Deitz J.E., Southam J.L. Contemporary Business Mathematics for Colleges

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Corporate

and Special

Applications

Part

21 Corporate Stocks

22 Corporate and Government

Bonds

23 Annuities

24 Business Statistics

Corporate

Stocks

Chapter 21 Corporate Stocks 425

Learning Objectives

By studying this chapter and completing all assignments, you will be able to:

Compute the costs and proceeds of stock buy-and-sell transactions.

Compute the costs and proceeds of round and odd lots.

Compute rates of yield and gains or losses on the purchase and sale

of stocks.

Compute comparative earning potential of the major classes of

corporate stocks.

Learning Objective

Many companies operate as corporations. A corporation is a body that is granted a

charter by a state legally recognizing it as a separate entity, having its own rights,

privileges, and liabilities distinct from those of its owners. A corporation acquires assets,

enters into contracts, sues or is sued, and pays taxes in its own name. Two primary

reasons for forming a corporation are to limit liability and facilitate broadening the

ownership base. A corporation raises capital by selling shares of ownership, which

increases its assets without increasing its debt.

The general term applied to the shares of a corporation is capital stock. Each share of

capital stock is a share of the ownership of the company’s net assets (assets minus liabili-

ties). The number of shares that a corporation is authorized to issue, or offer for sale, is

set forth in its charter, the basic approval document issued by the state, under which the

corporation operates. Ownership of stock is evidenced by a stock certificate.

Frequently, the shares of capital stock are assigned a value known as par, which is

stated on the stock certificate. For example, a company incorporated with capital stock

of $1,000,000 and 100,000 shares has a par value of $10 per share. Stock issued without

par value is known as no-par stock. The par value may differ from the market price. In

the marketplace, stock may be sold for any amount agreed upon by the buyer and seller.

426 Part 6 Corporate and Special Applications

21.1 Students are generally familiar

with the New York Stock Exchange

(NYSE),and it’s proper to point out that

all companies listed on the New York

and other major stock exchanges are

corporations with an issue of some

form of corporate stock.

Computing the Costs and Proceeds of

Stock Transactions

Learning Objective

Compute the costs and proceeds of

stock buy-and-sell transactions.

21.2 The NYSE has been in continuous

operation since 1792,or more than 200

years.It traces its beginning to the Rev-

olutionary War,when huge amounts of

money had to be mobilized.

21.3 Many students have never seen a

copy of The Wall Street Journal, so a copy

of a recent edition should be obtained

and shown to the class.

21.4 Today,the distinction between

“full-service” and “discount” brokers is

becoming less meaningful as more in-

stitutions such as banks are becoming

eligible to conduct stock exchange

transactions.The number of discount

brokers has increased dramatically in

the past decade.

After purchasing stock, a buyer may sell that stock at any price on the open market,

regardless of the par value. Stocks are usually bought and sold on stock exchanges, the

formal marketplaces set up for the purpose of trading stocks. Major exchanges in the

United States are the New York Stock Exchange (NYSE), the American Stock Exchange

(AMEX), and the National Association of Securities Dealers Automated Quotations

(NASDAQ). A stockbroker usually handles stock transactions—the purchase and sale

of stocks for clients. Today, many people also trade via the Internet.

The trading of shares of stock is published daily in newspapers. Figure 21-1 shows a

sample stock market report, in which stocks are quoted in the traditional manner—

dollars and fractions of a dollar. The NYSE, NASDAQ, and AMEX quote prices in

hundredths. Consequently, the smallest increase or decrease in a stock price that will

be reported is .01.

Both the buyer and the seller of stock pay commissions to the stockbroker. The total

amount paid by a buyer to purchase a stock includes the market price of the stock and

the stockbroker’s commission (charge). The total cost paid by the purchaser is equal to

the purchase price plus a broker’s commission. The proceeds received by the seller are

equal to the selling price minus the commission.

Broker commissions may be a flat rate per transaction, a percent of the value of the

stock, an amount per share traded, or an amount negotiated between the client and the

broker. Generally, commissions for brokers are less than 1% of the value of the stock,

ranging from $0.02 to $0.50 per share bought or sold. A number of discount brokerages

operating on the Internet now charge $7.00 to $22.99 per transaction, normally for up to

5,000 shares. Figure 21-2 shows a broker’s confirmation report of a stock purchase with a

commission rate of $50 and a transaction fee of $3.

