Chapter 9
Debt Valuation
and Interest
Rates
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Slide Contents
• Learning Objectives
• Principles Used in This Chapter
1.Overview of Corporate Debt
2.Valuing Corporate Debt
3.Bond Valuation: Four Key Relationships
4.Types of Bonds
5.Determinants of Interest Rates
• Key Terms
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9-2
Learning Objectives
1. Identify the key features of bonds and
describe the difference between private
and public debt markets.
2. Calculate the value of a bond and relate it
to the yield to maturity on the bond.
3. Describe the four key bond valuation
relationships.
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9-3
Learning Objectives (cont.)
4. Identify the major types of corporate
bonds.
5. Explain the effects of inflation on interest
rates and describe the term structure of
interest rates.
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9-4
Principles Used in This Chapter
• Principle 1: Money Has a Time Value.
– Debt securities require that the borrower repay
the lender over time so cash flows have to be
adjusted for time value of money.
• Principle 2: There is a Risk-Return
Tradeoff.
– The rate used to discount future cash flows
depends on the risk of default by the borrower.
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9-5
Principles Used in This Chapter
(cont.)
• Principle 3: Cash Flows Are the Source of
Value
– Debt securities provide value to the lender
through the interest payments on the
outstanding loan amount and the repayment of
the loan balance itself.
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9-6
9.1 Overview of
Corporate Debt
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Corporate Borrowings
• There are two main sources of borrowing
for a corporation:
1. Loan from a financial institution (known as
private debt)
2. Bonds (known as public debt since they can
be traded in public financial markets)
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9-8
Corporate Borrowings (cont.)
• Smaller firms choose to raise money from
banks in the form of loans because of the
high costs associated with issuing bonds.
• Larger firms generally raise money from
banks for short-term needs and depend on
the bond market for long-term financing
needs.
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9-9
Borrowing Money in the Private
Financial Market
• Financial Institutions are an important
source of capital for corporations. The loan
might be used to finance firm’s day-to-day
operations or it might be used for the
purchase of equipment or property.
• Such loans are considered private
market transactions since it only
involves the two parties to the loan.
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9-10
Borrowing Money in the Private
Financial Market (cont.)
• In the private financial market, loans are
typically floating rate loans i.e. the
interest rate is periodically adjusted based
on a specific benchmark rate.
• The most popular benchmark rate is the
London Interbank Offered Rate
(LIBOR)
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9-11
Borrowing Money in the Private
Financial Market (cont.)
• LIBOR is the daily interest rate that is
based on the interest rates at which banks
offer to lend in the London wholesale or
interbank market.
– Interbank market is the market where banks
loan each other money.
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9-12
Borrowing Money in the Private
Financial Market (cont.)
• A typical floating rate loan will specify the
following:
– The spread or margin between the loan rate
and the benchmark rate expressed as basis
points.
– A maximum and a minimum annual rate, to
which the rate can adjust, called the ceiling and
floor.
– A maturity date
– Collateral
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9-13
Borrowing Money in the Private
Financial Market (cont.)
• For example, a corporation may get a 1year loan with a rate of 300 basis points
(or 3%) over LIBOR with a ceiling of 11%
and a floor of 4%.
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9-14
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9-15
Checkpoint 9.1
Calculating the Rate of Interest on a Floating Rate Loan
The Slinger Metal Fabricating Company entered into a loan agreement
with its bank to finance the firm’s working capital. The loan called for a
floating rate that was 25 basis points (.25%) over an index based on
LIBOR. In addition, the loan adjusted weekly based on the closing
value of the index for the previous week within the bounds of a
maximum annual rate of 2.5% and a minimum of 1.75%. Calculate
the rate of interest for the weeks 2 through 10.
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9-16
Checkpoint 9.1
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9-17
Checkpoint 9.1
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9-18
Checkpoint 9.1
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9-19
Checkpoint 9.1
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9-20
Checkpoint 9.1: Check Yourself
Consider the same loan period as above but
change the spread over LIBOR from .25% to .75%.
Is the ceiling rate or floor rate violated during the
loan period?
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9-21
Step 1: Picture the Problem
• The graph on the next slide shows the
LIBOR index (series 1), LIBOR plus the
spread of 75 basis points (series 2) the
ceiling rate (series 3), and the floor rate
(series 4).
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9-22
Step 1: Picture the Problem (cont.)
