# Ch _7

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```					                                      Chapter 7

Interest Rates and Bond Valuation

Bond Features

Bond - evidence of debt issued by a corporation or a governmental body. A bond
represents a loan made by investors to the issuer. In return for his/her money,
the investor receives a legaI claim on future cash flows of the borrower. The
issuer promises to:

Make regular coupon payments every period until the bond matures, and
Pay the face/par/maturity value of the bond when it matures.

   Default - since the above mentioned promises are contractual obligations, an
issuer who fails to keep them is subject to legal action on behalf of the lenders
(bondholders).

   Bond Value = Present Value of the Coupons
+ Present Value of the Face Value

Bond Value = INT [1 – (1/(1 + rd)N)]/rd      +   M * 1/(1 + rd)N

where: INT = the promised coupon payment

M = the promised face value
N = number of periods until the bond matures
rd = the market’s required return, YTM

   If a bond has five years to maturity, an \$80 annual coupon, and a \$1000 face
value, its cash flows would look like this:

Time            0     1       2    3     4    5
Coupons             \$80     \$80   \$80   \$80 \$80
Face Value                                \$ 1000

Market Price            \$____

   How much is this bond worth? It depends on the level of current market
interest rates. If the going rate on bonds like this one is 10%, then this bond is
worth \$924.18.

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5N        10 I/Y      80 PMT     1000 FV      CPT PV (-924.18)

   Suppose a bond currently sells for \$932.90. It pays an annual coupon of \$70,
and it matures in 10 years. It has a face value of \$1000. What are its coupon
rate, current yield, and yield to maturity (YTM)?

   1. The coupon rate (or just “coupon”) is the annual dollar coupon as a
percentage of the face value:
Coupon rate = \$70 /\$1000 = 7%

   2. The current yield is the annual coupon divided by the current market price
of the bond:

Current yield = \$70 /932.90 = 7.5%

       3. The yield to maturity (or “YTM”) is the rate that makes the price of the
bond just equal to the present value of its future cash flows. It is the unknown r
in:

Value of Bond = Coupon Payment [1 –(1/(1 + rd)10]/rd + Face Value /(1 + rd )10

\$932.90 =                  \$70    [1 – (1/(1 + rd)10)]/rd + \$1000/(1 + rd )10

The only way to find the YTM is trial and error:

a.        Try 10%: \$70 * [(1 - 1/(1.10)10]/.10 + \$1000/(1.10)10 =
\$816

b.        Try 9%: \$70 * [1 - 1/(1.09)10]/.09 + \$1000/(1.09)10 = \$872

c.        Try 8%: \$70 * [1 - 1/(1.08)10]/.08 + \$1000/(1.08)10 = \$933

( ) The yield to maturity is closest to 8%.

Or using the BA II Plus Calculator

10 N   70 PMT - 932.90 PV       1000 FV      CPT I/Y

Valuing a Bond

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   Assume you have the following information.

Barnhart, Inc. bonds have a \$1000 face value
The promised annual coupon is \$100
The bonds mature in 20 years
The market’s required return on similar bonds is 10%

   Calculate the present value of the face value

= \$1000 X [1/1.1020 ] = \$1000 X .14864 = \$148.64

   Calculate the present value of the coupon payments

= \$100    [1 - (1/1.1020)]/.10 = \$100   8.5136 = \$851.36

   The value of each bond = \$148.64 + 851.36 = \$1000

Or 20 N 10 I/Y 100 PMT 1000 FV CPT PV (-1000)

   Assume you have the following information.

Barnhart, Inc. bonds have a \$1000 face value
The promised annual coupon is \$100
The bonds mature in 20 years
The market’s required return on similar bonds is 12%

   Calculate the present value of the face value

= \$1000     [1/(1.12)20 ] = \$1000   .10366 = \$103.66

   Calculate the present value of the coupon payments
= \$100 [1 - (1/1.1220)]/.12 = \$100 7.4694 = \$746.94

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   The value of each bond = \$103.66 + 746.94 = \$850.60

Or                 20 N   12 I/Y   100 PMT 1000 FV CPT PV (-850.60)

   Assume you have the following information.

