Introductory Beginning

Basic geometry: Manual for teachers by George David Birkhoff, Ralph Beatley

By George David Birkhoff, Ralph Beatley

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Return on equity measures how much profit the firm’s equity base is able to produce. 2 percent (£49 million/£300 million). As with ROA, the higher the figure, the more effective the company is in using its equity base to generate profits. Once again, however, the result must be compared against prior periods and industry peers in order to be meaningful. ’s case the gross margin is 20 percent (£130 million/ £650 million), meaning that for every pound of sales it generates, 80 pence is used to cover the cost of producing the goods/services.

The upward sloping line suggests that lower risk projects/investments earn a lower return, and higher risk projects/investments earn a higher return. This is consistent with the risk/return tradeoff mentioned earlier. It can also be useful examining expected returns versus risk over time to illustrate how two different projects that provide the same expected return might actually expose a firm to very different risks. 2. While Projects 1 and 2 generate the same average expected return, the standard deviation of the return varies significantly: Project 2 exposes the firm to much greater risk, as the realized return might be much higher, or much lower, than expected.

Ledger accounts The financial statements are used to produce trial statements, and trial statements are eventually converted into externally audited financial statements that are released to the public. Financial reporting is based on accepted accounting principles that add a degree of uniformity and standardization to the process; accounting principles do, however, allow for some amount of interpretation. The central financial statements include the balance sheet (a ‘‘point-in-time’’ representation of assets, liabilities, and capital), the income statement (a cumulative record of the firm’s profits and losses), and the statement of cash flows (a cumulative record of the firm’s cash inflows and outflows).

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