The value of a short series may be calculated by simple arith metical methods, and more easily by the aid of a table of present worth, when any rate of premium on the present is assumed. Suppose the rate to be .05 and the incomes expected are as follows : at the end of the 1st year, 100, of the 2nd year 75, of the 3d year 50, then ceasing. The present worth is the sum, = 95.238 + 68.027 + 43.192 = $206.46. Again it must be observed (see Chapter 22, sections 8, 9) that if the price is $206.46 it mathematically involves the rate of 5 per cent, quite independent of any thought; the calculation merely reveals and expresses exactly a rate inherent in the transaction.
§ 7. Depreciation funds. As a matter of practice the more difficult calculations of variable and terminable annuities are avoided by investors by taking the perpetual uniform series of incomes as the standard with which all the other series may be made comparable. They treat the original cap ital invested as a sum to be kept intact to be reinvested. The payments at the end of each year are treated as gross income to be divided between a depreciation fund sufficient to main tain the capital unimpaired at the end of the period, and net income which may either be spent or be saved (reinvested as an additional capital). In all bonds bought above par the amount to be treated as a depreciation fund is larger in proportion to the nearness of the maturity of the bond, and in turn, the more distant the date of maturity the higher the present price of a bond bought or sold above This method of calculating the capital investment as equivalent to a fixed sum of money is convenient, especially in distinguishing between income and principal. When losses are great they fall upon capital, and the income is a negative quantity. When prices of bonds rise, the income is larger than was expected, and (unless taken out in some way) is by a mere bookkeeping process counted as added to the capital, and the rate of income thereafter is reckoned on a higher basis of annual investment.* § 8. Corporate securities. Corporations are business enter prises which issue stock, or certificates of a share in their ownership and income. Doubtless the convenience of the sale and transfer of invested capital by the use of stock has been one of several reasons for the large increase of this form of organization since the beginning of the nineteenth century.
Originally the stock of a company taken collectively repre sented all the capital invested, and each share entitled the 3 E.g., in a circular issued in 1908 prices were quoted: "$100,000 City of Boston registered 4 per cent bonds, due June 1, 1928, price 106%, yielding 3.55 per cent; same kind due June 1, 1938, price 108% yielding 3.55 per cent; same kind due June 1, 1948, price 109%, yield ing 3.55 per cent." The gross yearly income is $4000, of which but $3550 would be treated as net income, and $450 would have to be reinvested each year to leave the capital undiminished at the end of the period for which the bonds run. The opposite is necessarily the case with bonds bought at a discount, the rate of net income on the investment being somewhat larger than the percentage that the annual payment is of the par value.
4 The practice of counting the capital as equal to a fixed sum of money has suggested to some the idea that capital is, in its very nature, a permanent quantity of value. But this is an illusion, for the "sum of value" may be both increased and diminished, and may be utterly swept away. Capital is no more than the bookkeeping expression of the present worth of a person's control over income, definite at the moment that the first investment has been made, and thereafter merely an estimate, until the property (right) is again sold at a price.
owner to a given portion (called a dividend) of the total in come earned. The shares are issued in regular denominations in terms of money; this amount expressed on the face of the share is the so-called nominal value, or par value, or face value' But as a business proves more or less profitable, the value of a share of its income rises and falls regardless of the nominal amount of stock issued. At once there is a divergence between the denomination and the market-price (often called value) of the stock. The nominal amount of stock is rela tively permanent, the same year after year; it may be in creased by further issues, or it may be decreased by cancel ation after purchase with funds in the corporation's treasury. But when stock is the only form of claim on the earnings that is issued, the fluctuations of the market-price of the stock record the market's judgment of the business ; that is, its expected dividends capitalized at a market-rate for investments of that grade of safety.