Floating Rate Loans
3.00%
2.50%
Interest Rate
2.00%
Series1
Series2
1.50%
Series3
Series4
1.00%
0.50%
0.00%
1
2
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3
4
5
6
7
8
9-23
Step 2: Decide on a Solution
Strategy
• We have to determine the floating rate for
every week and see if it exceeds the
ceiling or falls below the floor.
• Floating rate on Loan
= LIBOR for the previous week + spread of .75%
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9-24
Step 2: Decide on a Solution
Strategy
• The floating rate on loan cannot exceed
the ceiling rate of 2.5% or drop below the
floor rate of 1.75%.
– If the floating rate falls below the floor, the rate
will be reset at the floor rate.
– If the floating rate exceeds the ceiling, the rate
will be reset at the ceiling rate.
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9-25
Step 3: Solve
LIBOR
LIBOR +
Spread
(.75%)
Loan Rate
2/29/2008
1.98%
3/7/2008
1.66%
2.73%
2.50%
3/14/2008
1.52%
2.44%
2.41%
3/21/2008
1.35%
2.27%
2.27%
3/28/2008
1.60%
2.10%
2.10%
4/4/2008
1.63%
2.35%
2.35%
4/11/2008
1.67%
2.38%
2.38%
4/18/2008
1.88%
2.42%
2.42%
4/25/2008
1.93%
2.63%
2.50%
2.68%
2.50%
5/2/2008
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Ceiling
Violated
9-26
Step 3: Solve (cont.)
• The table shows the ceiling is violated
during the first week and last two weeks of
the loan period. The floor rate is never
violated.
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9-27
Step 4: Analyze
• The ceiling is the maximum rate charged on the
loan while floor is the minimum rate charged on
the loan. If the ceiling or floor rates are violated,
the loan rate is reset to the ceiling rate or the
floor rate.
• If there were no ceiling, the loan rate would have
been 2.73% during the first week of the loan, and
2.63% and 2.68% during the last two weeks of
the loan.
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9-28
Borrowing Money in the Public
Financial Market
• Firms also raise money by selling debt
securities to individual investors and
financial institutions such as mutual funds.
• In order to sell debt securities to the
public, the issuing firm must meet the
legal requirements as specified by the
securities laws.
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9-29
Borrowing Money in the Public
Financial Market
• Corporate bond is a debt security issued
by corporation that has promised future
payments and a maturity date.
• If the firm fails to pay the promised future
payments of interest and principal, the
bond trustee can classify the firm as
insolvent and force the firm into
bankruptcy.
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9-30
Basic Bond Features
• The basic features of a bond include the
following:
–
–
–
–
–
–
Bond Indenture
Claims on Assets and Income
Par or Face Value
Coupon Interest Rate
Maturity and Repayment of Principal
Call Provision and Conversion Features
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9-31
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9-32
Bond Ratings and Default Risk
• Bond ratings indicate the default risk i.e.
the probability that the firm will make the
promised payments.
• Bond ratings affect the rate of return that
lenders require of the firm and the firm’s
cost of borrowing.
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9-33
Bond Ratings and Default Risk
(cont.)
• Consistent with Principle 2 (There is a
Risk-Return Tradeoff), the lower the bond
rating, the higher the risk of default and
higher the rate of return demanded in the
capital market.
• Bond ratings are provided by three rating
agencies – Moody’s, Standard & Poor’s,
and Fitch Investor Services.
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9-34
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9-35
9.2 Valuing
Corporate Debt
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Valuing Corporate Debt
• The value of corporate debt is equal to the
present value of the contractually
promised principal and interest payments
(the cash flows) discounted back to the
present using the market’s required yield.
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9-37
Valuing Corporate Debt (cont.)
• The valuation of corporate debt relies on
the first three basic principles of finance:
– Principle 1: Money Has a Time Value.
– Principle 2: There is a Risk-Return Tradeoff.
– Principle 3: Cash Flows are the Source of
Value.
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9-38
Step-by-Step: Valuing Bonds by
Discounting Future Cash Flows
• Step 1: Determine the amount and timing of
bondholder cash flows. The total cash flows equal
the promised interest payments and principal
payment.
• Annual Interest = Par value × coupon rate
• Example 9.1: The annual interest for a bond with
coupon interest rate of 7% and a par value of
$1,000 is equal to $70, (.07 × $1,000 = $70).