We use a transaction charge of $0.20 per share or a flat fee of $19.95 per transaction

in computing the cost of commissions in this chapter.

Chapter 21 Corporate Stocks 427

Figure 21-1 Daily Stock Report from the NYSE

52 weeks Day’s Activity

Hi Low Stock Sym Div Yld-% PE Vol. (000) High Low Close Change

54.21 33.12 Bank of America BAC $0.64 0.64% 12.79 37,700 43.33 43.21 42.33 20.04

107.38 74.12 Boeing BA $0.40 1.96% 15.4 22,838 81.90 80.54 80.54 0.33

87.00 59.60 Caterpillar CAT $0.36 2.13% 12.57 7,304 69.05 67.55 67.90 20.46

65.59 45.56 Coca-Cola Co KO $0.34 2.37% 24.84 8,408 58.19 57.57 57.70 0.31

94.77 51.06 Deere Inc DE $0.25 1.20% 21.01 3,897 86.24 82.89 83.30 20.18

46.30 26.30 Disney DIS $0.35 1.16% 14.49 3,578 31.18 31.10 31.50 1.43

9.70 5.50 Ford Motor Co F $ - 0.00% 0 6,160 6.42 6.25 6.31 20.12

43.20 21.34 General Motors GM $0.25 3.78% 0 18,165 26.30 25.29 25.71 20.76

56.89 46.25 Kellogg’s KO $0.31 2.58% 17.45 4,740 49.33 48.30 49.09 0.94

78.79 61.89 PepsiCo PEP $0.38 2.21% 18.21 14,149 68.38 66.32 66.73 21.22

38.31 30.10 Safeway SWY $0.07 0.89% 15.41 2,569 31.97 30.98 31.03 0.23

195.58 84.72 Sears SHLD $ - 0.00% 12.93 1,933 104.74 97.28 97.67 24.63

59.34 42.80 Sony SNE $0.12 0.52% 18.08 1,323 43.89 42.50 43.82 20.46

23.42 8.07 Sprint S $0.03 1.01% 21.53 20,042 10.02 9.53 9.62 20.25

138.00 91.21 Toyota Motor Co TM $1.20 2.27% 9.76 1,096 110.63 107.73 107.78 2.41

45.57 10.73 Washington Mu WM $0.15 3.32% 0 44,220 18.31 16.71 17.12 20.96

[1] The highest price per share in the previous 52 weeks.

[2] The lowest price per share in the previous 52 weeks.

[3] Company names, often abbreviated to fit in stock tables, are listed alphabetically.

[4] The symbol is a stock’s designation on databases and quote machines.

[5] The dividend shown usually is the annual rate based on the company’s last payout.

[6] The dividend divided by the closing share price gives the stock’s yield.

[7] One measure of a stock’s value is its price/earnings ratio (P/E). It is based on the per-share earnings as reported

by the company for the four most recent quarters. The PE number is found by dividing the current price by those

most recent four-quarter earnings.

[8] Volume is the number of shares traded that day, shown in hundreds of shares.

[9] The high for the day’s trading range.

[10] The low for the day’s trading range.

[11] The closing price on that day.

[12] The net change in price lets you calculate something that isn’t in the stock table: the previous day’s closing price.

EXAMPLE A

Jennifer Low bought 200 shares of Sears (SHLD) stock at $103. What was her cost, includ-

ing commission of $0.20 per share?

200 shares 3 $103 price 5 $20,600 purchase price

200 shares 3 $0.20 commission 51 40 commission

$20,640 total cost

EXAMPLE B

Ken Yeager sold 800 shares of Verizon at $36.17, less commission of $0.20 per share.

What were the proceeds of the sale?

800 shares 3 $36.17 5 $28,936 selling price

800 shares 3 $0.20 commission 52 160 commission

$28,776 proceeds

PRESS)

428 Part 6 Corporate and Special Applications

EXAMPLE C

Juan Hernandez bought 500 shares of PepsiCo stock at $68.30. What was his cost,

including a flat fee of $19.95?

500 shares 3 $68.30 price 5 $34,150.00 purchase price

commission 5 1 19.95 flat fee

$34,169.95 total cost

David Cooper purchased 300 shares of Safeway at $31.02. He later sold the stock at

$33.10.What was his gain/loss on the purchase and sale, after counting commissions of

$0.20 per share on both the purchase and the sale?

