I. Premium, discount, and brokerage are each a percentage, computed upon the par value of the stock as the base.

II. The market value of stock, or the proceeds of a sale, is the amount or difference, according as the sum is greater or less than the par value.

NOTE 1.-In all examples relating to stocks, $100 will be considered a share, unless otherwise stated.

EXAMPLES FOR PRACTICE.

1. What cost 54 shares of Reading Railroad stock, at 41 % premium?

OPERATION.

$5400 x .045 = $243, premium.

ANALYSIS. We first compute the premium upon the par value of the

5643, Ans.

or market value, $5643. Or, since every dollar of the stock will cost $1 plus the premium, or $1.045, $5400 will cost 5400 × $1.045 $5643.

2. What do I receive for 32 shares of telegraph stock, which a broker sells for me at 15 % discount charging % brokerage?

3. I put $35400 into the hands of a broker to be invested in Missouri State Bonds, when their market value is 12% below par; how many shares shall I receive, if the broker charges his services?

% for

ANALYSIS. Since the stock is 12 % below par, the market value of $1 is $.88; adding the rate of brokerage, we find that every dollar of

the stock will cost me $.885. Hence for $35400 the broker can buy $35400.885

NOTES.

= $40000

= 400 shares.

2. The rate of brokerage in New York city has been fixed by custom at per cent.

3. Since brokerage has the same base as the premium or discount, the rate of brokerage may always be combined with the rate of premium or discount, by addition or subtraction, as the nature of the question may require.

4. The price of stock is usually quoted at a certain per cent. of the face, or nominal value. Thus stock at 4 % above par is quoted at 104 %; stock at 5 % below par is quoted at 95 %; and so on.

4. What is the market value of 15 Ohio State bonds at 112 %?

Ans. $1680.

5. What shall I realize on 20 shares of Panama railroad stock at 135 %, brokerage at 1 %?

Ans. $2665.

6. My agent bought for me 120 shares of N. Y. Central railroad stock, paying 80 %, and charging brokerage at %; what did the stock cost me? Ans. $9750. 7. What cost 36 shares in the Merchants' Bank, at a premium

of 7%, brokerage %?

35 200 8. A speculator invested $21910 in shares of the Harlem rail road, at a discount of 60% 784 464 mndly shares did he buy? 9. If 400 shares of the Bank of Commerce sell for $10150, what is the rate of premium? %.X 10. A broker receives $48447 to be invested in bonds of the Michigan Central railroad, at 94% %; how much stock can he buy, allowing 14% brokerage.

Ans.

11. My agent sells 830 barrels of Genesee flour at $6 per barrel, commission 5 %, and invests the proceeds in stock of the Pennsylvania Coal Company, at 82 %, charging % for making the purchase; how many shares do I receive? Ans. 57.x

12. I purchased 18 shares of Ocean Telegraph stock, par value $500 per share, at a premium of 2 %, and sold the same at a discount of 28%; what was my loss? Ans. $2700..

NOTE 5. The rate of loss is .02. + .28 .30, or .30 %.

=

13. A speculator exchanged $3600 of railroad bonds, at 5 % discount, for 27 shares of stock of the Suffolk Bank, at 3 % premium, receiving the difference in cash; how much money did he receive?

14. A merchant owning 525 shares in the American Exchange

00

Bank, worth 104 %, exchanges them for United States bonds worth 105 %; how much of the latter stock does he receive? 15. I purchased 12 shares of stock at a premium of 5 % and sold the same at a loss of $96; what was the selling price?//b 16. Having bought $64000 stock in the Cunard Line, at 2% premium, at what price must I sell it, to gain $2560 ?

Ans. 106 %.

17. A speculator bought 250 shares in a Carson Valley mining company at 103 %, and 150 shares of the Western Railroad stock at 95 %; he exchanged the whole at the same rates, for shares in the N. Y. Central Railroad at 80 %, which he afterward sold at 85%. How much did he gain? Ans. $2500.

18. I purchased stock at par, and sold the same at 3 % premium, thereby gaining $750; how many shares did I purchase?

19. A broker bought Illinois State bonds at 103 %, and sold at 105 %. His profits were $240; what was the amount of his purchase? Ans. $12000.