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9-39
Step-by-Step: Valuing Bonds by
Discounting Future Cash Flows (cont.)
• Step 2: Estimate the appropriate discount
rate on a similar risk bond. Discount rate is
the return the bond will yield if it is held to
maturity and all bond payments are made.
• Discount rate can be either calculated or
obtained from various sources (such as
Yahoo! Finance).
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9-40
Step-by-Step: Valuing Bonds by
Discounting Future Cash Flows (cont.)
• Step 3: Calculate the present value of the
bond’s interest and principal payments
from Step 1 using the discount rate
estimated in step 2.
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9-41
Calculating a Bond’s Yield to
Maturity (YTM)
• We can think of YTM as the discount rate
that makes the present value of the bond’s
promised interest and principal equal to
the bond’s observed market price.
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9-42
Checkpoint 9.2
Calculating the Yield to Maturity on a Corporate
Bond
Calculate the yield to maturity for the following bond issued by Ford Motor
Company (F) with a price of $744.80, where we assume that interest payments
are made annually at the end of each year and the bond has a maturity of
exactly 11 years.
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9-43
Checkpoint 9.2
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9-44
Checkpoint 9.2
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9-45
Checkpoint 9.2
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9-46
Checkpoint 9.2: Check Yourself
Calculate the YTM on the Ford bond where
the bond price rises to $900 (holding all
other things equal).
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9-47
Step 1: Picture the Problem
YTM=?
Years
Cash flow
0
1
-$900
$65
2
$65
3…
$65
11
$1,065
• Purchase price = $900
• Interest payments = $65 per year for years 1-11
• Final payment = $1,000 in year 11 of principal.
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9-48
Step 2: Decide on a Solution
Strategy
• We can use equation 9-2a to find YTM.
YTM is the rate that makes the present
value of all future expected cash flows
equal to the current market price.
• We can also solve for YTM using a
calculator and a spreadsheet.
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9-49
Step 3: Solve
• Using Mathematical Equation
• It is cumbersome to solve for YTM by hand
using the equation. It is more practical to
use the financial calculator or the spread
sheet.
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9-50
Step 3: Solve (cont.)
• Using Financial Calculator
Enter:
N = 11
I/Y = 7.89
PV = -900
PMT = 65
FV = 1,000
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9-51
Step 3: Solve (cont.)
• Using an Excel Spreadsheet
• YTM
= RATE(nper, pmt,pv,fv)
= RATE (11,65,-900,1000)
= 7.89%
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9-52
Step 4: Analyze
• The yield to maturity on the bond is
7.89%. The yield is higher than the
coupon rate of interest of 6.5%. Since the
coupon rate is lower than the yield to
maturity, the bond is trading at a price
below $1,000. We call this a discount
bond.
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9-53
Using Market Yield to Maturity Data
• Market yield to maturity is regularly
reported by a number of investor services
and is quoted in terms of credit spreads
or spreads to Treasury bonds.
• Table 9-4 contains some examples of yield
spreads.
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9-54
Using Market Yield to Maturity Data
(cont.)
• The spread values in table 9-4 represent basis
points over a US Treasury security of the same
maturity as the corporate bond. For example, a
30-year Ba1/BB+ corporate bond has a spread of
275 basis points over a similar 30-year US Treasury
bond.
• Thus this corporate bond should earn 2.75% over
the 4.56% earned on treasury yield or 7.31%.
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9-55
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9-56
Promised Returns versus Expected
Yield to Maturity
• The yield to maturity calculation assumes
that the bond performs according to the
terms of the bond contract or indenture.
Since corporate bonds are subject to risk
of default, the promised yield to maturity
may not be equal to expected yield to
maturity.
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9-57
Promised Returns versus Expected
Yield to Maturity (cont.)
• Example 9.2 Consider a one-year bond
that promises a coupon rate of 8% and
has a principal (par value) of $1,000.
Further assume the bond is currently
trading for $850. What is the promised
yield to maturity?
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9-58
Promised Returns versus Expected
Yield to Maturity (cont.)
• Promised YTM
= {(Interest year 1 + Principal) ÷ (Bond Value)} – 1
= {($80+$1,000) ÷
($850)} – 1
= 27.06%
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9-59
Promised Returns versus Expected
Yield to Maturity (cont.)
