1.1 Introduction
In accounting, finance and economics, an accounting identity is an equality that must be true regardless of the value of its variables, or a statement that by definition (or construction) must be true. Where an accounting identity applies, any deviation from numerical equality signifies an error in formulation, calculation or measurement. The term accounting identity may be used to distinguish between propositions that are theories (which may or may not be true, or relationships that may or may not always hold) and statements that are by definition true. Despite the fact that the statements are by definition true, the underlying figures as measured or estimated may not add up due to measurement error, particularly for certain identities in macroeconomics. The most basic identity in accounting is that the balance sheet must balance, that is, that assets must equal the sum of liabilities (debts) and equity (the value of the firm to the owner). In its most common formulation it is known as the accounting equation:
Assets = Debt + Equity where debt includes non-financial liabilities. Balance sheets are commonly presented as two parallel columns, each summing to the same total, with the assets on the left, and liabilities and owners’ equity on the right. The parallel columns of Assets and Equities are, in effect, two views of the same set of business facts.
As with other spreadsheets, Microsoft Excel works only to limited accuracy because it retains only a certain number of figures to describe numbers (it has limited precision). Excel nominally works with 8-byte numbers by default, a modified 1985 version of the IEEE 754 specification (Besides numbers, Excel uses a few other data types. Although Excel can display 30 decimal points, its precision for a specified number is confined to 15 significant figures, and calculations may have an accuracy that is even less due to three issues: round off, truncation, and binary storage. In the top figure the fraction 1/9000 in Excel is displayed. Although this number has a decimal representation that is an infinite string of ones, Excel displays only the leading 15 figures. In the second line, the number one is added to the fraction, and again Excel displays only 15 figures. In the third line, one is subtracted from the sum using Excel. Because the sum has only eleven 1’s after the decimal, the true difference when ‘1’ is subtracted is three 0’s followed by a string of eleven 1’s. However, the difference reported by Excel is three 0’s followed by a 15-digit string of thirteen 1’s and two extra erroneous digits. Thus, the numbers Excel calculates with are not the numbers that it displays. Moreover, the error in Excel’s answer is not just round-off error.
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