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with more liberal credit terms.

4 The higher the discount rate the less important are future sales. Because the value of repeat
sales is lower, the break-even probability on the initial sale is higher. For instance, we saw
that the break-even probability was 1/3 when the discount rate was 10 percent. When the
discount rate is 20 percent, the value of a perpetual flow of repeat sales falls to $200/.20 =
$1,000, and the break-even probability increases to 1/2:
1/2 — $1,000 “ 1/2 — $1,000 = 0

5 The customer pays bills 45 days after the invoice date. Because goods are purchased daily,
at any time there will be bills outstanding with “ages” ranging from 1 to 45 days. At any
time, the customer will have 30 days™ worth of purchases, or $10,000, outstanding for a pe-
riod of up to 1 month, and 15 days™ worth of purchases, or $5,000, outstanding for between
1 month and 45 days. The aging schedule will appear as follows:

Age of Account Amount
< 1 month $10,000
1“2 months $ 5,000

George Stamper, a credit analyst with Micro-Encapsulators Corp. had unused lines of credit totaling $5 million but had entered
(MEC), needed to respond to an urgent e-mail request from the into discussions with its bank for a renewal of a $15 million
South-East sales office. The local sales manager reported that she bank loan that was due to be repaid at the end of the year. Tele-
had an opportunity to clinch an order from Miami Spice (MS) for phone calls to MS™s other suppliers suggested that the company
50 encapsulators at $10,000 each. She added that she was partic- had recently been 30 days late in paying its bills.
ularly keen to secure this order since MS was likely to have a con- George also needed to take into account the profit that the
tinuing need for 50 encapsulators a year and could therefore company could make on MS™s order. Encapsulators were sold
prove a very valuable customer. However, orders of this size to a on standard terms of 2/30, net 60. So if MS paid promptly, MEC
would receive additional revenues of 50 — $9,800 = $490,000.
new customer generally required head office agreement, and it
was therefore George™s responsibility to make a rapid assessment However, given MS™s cash position, it was more than likely that
of MS™s creditworthiness and to approve or disapprove the sale. it would forgo the cash discount and would not pay until some-
George knew that MS was a medium-sized company, with a time after the 60 days. Since interest rates were about 8 percent,
patchy earnings record. After growing rapidly in the 1980s, MS any such delays in payment would reduce the present value to
had encountered strong competition in its principal markets and MEC of the revenues. George also recognized that there were
earnings had fallen sharply. George Stamper was not sure exactly production and transportation costs in filling MS™s order. These
to what extent this was a bad omen. New management had been worked out at $475,000, or $9,500 a unit. Corporate profits
brought in to cut costs and there were some indications that the were taxed at 35 percent.
worst was over for the company. Investors appeared to agree with
this assessment, for the stock price had risen to $5.80 from its low Questions
of $4.25 the previous year. George had in front of him MS™s lat-
1. What can you say about Miami Spice™s creditworthiness?
est financial statements, which are summarized in Table 2.12. He
2. What is the break-even probability of default? How is it af-
rapidly calculated a few key financial ratios and the company™s Z
fected by the delay before MS pays its bills?
3. How should George Stamper™s decision be affected by the
George also made a number of other checks on MS. The com-
possibility of repeat orders?
pany had a small issue of bonds outstanding, which were rated B
by Moody™s. Inquiries through MEC™s bank indicated that MS
Credit Management and Collection 251

TABLE 2.12
2000 1999
Miami Spice: summary
financial statements (figures Assets
in millions of dollars) Current assets
Cash and marketable securities 5.0 12.2
Accounts receivable 16.2 15.7
Inventories 27.5 32.5
Total current assets 48.7 60.4
Fixed assets
Property, plant, and equipment 228.5 228.1
Less accumulated depreciation 129.5 127.6
Net fixed assets 99.0 100.5
Total assets 147.7 160.9
Liabilities and Shareholders™ Equity
Current liabilities
Debt due for repayment 22.8 28.0
Accounts payable 19.0 16.2
Total current liabilities 41.8 44.2
Long-term debt 40.8 42.3
Shareholders™ equity
Common stocka 10.0 10.0
Retained earnings 55.1 64.4
Total shareholders™ equity 65.1 74.4
Total liabilities and shareholders™ equity 147.7 160.9
Income Statement
Revenue 149.8 134.4
Cost of goods sold 131.0 124.2
Other expenses 1.7 8.7
Depreciation 8.1 8.6
Earnings before interest and taxes 9.0 “ 7.1
Interest expense 5.1 5.6
Income taxes 1.4 “ 4.4
Net income 2.5 “ 8.3
Allocation of net income
Addition to retained earnings 1.5 “ 9.3
Dividends 1.0 1.0

a 10 million shares, $1 par value.
Section 3
Valuing Bonds

Valuing Stocks

Introduction to Risk, Return, and the
Opportunity Cost of Capital

Bond Characteristics
Reading the Financial Pages

Bond Prices and Yields
How Bond Prices Vary with Interest
Yield to Maturity versus Current Yield
Rate of Return
Interest Rate Risk
The Yield Curve
Nominal and Real Rates of Interest
Default Risk
Variations in Corporate Bonds