Barnhart, Inc. bonds have a \$1000 face value
The promised annual coupon is \$100
The bonds mature in 20 years
The market’s required return on similar bonds is 8%

20 N       8 I/Y      100 PMT      1000 FV CPT PV (-1196.36)

   Calculate the present value of the face value

= \$1000 x [1/1.0820 ] = \$1000     .21455 = \$214.55

   Calculate the present value of the coupon payments

= \$100 x [1 - (1/1.0820)]/.08 = \$100       9.8181 = \$981.81

   The value of each bond = \$214.55 + 981.81 = \$1,196.36

   Why do the bonds in this and the preceding example have prices that are
different from par?

   Bond Value = Present Value of the Coupons
+ Present Value of the Face Value

Bond Value = INT [1 – (1/(1 + rd)N)]/rd      +     M * 1/(1 + rd)N

where: INT = the promised coupon payment

M = the promised face value
N = number of periods until the bond matures
rd = the market’s required return, YTM

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SEMI ANNUAL COUPON PAYMENTS

Most bonds pay coupon payments semi-annually. So a bond with a 10% coupon rate and
a face value of \$1000 has annual coupon payment

Annual Coupon Payment = \$1000 *.10 = \$100

If the bond has 10 years to maturity and a yield to maturity of 12%

The bond will pay a \$50 coupon every six months (\$100/2). If the bond has 10 years to
maturity and a yield to maturity of 12%

0          1           2           3             4                           10
[-----[----[-----[-----[-----[------[-----[------[-----------------------------[
50 50 50 50 50 50 50 50                                                 50
\$1000

10*2 = 20 N 12/2 = 6 I/Y           100/2 = 50 PMT 1000 FV CPT PV (-885.30)

Value of Bond = 100/2             [1 - 1/(1 + (.12/2)2*10]/.12/2 + 1000 * 1/(1 + .12/2)2*10
885.30

    Reznik Corporation has bonds on the market with 12.5 years to maturity, a
yield-to-maturity of 8 percent, and a current price of \$875. The bonds make
semiannual payments. What must the coupon rate be on the bonds?

Total number of coupon payments = 12.5 * 2 = 25
Yield-to-maturity per period        = 8% / 2 = 4%
Maturity value                      = F = \$1000

1.        Callaghan Motors' bonds have 10 years remaining to maturity. Interest is paid annually,
the bonds have a \$1,000 par value, and the coupon interest rate is 8 percent. The bonds
have a yield to maturity of 9 percent. What is the current market price of these bonds?

2.        Thatcher Corporation's bonds will mature in 10 years. The bonds have a face value of
\$1,000 and an 8 percent coupon rate, paid semiannually. The price of the bonds is
\$1,100. The bonds are callable in 5 years at a call price of \$1,050. What is the yield to
maturity? What is the yield to call?

3         Nungesser Corporation has issued bonds that have a 9 percent coupon rate, payable
semi- annually. The bonds mature in 8 years, have a face value of \$1,000, and a yield to
maturity of 8.5 percent. What is the price of the bonds?

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4.        A bond that matures in 10 years sells for \$985. The bond has a face value of \$1,000 and
and a 7% coupon rate..

a.. What is the bond's yield to maturity (YTM)?
b. Assume that the yield to maturity remains constant for the next 3 years. What will be
the price of the bond 3 years from today?

5.      A bond that matures in 7 years sells for \$1,020. The bond has a face value of
\$1,000 and a yield to maturity of 10.5883 percent. The bond pays coupons semiannually. What is
the bond's current yield?

Factors Affecting Bond Yields
* The    real rate of interest
    Expected future inflation
    Interest rate risk

Features of a May Department Stores Bond

Term                                Explanation
Amount of issue \$125 million     The company will issue \$125 million worth of bonds.
Date of issue   2/28/86          The bonds were sold on 2/28/86.
Maturity        3/1/16           The principal will be paid in 30 years.
Face Value     \$1,000            The denomination of the bonds is \$1,000.
Annual coupon 9.25               Each bondholder will receive \$92.50 per bond
per year (9.25% of the face value).
Offer price      100             The offer price will be 100% of the \$1,000 face value per bond.

