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

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444 Part 6 Corporate and Special Applications

Assignment 21.2 Continued

11. Determine the price/earnings ratio (P/E) of each of the following stocks: (2 points for each correct

answer)

a. JBC common stock has a current market price of $49 and has had earnings per share of $0.72 each quarter for

the last four quarters.

b. The current market price of Cannon common stock is $72.88. Cannon has paid dividends of $1.20 per quarter

for each of the last four quarters.

Score for B (66)

Notes

$72.88 4 ($1.20 3 4) 5 15.18 rounded to 15

$49 4 ($0.72 3 4) 5 17.01 rounded to 17

Corporate and

Government

Bonds

Chapter 22 Corporate and Government Bonds 445

Learning Objectives

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

Learning Objective

Compute gains and losses on convertible and callable corporate bond

transactions.

Compute annual interest on bonds.

Compute accrued interest on bond transactions made between

interest payment dates.

Compute annual yield on bonds selling at a premium or a discount.

Compute a rate of yield to maturity.

Learning Objective

When a corporation or government entity needs cash for a long period of time, usually

10 years or more, it often will issue long-term notes known as bonds. Bonds are bought

and sold on the open market, much like stocks.

Two main types of government bonds are treasury bonds and municipal bonds.

Treasury bonds are issued by the United States government. These bonds are fully

guaranteed by the full faith and credit of the United States government. Bondholders are

protected against default unless the federal government becomes insolvent. Municipal

bonds are issued by states, cities, school districts, and other public entities. Unlike

treasury bonds, municipal bonds pose a risk that the issuer might fail to repay the

principal. Interest paid on municipal bonds generally is exempt from federal and state

income taxes.

There are many kinds of corporate bonds, two of which are convertible bonds and

callable bonds. Convertible bonds have a provision that they may be converted to a

designated number of shares or a designated value of the corporation’s stock. Callable

bonds have a provision that the issuer can repurchase, or call in, the bonds at specified

dates if the board of directors authorizes the retirement (payoff) of the bonds before

their maturity date. Such action by the board of directors would be appropriate if

interest rates fell significantly below the interest rate of the callable bond.

446 Part 6 Corporate and Special Applications

22.1 It should be noted that callable

bonds are usually called during

periods when interest rates fall

significantly.Suppose XYZ callable

bonds were issued at 12%.If interest

rates fall to 8%,XYZ Corporation can

secure a bank loan or issue new bonds

at 8% and call the 12% bonds,thus

saving 4% on borrowing costs.

EXAMPLE A

Steve Bando bought one ABC Corporation convertible bond for $1,000. The bond was

convertible to 100 shares of stock. At the time of the purchase, the stock was selling for

$10 per share. At the end of 1 year, the stock was selling for $15 per share. Steve converted

his bond. Assuming that the market value of the bond hadn’t changed, how much profit

did Steve realize by converting?

100 shares of stock 3 $15 per share 5 $1,500

$1,500 stock value 2 $1,000 bond value 5 $500 profit

EXAMPLE B

XYZ Corporation issued $1,000,000 worth of callable bonds paying 8% interest. The

maturity date for the bonds was in 10 years. Two years later, interest rates fell to 6%.

The bonds were called, and new bonds were sold at the 6% rate. How much did

XYZ Corporation save by calling the bonds?

10 years to maturity at issue 2 2 years 5 8 years remaining to maturity

8% 2 6% 5 2% savings per year

$1,000,000 3 2% 5 $20,000 interest saved per year

$20,000 3 8 years 5 $160,000 saved

Computing Gains and Losses

on Corporate Bonds

Learning Objective

Compute gains and losses on con-

vertible and callable corporate bond

transactions.

When first issued, bonds are sold either through brokerage houses or directly to

investors at or near the price of $1,000, called face value. Face value represents the

amount that will be paid to the holder when the bonds are redeemed at maturity. If the

market value becomes less than the face value, the bond sells at a discount. If the market

value becomes more than the face value, the bond sells at a premium. (The discount or

premium amount is the difference between the market value and the face value.)

Bonds are rated. By checking a bond’s rating, buyers can have some indication of how

safe their bond investment is. Bond ratings are information based on experience and

research; they are not a guarantee. One major firm rating bonds is Standard & Poor’s.

In Standard & Poor’s system, the ratings include AAA (the highest rating), AA, A,

BBB, BB, B, CCC, CC, C, and D. A bond with a low rating is a higher-risk bond and

sometimes is known as a junk bond. The lower a bond’s rating, the higher are its yield

and its risk.

EXAMPLE C

Kiley Moore purchased a $1,000 bond with a rating of B, paying 14% per year. Mary

Baker purchased a $1,000 bond with a rating of AAA, paying 5% per year. Jean Carlson

purchased a $1,000 junk bond, paying 25% per year. Each bond was to mature in

10 years.