20. A man invested in mining stock when it was 4 % above par, and afterward sold his shares at 5% discount. His loss in trade was $760; how many shares did he purchase?

21. I invested $6864 in Government bonds at 106 %, paying 1% brokerage, and afterward sold the stock at 112 %, paying 1% brokerage; what was my gain? Ans. $208.

22. How much money must be invested in stocks at 3 % advance, in order to gain $480 by selling at 7 % advance? 23. How many shares of stock must be sold at 4 % discount, brokerage %, to realize $4775?

Ans. 50.

INSTALLMENTS, ASSESSMENTS, AND DIVIDENDS.

481. An Installment is a portion of the capital stock required of the stockholders, as a payment on their subscription. 482. An Assessment is a sum required of stockholders, to meet the losses or the business expenses of the company.

483. A Dividend is a sum paid to the stockholders from the profits of the business.

484. Gross Earnings are all the moneys received from the regular business of the company.

485. Net Earnings are the moneys left after paying expenses, losses, and the interest upon the bonds, if there be any.

486. In the division of the net earnings, or the apportionment of dividends and assessments, the calculations are made by finding the rate per cent. which the sum to be distributed or assessed bears to the entire capital stock. Hence,

487. Dividends and assessments are a percentage computed upon the par value of the stock as the base.

EXAMPLES FOR PRACTICE.

1. The Long Island Insurance Company declares a dividend of 6%; what does A receive, who owns 14 shares?

OPERATION.

$1400 x .06 = $84

ANALYSIS. According to 449, we multiply the base, $1400, by the rate, .06, and obtain the dividend, $84.

2. A canal company whose subscribed funds amount to $84000, requires an installment of $6300; what per cent. must the stock

holders pay?

OPERATION.

$6300 84000 .071

=

ANALYSIS. According to 450, we divide the installment, $6300, which is

percentage, by the base, $84000, and obtain the rate, .07 = 7 %.

3. A man owns 56 shares of railroad stock, and the company has declared a dividend of 8 %; what does he receive?

Ans. $448.

4. I own $15000 in a mutual insurance company; how many shares shall I possess after a dividend of 6% has been declared, payable in stock? Ans. 159 shares.

5. The Pittsburgh Gas Company declares a dividend of 15 %; what will be received on 65 shares?

6. A received $600 from a 4 % dividend; how much stock did he own? Ans. $15000.

7. The paid-in capital of an insurance company is $536000. Its receipts for one year are $99280, and its losses and expenses are $56400; what rate of dividend can it declare? Ans. 8 %.

8. The net earnings of a western turnpike are $3616, and the amount of stock is $56000; if the company declare a dividend of 6 %, what surplus revenue will it have? Ans. $256.

9. The capital stock of the Boston and Lowell Railroad Co. is $1830000, and its debt is $450000. Its gross earnings for the year 1858 were $407399, and its expenses $217621. If the company paid expenses, and interest on its debt at 55 %, and reserved $78, what dividend would a stockholder receive who owned 30 shares? Ans. $270.

10. The charter of a new railroad company limits the stock to $800,000, of which 3 installments of 10 %, 25 %, and 35 %, respectively, have been already paid in. The expenditures in the construction of the road have reached the sum of $540,000, and the estimated cost of completion is $400,000. If the company call in the final installment of its stock, and assess the stockholders for the remaining outlay, what will be the rate %? Ans. 171.

11. The Bank of New York, having $156753.19 to distribute to the stockholders, declares a dividend of 5 %; what is the amount of its capital? Ans. $2,985,775 nearly.

12. The passenger earnings of a western railroad in one year were $574375.25, the freight and mail earnings were $643672.36, the whole amount of disbursements were $651113.53, and the company was able to declare a dividend of 8 %; how much scrip had the company issued? Ans. $7086676. 13. Having received a stock dividend of 5 %, I find that I own 504 shares; how many shares had I at first? Ans. 480.

14. I received a 6% dividend on Philadelphia City railroad stock, and invested the money in the same stock at 75 %. My stock had then increased to $16200; what was the amount of my dividend? Ans. $900.

15. A ferry company, whose stock is $28000, pays 5 % dividends semi-annually. The annual expenses of the ferry are $2950; what are the gross earnings? Ans. $5750.