• The yield of 27.06% is based on the
assumption of no default.
• Assume there is a 40% probability of
default on this bond and if the bond
defaults, the bondholders will receive only
60% of the principal and interest owed.
What is the expected YTM on this bond?
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9-60
Promised Returns versus Expected
Yield to Maturity (cont.)
• YTMdefault
= {(Interest year 1 + Principal)} ÷ (Bond Value)} – 1
= {($80+$1000) × .60} ÷ ($850)} – 1
= -23.76%
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9-61
Promised Returns versus Expected
Yield to Maturity (cont.)
= (27.06 × .60) + (-23.76 × .40)
= 6.73%
• The financial press quotes promised yield
and not expected YTM.
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9-62
Checkpoint 9.3
Valuing a Bond Issue
Consider a $1,000 par value bond issued by AT&T (T) with a maturity
date of 2026 and a stated coupon rate of 8.5%. On January 1, 2007, the
bond had 20 years left to maturity, and the market’s required yield to
maturity for similar rated debt was 7.5%. If the market’s required yield to
maturity on a comparable risk bond is 7.5%, what is the value of the
bond?
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9-63
Checkpoint 9.3
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9-64
Checkpoint 9.3
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9-65
Checkpoint 9.3
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9-66
Checkpoint 9.3: Check Yourself
Calculate the present value of the AT&T bond
should the yield to maturity for comparable risk
bonds rise to 9% (holding all other things equal).
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9-67
Step 1: Picture the Problem
i= 9%
Years
Cash flows
0
1
2
3…
$85
$85
$85
20
$1,085
PV of all
Cash flows
=?
$85 annual
interest
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$85 interest
+ $1,000
Principal
9-68
Step 2: Decide on a Solution
Strategy
• Here we know the following:
–
–
–
–
Annual interest payments = $85
Principal amount or par value = $1,000
Time = 20 years
YTM or discount rate = 9%
• We can use the above information to
determine the value of the bond by
discounting future interest and principal
payment to the present.
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9-69
Step 3: Solve
• Using Mathematical Equation
• Bond Value
[
= $ 85{ 1-(1/(1.09)20]
$1,000/(1.09)20
÷
(.20)} +
= $85 (9.128) + $178.43
= $954.36
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9-70
Step 3: Solve (cont.)
• Using a Financial Calculator
• Enter:
–
–
–
–
–
N = 20
1/y = 9.0
PMT = 85
FV = 1000
PV = 954.36
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9-71
Step 3: Solve (cont.)
• Using an Excel Spreadsheet
• Bond Value = PV (rate, nper, pmt, fv)
= PV (.09,20,85,1000)
= $954.36
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9-72
Step 4: Analyze
• The value of AT&T bond falls to $954.36
when the yield to maturity for comparable
risk bond rises to 9%. The bonds are now
trading at a discount as the coupon rate on
AT&T bonds is lower than the market yield.
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9-73
Step 4: Analyze (cont.)
• An investor who buys AT&T bonds at its
current discounted price will earn a
promised yield to maturity of 9%.
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9-74
Semiannual Interest Payments
• Corporate bonds typically pay interest to
bondholders semiannually. We can adapt
Equation (9-2a) from annual to
semiannual payments as follows:
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9-75
Checkpoint 9.4
Valuing a Bond Issue That Pays
Semiannual Interest
Reconsider the bond issued by AT&T (T) with a maturity date of
2026 and a stated coupon rate of 8.5%. AT&T pays interest to
bondholders on a semiannual basis on January 15 and July 15.
On January 1, 2007, the bond had 20 years left to maturity. The
market’s required yield to maturity for a similarly rated debt
was 7.5% per year or 3.75% for six months. What is the value
of the bond?
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9-76
Checkpoint 9.4
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9-77
Checkpoint 9.4
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9-78
Checkpoint 9.4
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9-79
Checkpoint 9.4
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9-80
Checkpoint 9.4: Check Yourself
Calculate the present value of the AT&T bond
should the yield to maturity on comparable bonds
rise to 9% (holding all other things equal).
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9-81
Step 1: Picture the Problem
40
6-month
periods
i= 9%
Periods
0
1
Cash flow
$42.5
2
$42.5
3…
$42.5
40
$1,042.50
PV=?