Kiley’s B-rated bond paid faithfully for 4 years. Then the company filed for bank-

ruptcy and paid 60 cents on the dollar. Mary’s AAA-rated bond paid interest during its

entire 10-year life and paid face value on maturity. Jean’s junk bond paid interest for

3 years. Then the company filed for bankruptcy and paid 30 cents on the dollar.

Compute how much each investor received for her $1,000 investment.

Kiley: $1,000 3 14% 5 $140 annual interest

$140 3 4 years 5 $560 interest

$560 interest 1 (0.60 3 $1,000) redemption 5 $1,160 total

Chapter 22 Corporate and Government Bonds 447

a. What would be the “stock” value of a bond that was convertible to 40 shares of stock if the

stock was priced at $37.62?

40 shares 3 $37.62 5 $1,504.80

b. If a company issued a callable bond at interest, would it be likely to call the bond if the

current rate of interest was 8%?

No, because it could invest the cash at an extra interest.

✔

CONCEPT CHECK 22.1

Computing Annual Interest on Corporate

and Government Bonds

Compute annual interest on bonds.

Learning Objective

22.2 Bond rating has become very

important for private and public

organizations.Today,many corporate

and government bonds are purchased

by pension funds,college reserve

funds,and insurance companies.These

organizations frequently work with a

“safety net”set by a board of trustees

or a management group.The safety net

limits purchases to bonds at or above a

certain rating,such as AAA or AA.

Mary: $1,000 3 5% 5 $50 annual interest

$50 3 10 years 5 $500 interest

$500 interest 1 $1,000 redemption 5 $1,500 total

Jean: $1,000 3 25% 5 $250 annual interest

$250 3 3 years 5 $750 interest

$750 interest 1 (0.30 3 $1,000) redemption 5 $1,050 total

How much would Kiley and Jean have received on their investments if the bonds had

paid full interest for the 10-year period and face value on maturity?

Kiley: $1,000 3 14% 3 10 years 5 $1,400

$1,400 1 $1,000 5 $2,400

Jean: $1,000 3 25% 3 10 years 5 $2,500

$2,500 1 $1,000 5 $3,500

NEWSPAPER INFORMATION ON BONDS

Information about the market value and sale of bonds on the major exchanges is reported

daily in financial newspapers. Figure 22-1 shows information usually included in a bond

report.

448 Part 6 Corporate and Special Applications

Current

Bonds Yield Volume Close Net Change

ATT s09 7.2 10 104 11

Aetna s12 6.6 25 96.80 . . .

ClrkOil s06 9.1 33 104.25 1.25

Hertz 7s12 7.0 13 99.70 1.70

IBM 7s25 7.4 102 94.50 1.80

RJR Nb 8s10 7.9 15 101.50 . . .

Figure 22-1 Bond Market Report

22.3 The business section of most

metropolitan newspapers provides

current real-world information.

Examples taken directly from a current

paper should be used to illustrate the

difference between interest rates for

government bonds with greater safety

and those for corporate bonds with

greater risk.

Prices of bonds are quoted in percents of face value. For example, a $1,000 bond

quoted at 104 would sell at a premium price of $1,040 ($1,000 3 104%). If quoted at 87,

the bond would sell at a discounted price of $870 ($1,000 3 87%).

Rule: Prices over 100 (100%) include a premium. Those under 100 (100%) include a

discount.

The two main factors that influence the market price are the interest rate and the bond

rating. For example, if a bond pays 8% interest and the current market rate of interest is

greater than 8% for similarly rated bonds, the bonds will sell at a discount sufficient to

make up for the difference in interest rates over the term of the bond.

Printed bond reports generally give a letter abbreviation for the company, the interest

rate, a small s to designate semiannual (every 6 months) interest payments, and the

maturity date, followed by the current yield, the number of bonds sold that day, the

closing price of the bond, and the net change in price from the prior day.

The first line of the bond market report in Figure 22-1 would be interpreted as ATT

(designating American Telephone and Telegraph), a 7 interest rate based on the face

value of the bond, and interest paid semiannually. The bond matures in 2009. The

current yield (average annual interest rate based on the current price of the bond) is

7.2%. The day’s volume of bonds sold was 10. The closing price was 104, up 1 from the

prior day.

EXAMPLE D

Calculate the amount of the semiannual interest check for a $1,000 bond reported in a

financial paper as R&S Corp s21.

$75 4 2 5 $37.50 semiannual interest payment

COMMISSIONS FOR BUYING AND SELLING BONDS

The charge for buying and selling bonds varies among brokers, but there is no standard

commission. Commissions are very small and thus comprise only a negligible part of the

bond transaction. We do not use commission costs for problems in this textbook.