Purchase: 300 shares 3 $31.02 price 5 $9,306 purchase price

300 shares 3 $0.20 commission 5 1 60 commission

$9,366 total cost

Sale: 300 shares 3 $33.10 price 5 $9,930 selling price

300 shares 3 $0.20 commission 52 60 commission

$9,870 proceeds

$9,870 proceeds 2 $9,366 cost 5 $504 gain

✔

CONCEPT CHECK 21.1

Figure 21-2 Confirmation Report of a Stock Purchase

BOUGHT

WE CONFIRM THE FOLLOWING TRANSACTION SUBJECT TO THE AGREEMENT ON THE REVERSE SIDE.

50 35.47

GENERAL ELECTRIC CO

YOU QUANTITY PRICE SECURITY DESCRIPTION

CUSIP NUMBER

369604103

ACCOUNT NUMBER IB T TRF MKT OFFICE PHONE NUMBER

47 1 4 3

WHEN COMMUNICATING WITH US PLEASE REFER TO YOUR ACCOUNT NUMBER

PRINCIPAL STATE TAX ACCRUED INTEREST COMMISSION SEC FEE

SYMBOL

TRADE DATE

12 31 08 01 08 09

1,773.50 50.00 3.00

1,720.50

SETTLEMENT

DATE

PLEASE PAY OR DELIVER BY THIS DATE

AMOUNT

Wachovia

TRANSACTION

CHARGE

Chapter 21 Corporate Stocks 429

EXAMPLE D

Carson Grant bought 160 shares of U.S. Steel at $43. What was his cost?

Odd-lot purchase price 5 $43 1 $0.125 5 $43.125 per odd-lot share

100 shares 3 $43.00 round-lot price 5 $4,300.00 round-lot total cost

60 shares 3 $43.125 odd-lot price 5 2,587.50 odd-lot total cost

160 shares 3 $0.20 commission 51 32.00 commission

$6,919.50 total cost

EXAMPLE E

Carson sold 160 shares of U.S. Steel at $43. What was the amount

of his net proceeds?

Odd-lot selling price 5 $43 2 $0.125 5 $42.875

100 shares 3 $43.00 round-lot price 5 $4,300.00 round-lot price

60 shares 3 $42.875 odd-lot price 5 2,572.50 odd-lot price

160 shares 3 $0.20 commission 52 32.00 commission

$6,840.50 net proceeds

James O’Brien bought 160 shares of Kelloggs at $48. What was his total cost?

Odd-lot purchase price 5 $48 1 $0.125 5 $48.125

100 shares 3 $48 round-lot price 5 $4,800.00

60 shares 3 $48.125 odd-lot price 5 $2,887.50

160 shares 3 $0.20 commission 51 32.00

Total cost $7,719.50

Sarah Loeb sold 220 shares of Aetna at $153.25. What was the amount of her net proceeds?

Odd-lot selling price 5 $153.25 2 $0.125 5 $153.125

200 shares 3 $153.25 round-lot price 5 $30,650.00

20 shares 3 $153.125 odd-lot price 513,062.50

220 shares 3 $0.20 commission 52 44.00

Net proceeds $33,668.50

✔

CONCEPT CHECK 21.2

Stocks are sold in round lots, odd lots, or a combination of the two. A round lot

usually is 100 shares. An odd lot consists of any number of shares less than 100

(1 to 99 shares is an odd lot for a stock with a 100-share round lot). When odd lots

are purchased, a small extra charge, or odd-lot differential, is commonly added to the

round-lot price. The differential is added to the price for a purchaser and deducted

from the price for the seller. In this book, we use a differential of 12.5 cents

as the odd-lot rate.

Computing the Costs and Proceeds of Round

and Odd Lots

Compute the costs and proceeds of

round and odd lots.

Learning Objective

430 Part 6 Corporate and Special Applications

EXAMPLE F

Aaron Ramos bought 300 shares of Wells Fargo stock at $32 and paid a $19.95 commis-

sion. A dividend of $2.15 per share was paid this year. What was the rate of yield?

300 3 $32 5 $9,600.00 purchase price

19.95 commission

$9,619.95 total cost

300 3 $2.15 5 $645 dividend for first year

$645 4 $9,619.95 5 6.7% rate of yield

GAIN OR LOSS ON SALE OF STOCK

For income tax and accounting purposes, the amount of gain or loss on a sale of stock is

determined by comparing the sale proceeds to the total cost.

21.5 For a realistic business assign-

ment,ask each student to select one

NYSE company appearing in the busi-

ness section of the local newspaper or

The Wall Street Journal. The student

can then use the current market

quotation to calculate the gain/loss

that would result from a sale today if

the share had been purchased at the

current year’s low and high.