$42.50
Semiannual
interest
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$42.5 interest
+ $1,000
Principal
9-82
Step 2: Decide on a Solution
Strategy
• Here we know the following:
–
–
–
–
Semiannual interest payments = $42.50
Principal amount or par value = $1,000
Time = 20 years or 40 periods
YTM or discount rate = 9% or 4.5% for 6months
• We can use the above information to
determine the value of the bond by
discounting future interest and principal
payment to the present.
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9-83
Step 3: Solve
• Using Mathematical Equation
• Bond Value
[
= $ 42.5{ 1-(1/(1.045)40]
÷
(.20)} + $1,000/(1.045)40
= $42.5 (18.40) + $171.93
= $954
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9-84
Step 3: Solve (cont.)
• Using a Financial Calculator
• Enter:
–
–
–
–
–
N = 40
1/y = 4.50
PMT = 42.50
FV = 1000
PV = 954
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9-85
Step 3: Solve (cont.)
• Using an Excel Spreadsheet
• Bond Value = PV (rate, nper, pmt, fv)
= PV (.045,40,42.5,1000)
= $954
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9-86
Step 4: Analyze
• Using semi-annual compounding we get a
value of $954 for AT&T bonds. This is very
close to the value of $954.26 found using
annual compounding.
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9-87
9.3 Bond
Valuation:
Four Key
Relationships
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Bond Valuation: Four Key
Relationships
• First Relationship The value of bond is
inversely related to changes in the yield to
maturity.
YTM = 12%
YTM rises to
15%
$1,000
$1,000
12%
12%
Maturity date
5 years
5 years
Bond Value
$1,000
$899.44
Par value
Coupon rate
Bond
Value
Drops
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9-89
Bond Valuation: Four Key
Relationships (cont.)
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9-90
Bond Valuation: Four Key
Relationships (cont.)
• Since future interest rates cannot be
predicted, a bond investor is exposed to
the risk of changing values of bonds as
interest rates change.
• The risk to the investor that the value of
his or her investment will change is known
as interest rate risk.
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9-91
Bond Valuation: Four Key
Relationships (cont.)
• Second Relationship: The market value of
a bond will be less than its par value if the
yield to maturity is above the coupon
interest rate and will be valued above par
value if the yield to maturity is below the
coupon interest rate.
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9-92
Bond Valuation: Four Key
Relationships (cont.)
• There are two sources of return from bond
investment:
– Periodic interest payments
– Capital gain or loss when the bond is sold
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9-93
Bond Valuation: Four Key
Relationships (cont.)
• When a bond can be bought for less than
its par value, it is called discount bond.
For example, buying a $1,000 par value
bond for $950.
• Bonds will trade at a discount when the
yield to maturity on the bond exceeds the
coupon rate.
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9-94
Bond Valuation: Four Key
Relationships (cont.)
• When a bond can be bought for more than
its par value, it is called premium bond.
For example, buying a $1,000 par value
bond for $1,110.
• Bonds will trade at a premium when the
yield to maturity on the bond is less than
the coupon rate.
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9-95
Bond Valuation: Four Key
Relationships (cont.)
• Third Relationship As the maturity date
approaches, the market value of a bond
approaches its par value.
• Regardless of whether the bond was
trading at a discount or at a premium, the
price of bond will converge towards par
value as the maturity date approaches.
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9-96
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9-97
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9-98
Bond Valuation: Four Key
Relationships (cont.)
• Fourth Relationship Long term bonds have
greater interest rate risk than short-term
bonds.
• While all bonds are affected by a change in
interest rates, long-term bonds are
exposed to greater volatility as interest
rates change.
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9.4 Types of
Bonds
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Types of Bonds
• Table 9-7 contains a listing of major types of
long-term debt securities that are sold in the
public financial market.
• The differences among the various types of bond
are based on the following bond attributes:
Secured versus Unsecured, Priority of claim,
Initial offering market, Abnormal risk, Coupon
level, Amortizing or non-amortizing, and
Convertibility.
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Types of Bonds (cont.)
• Secured versus Unsecured
– Secured bonds have specific assets pledged
to support repayment of the bond.
– Unsecured bond are referred to as
debentures.
– Bonds secured by lien on real property is called
a mortgage bond.
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Types of Bonds (cont.)
• Priority of Claim
– The priority of claim refers to the order of
repayment when the firm’s assets are
distributed, as in the case of liquidation.