$1,000 face value 3 7

% 5 $75;

Chapter 22 Corporate and Government Bonds 449

22.4 Some government bonds,such as

treasury bonds,can be purchased

directly from the government without

commission;however,there is usually a

minimum purchase amount of $5,000

or more.

22.5 In computing the days of accrual

for interest,interest is paid through

December 31,which places the income

in the year ending December 31.Interest

for the next 6-month period will then

begin on January 1,and that day is

therefore counted in determining the

number of days of accrual.

If James Kun purchased 27 triple-A bonds that pay 7.1% and mature in 8 years, what amount

of interest income could he expect annually?

$1,000 3 0.071 3 27 5 $1,917

If James holds the bonds until maturity, how much will he receive on redemption of the bonds?

$1,000 3 27 5 $27,000 total face value

✔

CONCEPT CHECK 22.2

Compute accrued interest on bond

transactions made between interest

payment dates.

Learning Objective

Most bonds specify that interest is payable quarterly, semiannually, or annually. The

interest payment dates—such as January 1 (for interest through December 31) and July 1

(for interest through June 30)—are stated on the bond. When a bond is purchased

between these dates, it is customary to add the accrued interest (interest earned from

the last payment date to the purchase date). This interest is calculated by finding the

number of days from the day on which interest was last paid through the day before the

purchase and dividing this number by 360.

The buyer pays the seller for the interest accumulated or accrued on the bond since

the last interest payment date. On the next regular interest payment date, the new owner

receives the interest for the full interest period. This procedure allocates the interest

correctly between the buyer and the seller for the split interest period because the

corporation that issued the bond will pay the entire amount to whomever owns the bond

as of each interest date.

Computing Accrued Interest on Bond

Transactions

EXAMPLE E

A $1,000 bond, with interest at 8% payable semiannually on January 1 and July 1, was

purchased on October 8 at 104 plus accrued interest. What is the number of days for

which the accrued interest is paid?

Purchase date: October 8

Days of accrued interest: (July) 31 1 (August) 31 1 (September) 30 1 (October) 7 5 99

What is the purchase payment for the bond?

$1,000 3 104% 5 $1,040 market value

$1,000 3 0.08 interest 3 accrued days 5 $22 accrued interest

$1,040 1 $22 5 $1,062 purchase payment for bond

In example E, although the accrued interest is an additional payment by the buyer, the

buyer will get it back in the $40 ($1,000 3 8% 3 ) interest payment on January 1.

360

450 Part 6 Corporate and Special Applications

Ann Ahn purchased two Hertz 7s08 bonds at 95.6 on March 15. What amount did she pay

her broker?

$2,000 3 0.956 5 $1,912.00

Purchase date: March 15

(January) 31 1 (February) 28 1 (March) 14 5 73 days

$2,000 3 0.07 35$28.39 accrued interest

$1,912.00 1 $28.39 5 $1,940.39 paid to her broker

360

✔

CONCEPT CHECK 22.3

Learning Objective

Compute annual yield on bonds

selling at a premium or a discount.

Interest on bonds provides income to bondholders. This income is referred to as yield.

Newspapers and bond brokers refer to the annual yield of a bond as its current yield.

Many newspaper bond reports include a column showing current yield. To calculate the

current yield from an investment in bonds, use the following formula:

Annual interest 4 Current purchase price 5 Current yield

When a bond is purchased at a discount, the current yield is greater than the face

rate. For example, a $1,000 bond, purchased at 90, pays 7% interest and matures in

10 years. Interest of $70 ($1,000 3 7%) is paid annually, but as the bond was purchased

for $900 ($1,000 3 90%), the effective rate, or yield, as a percent of cost is 7.8%

($70 4 $900).

When a bond is purchased at a premium, the current yield is less than the face rate.

The reason is that the interest paid is calculated on the face value, and the yield is based

on the higher market price.

Computing the Rate of Yield for Bonds

EXAMPLE F

Five $1,000 Levi Strauss 9 s19 bonds were purchased at 80. What was the current yield

on the bonds?

$1,000 3 5 5 $5,000 face value

$5,000 3 80% 5 $4,000 purchase price

$5,000 3 0.095 5 $475 annual interest

$475 4 $4,000 5 0.11875 5 11.9 % current yield

or 9.5 4 0.80 5 11.875 5 11.9% current yield

In example F, the bonds sold at a discount of $1,000 ($5,000 2 $4,000) because the

investor paid that much less for them than the maturity (face) value. Therefore, the

current yield of 11.8% is more than the stated interest rate of .9

Chapter 22 Corporate and Government Bonds 451

22.6 When bonds are sold at discount,

the yield rate will always be higher

than the stated (face) rate.Likewise,

when bonds are sold at a premium, the

yield rate will always be lower than the

stated (face) rate.