EXAMPLE G

Refer back to example F. If Aaron sold his stock after 3 years at $36.50, less $19.95

commission, what were the amount and the percent of gain or loss?

300 3 $36.50 5 $10,950.00 selling price

2 19.95 commission

$10,930.05 proceeds

$10,930.05 proceeds 2 $9,619.95 cost (example F) 5 $1,310.10 net gain

$1,310.10 4 $9,619.95 5 13.6% gain on sale

EXAMPLE H

Suppose that Aaron held his stock for 3 years and received a $645 dividend each year.

Then to determine the total change in value (example G) he would need to add to his

proceeds the $1,935 in dividends received.

Total Total

oceeds Dividends Cost

($10,930.05 1 $1,935) 2 $9,619.95 5 $3,245.10 total gain in value

$3,245.10 total gain 4 $9,619.95 initial cost 5 33.7% gain in value

Computing the Rate of Yield and Gains or Losses

THE RATE OF YIELD

The board of directors is a group of people elected by shareholders to oversee the

operations of the corporation. The board has sole authority to distribute earnings to

shareholders. When such action is taken, the directors are said to declare a dividend.

The rate of dividend is either a certain percent of the par value of the stock or a flat

amount of money per share. Thus, a dividend of 8% on a stock with a par value of

$100 would be $8.00 per share. Most large corporations pay dividends quarterly.

The rate of yield from an investment in stock is the ratio of the dividend to the total

cost of the stock.

Learning Objective

Compute rates of yield and gains or

losses on the purchase and sale of

stocks.

Chapter 21 Corporate Stocks 431

a. Maria Sanchez owns 700 shares of stock with a par value of $100. If she receives a dividend of 5%, how much will

her total dividend be?

$100 par value 3 5% per share 5 $5.00 per-share dividend

700 shares 3 $5.00 per share 5 $3,500 total dividend

b. Maria also owns 300 shares of a stock without a stated par value. If she receives a dividend of $2.00 per share, what

will her total dividend be?

300 shares 3 $2.00 per share 5 $600 total dividend

c. Magdalena Kaur bought 200 shares of Clorox at $32.25. A dividend of $0.45 per share was paid this year. What was

the rate of yield?

200 shares 3 $32.25 5 $6,450 purchase price

200 shares 3 $0.20 51 40 commission

$6,490 total cost

200 shares 3 $0.45 dividend 5 $90 for first year

$90 dividend 4 $6,490 total cost 5 1.39% rate of yield

d. After 4 years, Magdalena sold the Clorox stock for $32.50. What were the amount and percent of gain or loss on

the sale?

200 shares 3 $32.50 selling price 5 $6,500 selling price

200 shares 3 $0.20 commission 52 40 commission

$6,460 proceeds

$6,460 proceeds 2 $6,490 total cost 5 $(30) loss

$(30) loss 4 $6,490 total cost 5 0.46% loss

e. If Magdalena held the Clorox stock for 4 years, receiving the same $90 dividend each year, what was the total

change in the value over the 4 years?

Total Dividends Total Gain in

Proceeds 1 (4 years) 2 Cost 5 Value

($6,460 1 $360) 2 $6,490 5 $330

$330 gain in value 4 $6,490 total cost 5 5.08% gain

✔

CONCEPT CHECK 21.3

Computing Comparative Earning Potential

Learning Objective

Common stock is the usual type of stock issued by a corporation. Another type fre-

quently issued, preferred stock, gives holders a right to share in earnings and liquidation

before common shareholders do. For example, a company that has a 7% preferred stock

must first pay dividends of 7% of the par value to the holders of preferred stock before

anything is paid to the holders of common stock. Preferred stock may be designated as

cumulative—that is, if the corporation doesn’t pay the specified percentage, the unpaid

amount, called a dividend in arrears, carries over to the following year or years. If divi-

dends aren’t paid on noncumulative preferred stock during one year, the unpaid amount

doesn’t carry over to the next year.

Compute comparative earning

potential of the major classes of

corporate stocks.

Learning Objective

432 Part 6 Corporate and Special Applications

21.6 Preferred stock becomes most

important when a company is having

financial difficulty.In case of liquida-

tion,funds are used first to pay credi-

tors and then to pay shareholders.In

the event that there are insufficient

funds to pay all shareholders,those

holding preferred stock are paid first.

