A.1.4 Accrual Accounting vs Cash

Basic Prerequisites: 03 · The Three Statements.

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1. Intuition & Practical Objective

Here is the single most important idea in all of accounting, and the one that separates people who can read statements from people who cannot:

Earnings is not the same as cash flow, and the difference is the accruals. Earnings is the accountant’s estimate of value added during the period; cash flow is the literal money that moved. Accounting deliberately books value when it is created, not when cash arrives - and the gap between the two is precisely the accruals (Penman Ch 5, eq. 5.1).

Why does this gap exist? Because of the matching principle: accountants match value in (revenue) to the value out (expenses) in the same period, so net income measures how much value was added by selling. To do that, they must book:

• Revenue accruals - a credit sale is booked as revenue before cash arrives (creating a receivable); cash received in advance is deferred until the goods ship.
• Expense accruals - an expense incurred but not yet paid (pensions, wages payable) is booked now; cash paid for future benefit (prepaids) is deferred; and past investments are recognized gradually as depreciation.

The practical objective: understand the accrual bridge equation, be able to compute the accruals from the statements, and know why cash and earnings differ - because every earnings-quality question downstream (05 · Failure Modes) and every valuation model rests on it.

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2. Mathematical Ground Truth - the accrual bridge (Penman eq. 5.1, 5.2)

The two presentations of cash flow from operations, and the identity that ties them:

Direct method - list the actual cash receipts and payments:

$$\text{CFO}=\text{cash from customers}-\text{cash paid to suppliers}-\text{cash paid for expenses}$$

Indirect method - start from earnings, add back non-cash expenses, and adjust for working-capital changes (this is how public statements present it, Box 10.3):

$$\text{CFO}=\text{Net income}+\text{Depreciation}-\Delta \text{Accounts receivable}-\Delta \text{Inventory}+\Delta \text{Accounts payable}$$

The accrual identity (rearrange the indirect method - Penman eq. 5.1):

$$\boxed{\text{Earnings}=\text{Cash flow from operations}+\text{Accruals}}$$

where the total accruals (the non-cash portion of earnings) are

$$\text{Accruals}=\Delta \text{AR}+\Delta \text{Inventory}-\Delta \text{AP}-\text{Depreciation}+\cdots$$

and the broader view (Penman eq. 5.2) shows how investment is handled: accrual accounting adds investment back to free cash flow by placing it on the balance sheet as an asset, then recognizes its cost later as depreciation:

$$\text{Earnings}=\text{Free cash flow}-\text{Net interest}+\text{Investments}+\text{Accruals}$$

The sign intuition: an increase in receivables means more revenue than cash (positive revenue accrual, lowers CFO relative to earnings); an increase in inventory means cash paid but not yet expensed (lowers CFO); depreciation is a non-cash expense (raises CFO relative to earnings).

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3. Computational Implementation - compute CFO both ways, then verify the identity

We take the same lemonade ledger and compute CFO by both the direct and indirect method, then confirm $\text{Earnings}=\text{CFO}+\text{Accruals}$ exactly. Stdlib only.

Both methods give the same $1,500. The accruals are −$700: depreciation (−$1,200) is a non-cash expense that makes earnings lower than cash, while the inventory build (+ $500) made cash lower than earnings because the business paid for goods not yet sold. Negative total accruals mean cash flow from operations exceeded earnings - a sign of high earnings quality (see 05 · Failure Modes).

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4. Failure Modes & First-Principles Breakdowns

1. Assuming profit means cash. A company can report $800 profit while its checking account shrinks (heavy capex, unpaid receivables). Earnings measures value created; only the cash flow statement tells you if the money is actually there.
2. Reading a positive accrual as automatically bad. Accruals are not inherently manipulation - growth requires building receivables and inventory, which mechanically raises accruals and lowers CFO. The red flag is accruals out of line with the business model, not any single level.
3. Mixing the two methods’ mechanics. The direct method lists real cash flows; the indirect method reconciles from earnings. Conflating them (e.g. “adding back” depreciation to a direct-method number) double-counts. Public firms report indirect; if you want the direct picture you must reconstruct it (Penman Ch 10).
4. Forgetting that estimates live in the accruals. Receivables embed bad-debt estimates, depreciation embeds a method/life choice, pension expense embeds actuarial assumptions. Cash is objective; accruals depend on rules and estimates - which is exactly where manipulation enters (05 · Failure Modes, and the accounting-quality literature).

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5. References

• Penman, Financial Statement Analysis and Security Valuation
• Penman
• Sloan (1996), “Do Stock Prices Fully Reflect Information in Accruals and Cash Flows About Future Earnings?” (TAR)
• O’Glove, Quality of Earnings (1987)

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6. Connected Graph Bridges

• Back: 03 · The Three Statements · Index Hub
• Forward: 05 · Failure Modes · 06 · Advanced Extensions
• Quality & factors: Accounting Quality & Red Flags · Fundamental Multi-Factor Models (Sloan accruals factor lives here)