Bondholders once received a beautifully engraved certificate like this 1909 one for an Erie
and Union Railroad bond.
Nowadays their ownership is simply recorded on an electronic database.
Courtesy of Terry Cox

nvestment in new plant and equipment requires money”often a lot of

I money. Sometimes firms may be able to save enough out of previous
earnings to cover the cost of investments, but often they need to raise
cash from investors. In broad terms, we can think of two ways to raise new
money from investors: borrow the cash or sell additional shares of common stock.
If companies need the money only for a short while, they may borrow it from a bank;
if they need it to make long-term investments, they generally issue bonds, which are
simply long-term loans. When companies issue bonds, they promise to make a series of
fixed interest payments and then to repay the debt. As long as the company generates
sufficient cash, the payments on a bond are certain. In this case bond valuation involves
straightforward time-value-of-money computations. But there is some chance that even
the most blue-chip company will fall on hard times and will not be able to repay its
debts. Investors take this default risk into account when they price the bonds and de-
mand a higher interest rate to compensate.
In the first part of this material we sidestep the issue of default risk and we focus on
U.S. Treasury bonds. We show how bond prices are determined by market interest rates
and how those prices respond to changes in rates. We also consider the yield to matu-
rity and discuss why a bond™s yield may vary with its time to maturity.
Later in the material we look at corporate bonds where there is also a possibility of
default. We will see how bond ratings provide a guide to the default risk and how low-
grade bonds offer higher promised yields.
Later we will look in more detail at the securities that companies issue and we will
see that there are many variations on bond design. But for now, we keep our focus on
garden-variety bonds and general principles of bond valuation.
After studying this material you should be able to
Distinguish among the bond™s coupon rate, current yield, and yield to maturity.
Find the market price of a bond given its yield to maturity, find a bond™s yield given
its price, and demonstrate why prices and yields vary inversely.
Show why bonds exhibit interest rate risk.
Understand why investors pay attention to bond ratings and demand a higher inter-
est rate for bonds with low ratings.

Bond Characteristics
Governments and corporations borrow money by selling bonds to investors. The money
Security that
they collect when the bond is issued, or sold to the public, is the amount of the loan. In
obligates the issuer to make
return, they agree to make specified payments to the bondholders, who are the lenders.
specified payments to the
When you own a bond, you generally receive a fixed interest payment each year until

Valuing Bonds 257

Cash flows to an investor in $1,060
the 6% coupon bond
maturing in the year 2002.

$60 $60


Year: 1999 2000 2001 2002


the bond matures. This payment is known as the coupon because most bonds used to
have coupons that the investors clipped off and mailed to the bond issuer to claim the
The interest
interest payment. At maturity, the debt is repaid: the borrower pays the bondholder the
payments paid to the
bond™s face value (equivalently, its par value).
How do bonds work? Consider a U.S. Treasury bond as an example. Several years
ago, the U.S. Treasury raised money by selling 6 percent coupon, 2002 maturity, Trea-
sury bonds. Each bond has a face value of $1,000. Because the coupon rate is 6 per-
at the maturity of the bond.
cent, the government makes coupon payments of 6 percent of $1,000, or $60 each year.1
Also called par value or
When the bond matures in July 2002, the government must pay the face value of the
maturity value.
bond, $1,000, in addition to the final coupon payment.
Suppose that in 1999 you decided to buy the “6s of 2002,” that is, the 6 percent
coupon bonds maturing in 2002. If you planned to hold the bond until maturity, you
interest payment as a
would then have looked forward to the cash flows depicted in Figure 3.1. The initial
percentage of face value.
cash flow is negative and equal to the price you have to pay for the bond. Thereafter, the
cash flows equal the annual coupon payment, until the maturity date in 2002, when you
receive the face value of the bond, $1,000, in addition to the final coupon payment.

The prices at which you can buy and sell bonds are shown each day in the financial
press. Figure 3.2 is an excerpt from the bond quotation page of The Wall Street Journal
and shows the prices of bonds and notes that have been issued by the United States Trea-
sury. (A note is just a bond with a maturity of less than 10 years at the time it is issued.)
The entry for the 6 percent bond maturing in July 2002 that we just looked at is high-
lighted. The letter n indicates that it is a note.
Prices are generally quoted in 32nds rather than decimals. Thus for the 6 percent
bond the asked price”the price investors pay to buy the bond from a bond dealer”is
shown as 101:02. This means that the price is 101 and 2/32, or 101.0625 percent of face
value, which is $1,010.625.
The bid price is the price investors receive if they sell the bond to a dealer. Just as
the used-car dealer earns his living by reselling cars at higher prices than he paid for
them, so the bond dealer needs to charge a spread between the bid and asked price. No-

1In the United States, these coupon payments typically would come in two semiannual installments of $30
each. To keep things simple for now, we will assume one coupon payment per year.

Treasury bond quotes from
The Wall Street Journal, July
16, 1999. Thursday, July 15, 1999
Representative Over-the-Counter quotations based on transactions of $1
million or more.
Treasury bond, note and bill quotes are as of mid-afternoon. Colons in bid-
and-asked quotes represent 32nds; 101:01 means 101 1/32. Net changes in
32nds. n-Treasury note. Treasury bill quotes in hundredths, quoted on terms of a
rate of discount. Days to maturity calculated from settlement date. All yields are
to maturity and based on the asked quote. Latest 13-week and 26-week bills are


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