EXAMPLE I

The ABC Company earned $48,000 last year. The capital stock of the company consists

of 10,000 shares of 7% preferred stock, with a par value of $40 per share, and 50,000

shares of no-par common stock. If the board of directors declared a dividend of the

entire earnings, what amount would be paid in total to the preferred and common

shareholders and how much would each common shareholder receive?

Preferred: 10,000 shares 3 $40 par value 5 $400,000 total value

$400,000 value 3 0.07 5 $28,000 paid to preferred

Common: $48,000 total earnings 2 $28,000 paid to preferred 5 $20,000

$20,000 4 50,000 shares 5 $0.40 paid per share to common

EXAMPLE J

Assume in example I that the preferred stock is cumulative and that for the preceding year

the company had declared a dividend of only $16,000, or enough to pay a 4% dividend on

preferred stock. The earnings of $48,000 for this year would be divided as follows:

Unpaid dividend from preceding year: 7% 2 4% 5 3%

$400,000 preferred par value 3 0.03 5 $12,000 cumulative (dividend in arrears)

$400,000 3 0.07 dividend for current year 5 $28,000

Total paid on preferred stock 5 $40,000

$48,000 total earnings 2 $40,000 paid to preferred 5 $ 8,000

$8,000 4 50,000 common shares 5 $0.16 dividend per common share

Another feature that sometimes makes preferred stock an attractive investment is the

possibility of converting the preferred stock into common stock. Convertible preferred

stock gives the owner the option of converting those preferred shares into a stated num-

ber of common shares. For example, a stated conversion of 1 to 3 means that 1 share of

preferred stock could be changed into 3 shares of common stock. The conversion feature

combines the safety of preferred stock with the possibility of growth through conversion

to common stock.

EXAMPLE K

Joel Turner owned 200 shares of GM convertible preferred stock at $20 par value. He

converted each share of preferred into 3 shares of common. How many shares of com-

mon stock did Joel receive when he converted?

200 3 3 5 600 shares of common stock

If common stock was selling at $22 per share on the date of conversion, how much was

Joel’s common stock worth?

$22 3 600 shares 5 $13,200 common stock value

If Joel paid $42 per share for his preferred stock, how much had his investment increased?

$42 3 200 preferred 5 $8,400 preferred stock value

$13,200 2 $8,400 5 $4,800 increase in value

Chapter 21 Corporate Stocks 433

a. The XYZ Corporation had a net profit of $120,000 in the fiscal year just ended. The capital stock consists of 8,000

shares of 8% convertible preferred stock with a par value of $50 per share and 20,000 shares of no-par common

stock. If the board of directors declared a dividend of the entire earnings, what amount would be paid to preferred

and common shareholders?

Preferred: 8,000 shares 3 $50 per share 5 $400,000 total par value

$400,000 par value 3 8% 5 $32,000 paid to preferred shareholders

Common: $120,000 total earnings 2 $32,000 paid to preferred 5 $88,000 to be paid to common shareholders

b. Seth Ames owns 1,000 shares of convertible preferred stock in the XYZ Corporation, with a current market price of

$52.00 per share. The preferred stock is convertible to common stock at the rate of 2 shares of common for each

share of preferred. After the end of the year in part (a), common stock was selling for $32 per share. What would be

the current market value of his stock before and after a conversion?

Preferred: 1,000 shares 3 $52 per share 5 $52,000 current value

Common: 1,000 shares preferred 3 2 5 2,000 shares common

2,000 shares 3 $32 per share 5 $64,000 current value

COMPLETE ASSIGNMENTS 21.1 AND 21.2.

✔

CONCEPT CHECK 21.4

board of directors

capital stock

charter

common stock

convertible preferred stock

corporation

cumulative preferred stock

declare a dividend

dividend in arrears

no-par stock

odd lot

odd-lot differential

par

preferred stock

price/earnings ratio (P/E)

proceeds (from sale of stock)

rate of yield

round lot

stockbroker

stock certificate

stock exchanges

stock transactions

total cost (for purchaser of stock)

Chapter Terms for Review

If the convertible stock pays 7% annually and the common stock usually pays $0.60 per

share, how much more dividend might Joel expect to receive annually?

$20 par value 3 200 shares 5 $4,000

$4,000 3 0.07 5 $280 preferred stock dividend

600 shares 3 $0.60 5 $360 common stock dividend

$360 2 $280 5 $80 more dividend annually