ equity = leverage. There are only two ingredients; the names are the catalog, the ratio itself is the single habit of matching a flow to the stock that produced it. (Penman Ch 5 opens exactly here.)

2. The denominator determines what you’re actually asking. Ask “return on equity” and you measure what the shareholders’ own capital earned. Ask “return on invested capital” (equity + debt, minus cash) and you remove financing from the picture entirely - you now see how well the operations work, before anyone’s claim on the money. Pick the wrong stock for your flow and you answer the wrong question. (Penman’s reformulation of the statements in Ch 7 exists precisely to make these “stocks” unambiguous.)

3. A ratio is a comparison instrument, never an absolute verdict. An ROE of 15% is ordinary for a retailer and remarkable for a bank’s operations; a P/B of 5 is cheap for a software compounder and expensive for a cyclical manufacturer. The ratio’s power is cross-sectional and over-time - how does this firm sit relative to its sector and its own history - not its standalone size. This is the single most important discipline on this page, and it is why 05 · Failure Modes exists.

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2. Mathematical Ground Truth & Derivations

The one flow-over-stock idea, in three families.

Profitability - how hard the capital worked. Relate a profit flow to the stock of capital that earned it:

$$\text{ROE}=\frac{\text{Net Income}}{\text{avg Common Equity}},\text{ROA}=\frac{\text{Net Income}}{\text{avg Total Assets}},\text{ROIC}=\frac{\text{NOPAT}}{\text{avg Invested Capital}}.$$

The trick lives in the denominators: ROE uses equity only; ROA uses everything (and so “forgets” leverage); ROIC uses operating capital (debt + equity − cash) so the financing noise is removed. Penman’s key distinction - equity vs. operating base - is exactly the difference between ROCE and RNOA/ROIC.

Valuation multiples - price against a fundamental. Relate the market price (a stock) to a fundamental flow:

$$\text{P/E}=\frac{\text{MV}}{\text{NI}},\text{P/B}=\frac{\text{MV}}{\text{BVE}},\text{EV/EBITDA}=\frac{\text{MV}+\text{NetDebt}}{\text{EBITDA}},\text{FCF yield}=\frac{\text{FCF}}{\text{MV}}.$$

The deep point (Penman Ch 2, Ch 6): each multiple answers “what is the market paying per unit of this fundamental?” A high P/B means the market is paying for growth - intrinsic value above book - while a low P/B anchors value on the book itself.

Liquidity & leverage - how the balance sheet stands up.

$$\text{Current}=\frac{\text{CA}}{\text{CL}},\text{Quick}=\frac{\text{CA}-\text{Inv}}{\text{CL}},\text{D/E}=\frac{\text{Total Debt}}{\text{BVE}},\text{IntCoverage}=\frac{\text{EBIT}}{\text{Interest}},\text{NetDebt/EBITDA}=\frac{\text{TD}-\text{Cash}}{\text{EBITDA}}.$$

The first two ask “can the firm meet what comes due?”; the last three ask “how much of the capital is borrowed, and how comfortably is the interest covered?“

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3. Computational Implementation - the whole catalog from one sample company

This is the single most convincing way to see the idea: take one company’s statements and compute every ratio on the hub table with stdlib only, then watch the two consistency identities line up - ROE must equal the Penman decomposition of ROCE, and P/E × Earnings-Yield must equal 1. If either fails, the math is wrong.

Note on the operating-liability constants (80, 105): they are the sample’s non-debt operating liabilities (AP + accrued, BOY and EOY) used to get net operating assets in the Penman RNOA - see 06 · Advanced Extensions for the clean form.

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4. Failure Modes & First-Principles Breakdowns

1. The “bigger number = better” trap. A ratio’s level is almost never the answer - its sector-relative and history-relative position is. A high current ratio can signal safety or a bloated, unproductive inventory pile; only comparison tells you which. (This is the entire thesis of 05 · Failure Modes.)
2. Mismatched flow/stock pairs. Dividing net income by total assets (ROA) quietly folds in financing effects; dividing EBIT by equity mixes a pre-financing flow with a post-financing stock. Always match the flow to the stock that earned it.
3. Averages or point-in-time? Balance-sheet stocks are measured at a point; profit flows over a period. Using ending balances (not averages) distorts the ratio whenever the balance changed during the year - the exact failure Penman’s average-denominator convention exists to prevent.

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5. References

• Penman, Financial Statement Analysis and Security Valuation
• Ittelson, Financial Statements: A Step-by-Step Guide
• Fridson & Alvarez, Financial Statement Analysis: A Practitioner’s Guide

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6. Connected Graph Bridges

• Base: Financial Statements & Accounting · Financial Statement Analysis
• Continue: 02 · Profitability Ratios · Index Hub