– Secured bonds are paid first followed by
debentures; Among debentures, subordinated
debentures have lower priority than secured
debt and unsubordinated debentures.
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Types of Bonds (cont.)
• Initial Offering Market
– Bonds are classified by where they were
originally issued (in the domestic bond market
or not).
– For example, Eurobonds are issued in a
foreign country but are denominated in
domestic currency. For example, a US
corporation issuing bonds in Germany in US
dollars.
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Types of Bonds (cont.)
• Abnormal Risk
– Junk, or high-yield, bonds have a belowinvestment grade bond rating. These bonds
have a high risk of default as the firms that
issued these bonds are facing severe financial
problems.
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Types of Bonds (cont.)
• Coupon Level
– Bonds with a zero or very low coupon are
called zero coupon bonds.
– These bonds are issued at substantial discounts
from their par value and promise to repay a
zero or very low coupon rate each year. The
par value is repaid at the maturity of the bond.
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Types of Bonds (cont.)
• Amortizing or Non-Amortizing
– The payments from amortizing bonds, like a
home mortgage, include both the interest and
principal.
– The payments from a non-amortizing bonds
include only interest. At maturity, the bonds
repay the par value of bond.
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Types of Bonds (cont.)
• Convertibility
– Convertible bonds are debt securities that can
be converted into a firm’s stock at a prespecified price.
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9.5 Determinants
of Interest Rates
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Determinants of Interest Rates
• As we observed earlier, bond prices vary
inversely with interest rates.
• Therefore in order to understand bond
pricing we need to know the determinants
of interest rates.
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Real Rate of Interest and the
Inflation Premium
• Quotes of interest rates in the financial
press are commonly referred to as the
nominal (or quoted) interest rates.
• Real rate of interest adjusts the nominal
rate for the expected effects of inflation.
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Real Rate of Interest and the
Inflation Premium (cont.)
• The nominal return or interest rate on a
note or bond can be thought of including
four basic components:
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Fisher Effect
• The relationship between the nominal rate
of interest, rnominal , the anticipated rate of
inflation, rinflation , and the real rate of
interest is known as the Fisher effect.
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Fisher Effect (cont.)
• Example 9.3 What will be the real rate of
interest if the nominal rate of interest is
10% and the anticipated rate of inflation is
3%?
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Fisher Effect (cont.)
• rreal = {(1+.10) ÷ (1+.03)} – 1
= .0679 or 6.79%
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Fisher Effect (cont.)
• We can approximate the real rate of
interest as follows:
• Real Rate of Interest
≈ Nominal interest rate – Inflation
premium
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Checkpoint 9.5
Solving for the Real Rate of Interest
You have managed to build up your savings over the three years
following your graduation from college to a respectable $10,000 and
are wondering how to invest it. Your banker says they could pay you
5% on your account for the next year. However, you recently saw on
the news that the expected rate of inflation for next year is 3.5%. If
you are earning a 5% annual rate of return but the prices of goods
and services are rising at a rate of 3.5%, just how much additional
buying power would you gain each year? Stated somewhat differently,
what real rate of interest would you earn if you made the investment?
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Checkpoint 9.5
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Checkpoint 9.5: Check Yourself
Assume now that you expect that inflation will be
5% over the coming year and want to analyze how
much better off you will be if you place your
savings in an account that also earns just 5%.
What is the real rate of return in this circumstance?
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Step 1: Picture the Problem
• Let us assume that the prices of goods and
services today is $1.00 per unit.
• With a 5% inflation, these goods and
services will cost $1.05.
• Thus, $10,500 expected in the savings
account at the end of the year will buy you
only 10,000 units (10,500/1.05) at the end
of the year.
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Step 1: Picture the Problem (cont.)
Year 0
Year 1
$10,000.00
$10,500.00
Price Index (5% inflation)
$1.00
$1.05
Purchasing Power (units)
10,000.00
10,000.00
Savings Account Balance
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Step 2: Decide on a Solution
Strategy
• We can estimate the real rate of interest
by using equation 9-4b.
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Step 3: Solve
• rreal = {(1+.05) ÷ (1+.05)} – 1
= 0%
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Step 4: Analyze
• Here the nominal rate of interest is equal
to the expected rate of inflation.
Therefore, the real rate of return is equal
to zero i.e. there is no increase in
purchasing power from investing the
savings at 5%.
