A.2.2 Profitability Ratios

Basic Prerequisites: 01 · From Zero.

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1. Intuition & Practical Objective

Profitability ratios answer the founding question of financial analysis: how well does the capital in this business earn? They are the flow-over-stock ratios - profit earned over the period divided by the capital that produced it. There are two distinct families, and conflating them is the most common beginner error:

• Return ratios put profit against a capital base: ROE (return on shareholders’ book equity), ROA (return on all assets), ROIC/ROCE (return on invested capital / on common equity).
• Margin ratios put profit at a given stage against sales: gross, operating, net margins. Margins answer “how much of each sales dollar survives past a cost layer”; return ratios answer “how hard the whole capital stock worked.”

Penman’s discipline (Ch 5, 7, 8) is to make the base precise: ROCE = comprehensive earnings / average common equity (his “primary financial statement ratio”), while ROIC = RNOA = operating income after tax / average net operating assets - the return on the operating engine, with financing stripped out so you see the business itself rather than how it was funded. A firm with enormous financial leverage can show a high ROE on a mediocre business; only RNOA/ROIC reveals the business underneath.

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2. Mathematical Ground Truth & Derivations

The return ratios. Let $\tau$ be the tax rate, NI net income, BVE book value of common equity, TA total assets, NOPAT $=$ EBIT$(1-\tau )$, IC $=$ TotalDebt $+$ BVE $-$ Cash.

$$\text{ROE}=\frac{\text{NI}}{\text{avg BVE}},\text{ROA}=\frac{\text{NI}}{\text{avg TA}},\text{ROIC}=\frac{\text{NOPAT}}{\text{avg IC}}.$$

The margins. With S sales, COGS cost of goods sold:

$$\text{Gross margin}=\frac{S-\text{COGS}}{S},\text{Operating margin}=\frac{\text{EBIT}}{S},\text{Net margin}=\frac{\text{NI}}{S}.$$

The DuPont decomposition (Subramanyam; Penman Ch 11). The headline ROE is not a black box - it is the product of three drivers, each independently attackable:

$$\text{ROE}=\underset{\text{net margin}}{\underbrace{\frac{\text{NI}}{S}}}\times \underset{\text{asset turnover}}{\underbrace{\frac{S}{\text{avg TA}}}}\times \underset{\text{equity multiplier}}{\underbrace{\frac{\text{avg TA}}{\text{avg BVE}}}}.$$

A high ROE is then three different kinds of story: high-margin (a luxury goods firm), high-turnover (a supermarket), or high-leverage (a bank). All three produce the same ROE for entirely different reasons - which is why reading only the ROE number tells you almost nothing.

Penman’s operating decomposition (Ch 11). Even sharper: split ROE into the operating return and the financing leverage effect,

$$\text{ROCE}=\text{RNOA}+[\text{FLEV}\times (\text{RNOA}-\text{NBC})],$$

where RNOA $=$ NOPAT/avgNOA, FLEV $=$ NFO/CSE is financial leverage, and NBC is the net borrowing cost (after-tax net financial expense / NFO). The bracket is the leverage effect: borrowing adds to ROCE only when the operating spread (RNOA − NBC) is positive - the exact accounting expression of the “leverage amplifies, it does not create.”

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3. Computational Implementation - the full profitability set + DuPont & Penman cross-checks

Stdlib only. Builds the return ratios, margins, the DuPont chain, and the Penman ROCE decomposition from one company’s statements, then verifies ROE = DuPont = Penman-ROCE to floating-point precision.

(Penman Ch 11 verifies the identical machinery against real firms: e.g. his worked General Mills case shows a negative leverage effect because RNOA fell below the after-tax borrowing cost.)

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4. Failure Modes & First-Principles Breakdowns

1. ROE conflates business and financing. Two firms with identical operations but different leverage have different ROEs - so ROE is a financing-and-operations number, not a pure quality score. Read RNOA/ROIC for the business itself and ROE for the shareholders’ actual experience. (This is precisely why Penman drives analysis through RNOA first.)
2. “ROIC” is not standardized. Some compute it with after-tax operating income, some before; some use average IC, some ending; some include operating leases and some do not. Quote your convention or your ROIC is not comparable across sources.
3. Margins ignore the balance sheet. A 30% net margin can coexist with a terrible asset turnover (a capital-hungry business); margin alone never tells you how hard the capital worked. Always pair margin with turnover - the DuPont chain exists to force that pairing.
4. Negative / tiny equity breaks ROE and DuPont. If equity is near zero or negative, ROE explodes or flips sign meaninglessly, and the equity-multiplier term goes singular - see 05 · Failure Modes for the handling.

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5. References

• Penman, Financial Statement Analysis and Security Valuation
• Subramanyam, Financial Statement Analysis
• Novy-Marx, Robert: “The Other Side of Value: The Gross Profitability Premium” (JFE, 2013)
• Hou, Xue & Zhang: “Digesting Anomalies” (RFS, 2015)

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6. Connected Graph Bridges

• Back: 01 · From Zero · Index Hub
• Forward: 06 · Advanced Extensions (ROIC decomposition) · Equity Valuation
• Base: Financial Statement Analysis