Term                          Explanation

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Coupon payment dates 3/1, 9/1        Coupons of \$92.50/2 = \$46.25 will be paid on these dates.
Security       None                  The bonds are debentures.
Sinking fund Annual,                 The firm will make annual payments beginning 3/1/97
toward the sinking fund.
Call provision    Not callable        The bonds have a deferred call feature.
before 2/28/93
Rating           Moody’s A2          This is one of Moody’s higher ratings. The bonds have a
low probability of default.

Call price 106.48 initially, After 2/28/93, the company can buy declining to 100 back the bonds
for \$1,064.80 per bond, declining to \$1,000 on 2/28/05.

The Bond Indenture

   The bond indenture is a three-party contract between the bond issuer, the
bondholders, and the trustee. The trustee is hired by the issuer to protect
the bondholders’ interests. (What do you think would happen if an issuer
refused to hire a trustee?)

   The indenture includes

   The basic terms of the bond issue
   The total amount of bonds issued
   A description of the security
   The repayment arrangements
   The call provisions
   Details of the protective covenants

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Bond Ratings
Low Quality, speculative,
Investment-Quality Bond Ratings                 and/or “Junk”

Standard & Poor’s    AAA AA A BBB                   BB B     CCC CC         C D
Moody’s              Aaa Aa A Baa                   Ba B     Caa Ca         C C

Moody’s S&P

Aaa    AAA    Debt rated Aaa and AAA has the highest rating. Capacity to pay interest
and principal is extremely strong.

Aa      AA     Debt rated Aa and AA has a very strong capacity to pay interest and repay
principal. Together with the highest rating, this group comprises the high-

A       A      Debt rated A has a strong capacity to pay interest and repayrincipal,
although it is somewhat more susceptible to the adverse effects of
changes in circumstances and economic conditions than debt in high rated
categories.

Baa     BBB    Debt rated Baa and BBB is regarded as having an adequate capacity to pay
interest and repay principal. Whereas it normally exhibits adequate
protection parameters, adverse economic conditions or changing
circumstances are more likely to lead to a weakened capacity to pay
interest and repay principal for debt in this category than in higher rated
categories. These bonds are medium-grade obligations.

Ba, B   BB, B Debt rated in these categories is regarded, on balance, as Ca, CCC, C
predominantly speculative with respect to capacity to pay interest and
repay principal in accordance with the terms of the obligation. BB
and Ba indicate the lowest degree of speculation, and CC and Ca the
highest degree of speculation. Although such debt will likely have some
quality and protective characteristics, these are out-weighed by large
uncertainties or major risk exposures to adverse conditions. Some issues
may be in default.

D       D      Debt rated D is in default, and payment of interest and/or repayment of
principal is in arrears

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NEW YORK EXCHANGE BONDS

Quotations as of 4 p.m. Eastern Time
Thursday, March 5, 1998

CORPORATION BONDS
Volume, \$15,786,000

Co     Cp Mat       YTM      Vol      Price    CHG
Rate
ATT   4 3/4 98      4.8      10       99 9/16 ...
ATT   7 1/8 02      6.9      10       104      1/8
ATT   6 3/4 04      6.6      118      102 5/8 +1/8
ATT   7 1/2 06      7.0      30       107 3/8 ...
ATT   8 1/8 22       7.6     72       107 1/8  1/4
ATT   8 1/8 24      7.6      78       106 1/2 + 5/8
ATT   8 5/8 31      7.9      24       108 7/8  1/2

TREASURY BONDS, NOTES & BILLS
Cp Rate     MAT     Price    Price  CHG        YTM
53/8     Jan 00n   99:17    99:18   +1        5.62
73/4     Jan 00n   103:24   103:26 +1         5.61
77/8     Nov 04n   111:07   111:11 . . . .    5.80
.      .         .        .       .
.      .         .        .       .
.      .         .        .       .
9         Nov 18    133:10   133:16 4        6.12
8 7/8     Feb 19    131:31   132:05  6        6.13
8 1/8     Aug 19    123:13   123:19 5        6.13
8 3/4     May 20    131:09   131:15 8        6.13
8 3/4     Aug 20    131:14   131:20 7        6.14
7 7/8     Feb 21    121:00   121:06 6        6.14

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