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Checkpoint 9.6
Solving for the Nominal Rate of Interest
After considering a number of investment opportunities, you
have decided that you should be able to earn a real return of
2% on your $10,000 in savings over the coming year. If the
expected rate of inflation is expected to be 3.5% over the
coming year, what nominal rate of return must you anticipate
in order to earn the 2% real rate of return?
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Checkpoint 9.6
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Checkpoint 9.6
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Checkpoint 9.6: Check Yourself
If you anticipate that the rate of inflation will now
be 4% next year, holding all else the same, what
rate of return will you need to earn on your savings
in order to achieve a 2% increase in purchasing
power?
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Step 1: Picture the Problem
• Let us assume that the prices of goods and
services today is $1.00 per unit.
• If the expected rate of inflation is 4% and
you want to be able to purchase 2% more,
you will need to earn a nominal rate of
interest on your savings that will allow you
to buy 10,200 units at $1.04 each.
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Step 1: Picture the Problem (cont.)
Year 0
Year 1
$10,000.00
$10,608
Price Index (5% inflation)
$1.00
$1.04
Purchasing Power (units)
10,000.00
10,200.00
Savings Account Balance
Real rate (% increase in
purchasing power)
2%
Interest rate of
6.08% solved
in step 3
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Step 2: Decide on a Solution
Strategy
• Here we know the real rate of interest and
the expected rate of inflation.
• We can use the Fisher model found in
equation 9-4a to determine the nominal
rate of interest.
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Step 3: Solve
• rnominal =.02 + .04 + (.02 × .04)
= .0608 or 6.08%
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Step 4: Analyze
• In order to achieve a 2% increase in
purchasing power in the face of a 4% rate
of inflation, you must earn a 6.08% rate
on your savings.
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Default Premium
• In addition to accounting for the time
value of money and inflation, the interest
rate that a firm’s bonds pay must also
offer a default premium i.e. risk that the
issuer will fail to repay interest and
principal in a timely manner.
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Maturity Premium – The Term
Structure of Interest Rates
• Long-term bonds are more sensitive to
interest rate changes.
• Maturity premium is the compensation
that investors demand for bearing interest
rate risk on long-term bonds.
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Maturity Premium – The Term
Structure of Interest Rates (cont.)
• The relationship between interest rates
and time to maturity with risk held
constant is known as the term structure
of interest rates or the yield curve.
• Figure 9-3 illustrates a hypothetical yield
curve of US Treasury Bonds.
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Shifts in the Yield Curve
• The term structure of interest rates
changes over time as expectations
regarding each of the three factors that
underlie interest rates change.
• Figure 9-4 shows the yield curve one day
before 911 attack and again two weeks
later.
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Shifts in the Yield Curve (cont.)
• We observe a significant shift in the yield
curve in figure 9-4 for short-term interest
rates.
• Investors shifted their funds to the safety
of Treasury securities, pushing up the
prices and bringing down the yields.
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Shifts in the Yield Curve (cont.)
• The yield curve is generally upward sloping
but it can assume different shapes i.e.
downward sloping or flat.
• Figure 9-5 illustrates different shapes of
yield curves at different dates.
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Key Terms
•
•
•
•
•
•
Amortizing bond
Bond rating
Bond indenture
Call provision
Collateral
Conversion feature
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Key Terms (cont.)
•
•
•
•
•
•
•
Convertible bond
Corporate bond
Coupon interest rate
Credit spread
Current yield
Debenture
Default premium
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Key Terms (cont.)
•
•
•
•
•
•
•
Discount bond
Eurobonds
Fisher effect
Fixed rate loan
Floating rate bonds
Floating rate
Inflation premium
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Key Terms (cont.)
•
•
•
•
•
•
•
Interest rate risk
Junk (high-yield) bonds
LIBOR
Maturity premium
Mortgage bonds
Nominal (or quoted) rate of interest
Non-amortizing bond
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Key Terms (cont.)
•
•
•
•
•
•
•
Par or face value of a bond
Private market transaction
Premium bond
Real rate of interest
Recovery rate
Secured debt
Spread to Treasury
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Key Terms (cont.)
•
•
•
•
•
•
•
Subordinated debentures
Term structure of interest rates
Transaction loans
Unsubordinated debentures
Yield curve
Yield to maturity
Zero coupon bond
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