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Applied Mathematics · Ch 9 — Financial Mathematics

Stock, Shares and Debentures

9.6

Stock, Shares and Debentures

Starting a large business needs more money than one or two people can raise, so people join together to form a company. The company drafts a proposal and issues a prospectus setting out the project, then invites the public to invest by taking up shares in the company. In this way it pools funds from many investors.

Important facts and terms. The total money needed to run the company is its stock capital. This whole capital is split into small equal units called shares (or stock); for each investment the company issues a share certificate stating the value and number of shares held. A person who holds shares is a shareholder (stockholder). Companies may issue equity shares or preference shares — preference shareholders enjoy preferential rights such as being paid dividend and repaid before equity shareholders.

Debentures take their name from the Latin debere, "to borrow." A debenture is a written instrument of debt issued under the company's common seal — much like a loan certificate — by which the company agrees to repay money borrowed from the public. Debentures run for a fixed period at a fixed rate of interest, payable yearly or half-yearly, and may be secured against the company's assets.

Dividend is the annual profit shared out among shareholders, quoted either per share or as a percentage. The face value (nominal or par value) is the original value printed on the certificate; crucially, dividend is always calculated on the face value. The market value is the price at which the share is bought and sold through brokers on a stock exchange. A share is quoted at premium (above par) when its market value exceeds face value, at par when the two are equal, and at discount when market value is below face value. A broker's charge is called brokerage: it is added to the cost price when stock is bought and subtracted from the selling price when stock is sold.

Remember

The face value of a share never changes; the market value changes constantly; and dividend is always paid on the face value, not the market value.

The number of shares a person holds ties three totals together:

Number of shares=Total investmentInvestment in one share=Total incomeIncome from one share=Total face valueFace value of one share\text{Number of shares} = \dfrac{\text{Total investment}}{\text{Investment in one share}} = \dfrac{\text{Total income}}{\text{Income from one share}} = \dfrac{\text{Total face value}}{\text{Face value of one share}} …