Thus, when a number of capitalists, about to establish a bank or construct a railway, find that (say) £500,000 will be necessary, they subscribe the amount in 5,000 shares of 100 each, or in 10,000 shares of £50 each, or in 50,000 shares of £10 each, &c.: one person taking, perhaps, 100 shares, another 50, another 20, another 5, and so on. Sometimes the "promoters "-i.e., the projectors of the speculation contribute only a portion of the required capital, and invite the public to contribute the remainder. When "allotted" a number of shares in a new undertaking, a person usually pays, at the time, only an instalment of the amount for which he becomes responsible; other instalments being subsequently paid, according as "calls" are made by the directors. In some instances, however, it is found that the full amount is not required for the purposes of the undertaking; and thus it is that the subscribed capital of a company is not unfrequently a good deal in excess of the paid-up capital. If, for example, the stock of a company consisted (nominally) of 5,000 shares of £100 each, and the sum paid on each share were £80, the "subscribed" capital would be (5,000 × 100=) £500,000, whilst the "paid-up" capital would be only (5,000 x 80=) £400,000. 200. As to their liabilities, some companies are LIMITED and some UNLIMITED. If a "limited-liability" company failed, the shareholders would not be legally responsible for more than their respective portions of the subscribed capital; but should an "unlimited" company become insolvent, the shareholders would all be liable-collectively and individually-for the full amount of the debts. A limitedliability company is known by its having the word "Limited" after its name; thus-" The Munster Bank, Limited." 201. Railway and other shares are very extensively dealt in, and are quoted at, above, or below par-according to the dividends they are likely to realise. When buying or selling shares, a stockbroker charges, in most cases, a fee of per cent. ; i.e., 58. on every £100.* [In the following examples-which, it will be seen, belong to Proportion-the price mentioned, as that of £100 of stock, is supposed in every instance to be the price actually paid or received; in other words, the quoted" price plus or minus (as the case may be) the fee charged by the broker :-) 66 EXAMPLE I.-How much stock can be bought, at 89%, for £750? Worded somewhat differently, the question is this: If £89 (cash) will purchase £100 of stock, what quantity of stock will £750 (cash) purchase? The proportion is (Cash) (Cash) (Stock) (Stock) £898: £750 :: £100 : α α= =(750× 100÷89§=) £836 16s. 5d. nearly. EXAMPLE II.-If £365 of stock were sold at 91, what would the seller receive in ready-money? In other words: If £100 of stock would realise £911 (cash), how much (cash) would £365 of stock realise? The proportion is £100 £365 £913: a a=(365×911÷100=) £332 128. Id.† EXAMPLE III.-What annual income could a person secure by investing £2,394 in 3-per-cent, stock, at 105 ? "Notwithstanding the low interest paid by the Funds, it is by far the best investment that any ordinary person can select for the money which he does not employ in his own business. Many investments promise a higher rate of interest, but they are suitable only for persons with large capital, who make it their special business to know what investments offer sufficient security. But the man wbo has a few hundred, or even a few thousand pounds to dispose of, if he selects any other investment will generally find in the end that, owing to the failure of public companies, law expenses, bad debts, and other losses, he would have been much richer if he had invested his money in the Funds."-Judge Longfield. + More accurately, £332 128. 13d.; but, in practice, the halfpenny would be disregarded. When 3 a year can be bought for £105, the annual income which £2,394 would purchase is the fourth term of the proportion £105: £2,394 :: £31: a a=(2,394×312÷105=) £79 16s. EXAMPLE IV.-What ready-money would, if invested in 3-per-cent. stock, at 894, produce an annual income of £70? When 3 a year can be bought for £89, the sum which would purchase £70 a year is the fourth term of the proportion £3: £70 :: £893: α EXAMPLE V.-What actual per-centage does a person get for money which he invests in 4-per-cent. stock, at 125? When £4 a year is bought for £125, the sum which £100 produces annually is the fourth term of the proportion— £125: £100 :: £4: a a=(100×4+125=)£33, the actual per-centage required. EXAMPLE VI.-Which is the more profitable investment-3-per-cent. stock at 94, or 5-per-cent. stock at 156? This is another way of saying Which of the two fractions is the larger-4 or 16? Because when £94 produces £3 a year, 1 produces a year; and when £156 produces £5 a year, £1 produces £16 a year :£ £ In determining which of the two fractions is the larger, we simply compare 156 × 3 with 94×5; these being the numerators when 94 × 156 is taken for common denominator-i.e., when the terms of each fraction are multiplied by the denominator of the other fraction. Without taking the trouble to multiply 156 by 94-without even setting down 156×94-we then see, at a glance, that the 5-per-cent. stock is slightly more profitable than the other; 94 × 5 being a little more than 156×3. 3 94 3×156 5×94 156X94 470 94×156 468 EXAMPLE VII.-What quantity of New Threes, at 90, could be obtained for £1,500 of 3-per-cent. stock, at 964? The lower the price of stock, the larger the quantity required to realise a certain sum of money, and vice versa. As small, therefore, as 90 is, compared to 961, so large must be the quantity of New Threes, compared to that of the 3-per-cent. stock-in other words, so small must be the quantity of the latter stock, compared to that of the former. We thus have the (inverse) proportion— 901 961: 1,500 a =(1,500 × 961÷901=) £1,595 6s. id. nearly. Here is a more roundabout solution: £1,500 of stock, if sold at 961, would realise, in cash, £1,443 a=(1,500 × 964÷100=) £1,4432. And £1,443, if invested in New Threes at 90, would purchase 1,595 68. 1d. (nearly) of that stock: £90: £1,443 :: £100 : a EXAMPLE VIII.-By investing £3,885 in Consols, a person secured an annual income of £126: at what price did he buy? This is another way of saying-When 126 a year can be purchased for £3,885, what sum would purchase £3 a year (or £100 of Consols)? The proportion is £126: £3:: £3,885 : a PROFIT AND LOSS. 202. Under this head, we apply our knowledge of Proportion to questions relating to the gains and losses of people in trade. Such gains and losses are usually expressed as so much PER CENT.—that is, (at the rate of) so much on £100, cost-price. When an article which cost £5 is sold for £6, there is a gain of £; and when an article which cost £20 is sold for £22, there is a gain of £2. The first of these gains, although absolutely less, is relatively greater, than the second; a gain of 1 on an outlay of 5 being at the same rate as a gain of (not £2, but) £4 on an outlay of £20: I £5: £20:: £1;a; a=(20÷5=) £4• Or thus: The gain is of the outlay in the first, and or of the outlay in the second case; and is a larger fraction than Again: when an article which cost 1 is sold for 19s. 8d., there is a loss of 4d.; and when an article which cost 38. 4d. is sold for 38., there is a loss of 4d. also. The first loss, however, although absolutely the same as the second, is relatively smaller; a loss of 4d. on an outlay of £1 being at the same rate as a loss of twothirds of Id. on an outlay of 3s. 4d.: 240d.: 40d.:: 4d. : a; a=(40×4÷240=) 3d. Or thus: The loss is or of the outlay in the first, and or of the outlay in the second case; and is a smaller fraction than. In order, therefore, to form a just estimate of gains and losses, we must, in every case, take the cost-price into account; and the adoption of £100 as a standard cost |