The RJR Nb bonds listed in Figure 22-1 recently rose to a price of 109. Zelda Morantz

purchased four at 109. What will be her annual current yield?

$4,000 3 109% 5 $4,360 purchase price

$4,000 3 0.08 5 $320 annual interest

$320 4 $4,360 5 0.0734, or 7.34%,

or 0.08 4 1.09 5 0.0734, or 7.34%

✔

CONCEPT CHECK 22.4

Careful investors calculate the rate of yield to maturity, or the rate of interest they will

earn if they hold the bond to its maturity date. The yield to maturity calculation involves

use of the true annual interest by adding a part of the discount or subtracting a part of

the premium and basing the rate on the average principal invested (the average of the

investor’s purchase price and the bond’s maturity value).

Computing the Rate of Yield to Maturity

Compute a rate of yield to maturity.

Learning Objective

to Compute the Rate of Yield to Maturity

1. Compute the annual interest: Multiply the face value by the stated

(face) rate.

2. Determine the annual discount (or premium) amortization: Divide the

discount (or premium) by the number of years from purchase to maturity.

3. Determine the average principal invested: Add the maturity value and

the cost price and then divide by 2.

4. The following formula computes the rate:

Again, because brokerage charges are such a small part of the cost, they

usually are omitted from the calculations of yield to maturity.

Annual interest 1 Annual discount amortization

(or 2 Annual premium amortization)

Average principal invested

STEPS

452 Part 6 Corporate and Special Applications

EXAMPLE G

Assume that the Levi Strauss bonds in example F matured 20 years after the purchase date.

$5,000 3 0.095 5 $475 annual interest

$1,000 4 20 years 5 $50 annual discount amortization

($5,000 1 $4,000) 4 2 5 $4,500 average principal invested

($475 1 $50) 4 $4,500 5 0.1167 5 11.67% yield to maturity

This rate is somewhat less than the 11.9% current yield, but it is more accurate with

respect to actual income if the bond is held to maturity.

EXAMPLE H

To calculate the yield to maturity on bonds sold at a premium, assume that five IntTT

9 s20 bonds were bought at a premium price of 124 and that the bonds will mature in

15 years. The market value of the five bonds is $6,200 ($5,000 3 124%).

$5,000 3 0.095 5 $475 annual interest

($6,200 2 $5,000) 4 15 years 5 $80 annual premium amortization

($5,000 1 $6,200) 4 2 5 $5,600 average principal invested

($475 2 $80) 4 $5,600 5 0.0705 5 7.05% yield to maturity

This rate is less than the stated rate of on the premium bonds.9

STEP 4

STEP 3

STEP 2

STEP 1

STEP 4

STEP 3

STEP 2

STEP 1

If the four RJR Nb 8s10 bonds Zelda Morantz purchased at 109 (Concept Check 22.4) had 5

years to maturity, what would be her rate of yield to maturity?

$4,000 3 0.08 5 $320 annual interest

$360 premium 4 5 years 5 $72 annual premium amortization

($4,000 1 $4,360) 4 2 5 $4,180 average principal invested

($320 2 $72) 4 $4,180 5 0.0593 5 5.93% yield to maturity

COMPLETE ASSIGNMENTS 22.1 and 22.2.

✔

CONCEPT CHECK 22.5

Chapter 22 Corporate and Government Bonds 453

accrued interest

annual discount amortization

annual premium amortization

average principal invested

bond ratings

bonds

callable bonds

convertible bonds

corporate bonds

current yield

discount

face value

government bonds

junk bond

municipal bonds

premium (bond)

rate of yield to maturity

treasury bonds

yield

Chapter Terms for Review

Try Microsoft

Excel

Try working the following problems using the Microsoft Excel templates found on your

Student CD. Solutions for the problems are also found on the CD.

1. Complete the following Excel worksheet by entering formulas in the shaded cells

to calculate the Total Cost and Premium or (Discount) for each bond purchase.

Hint: Remember that each bond has a face value of $1,000.

2. Complete the following Excel worksheet by entering formulas in the shaded cells

to calculate the Annual Interest, Current Purchase Price, and Current Yield

for each bond.

Hint: Calculations are for one bond (face value $1,000). Current yield should be

shown as a percent.

Current

Annual Purchase Current

Bond Price Interest Price Yield

IBM 7s12 90

SBC 9s08 107

CXL 6.2s09 86.5

Number Price Total Premium

Purchased Paid Cost (Discount)

592

12 108

8 112

288

16 92