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Bonds
A bond is a long-term debt instrument in which a
borrower agrees to make payments of principal and
interest, on specific dates, to the holders of the bond.
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Bond Characteristics
Par (face) value: principal amount to be repaid at maturity
Coupon rate, coupon payment: Each period (may be every 6
months, every year etc.) there is coupon payment. It is a fixed
amount (unless it is a floating rate bond)
Floating rate may be tied to t-bill rate. It has caps or floors, it may
be convertible to fixed rate.
Another type:
zero coupon bonds
Maturity: maturity date on which the contract expires and
principal (face value) is repaid
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Call provision
issuer may call the bond for redemption before maturity. It is an
option given to the issuer. Callable bonds therefore sell at a
Discount
Call premium: cost to the issuer of calling a bond issue. It
typically declines over time
Call protection: exists if a bond can not be called for a period of
time after its issuance
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Sinking fund arrangement
requires the issuer to retire a portion of the bond each year
How:

Redeem a portion, determine by lottery (no call premium)
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Buy on the open market

issuer may deposit cash with a trustee rather than repurchasing
bonds
Sinking funds are designed to protect bondholders
Large amounts of cash outflow at maturity may create a problem
for the issuer
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Other features:
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Bond may be convertible to common stock
Bonds may be packaged together with warrants
(warrant: a long-term option to buy a stated number
of common stock at a specified price)
Income bond: A company agrees to pay interest only
if it meets a threshold income requirement (e.g.
interest will be paid at 12% if income is greater than
$15 million)
Indexed bond: interest paid is based on Consumer
Price Index (plus real rate)
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Bond Value
Bond Value = PV of cash flows it will generate
Given kd, N, INT, M
VB= INT PVIFAkd,N + M PVIFkd,N
Coupon rate vs kd (current market rate)
The discount rate (kd ) is the opportunity cost of
capital, and is the rate that could be earned on
alternative investments of equal risk.
ki = k* + IP + MRP + DRP + LP
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Semiannual Coupons
Coupon rate is given as APR (annualized rate)
plus frequency of coupon payments
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Relationship between coupon rate, required
yield, and price
As yields in the marketplace change, the only
variable that can change to compensate an
investor for the new required yield in the
market is the price of the bond.
When the coupon rate is equal to the required
yield, the price of the bond will be equal to its
par value.
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Relationship between coupon rate, required
yield, and price
When yields in the marketplace rise above the coupon rate at a
given point in time, the price of the bond adjusts so that an
investor thinking of the purchase of the bond can realize some
additional interest. If it did not, investors would not buy the issue
because it offers a below market rate. The opposite holds if yields
in the marketplace fall below the coupon rate.
when
kd<kc VB > M
kd=kc VB = M
kd>kc VB < M
Selling at a premium
Selling at par
Selling at a discount
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Evolution of bond value over time
Special case: kd=constant over time
Example:
M=1,000
N=30 years
kc = 10%
annual coupon
Coupon Rate
Face Value
TTM
# Coupons per year
YTM
Bond Value
$
10%
1,000
30
1
13%
$775.13
Special case: kd=constant over time
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The graph shows
advantage or disadvantage will last for a shorter
period time as time passes
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Bond Yields
YTM
YTC
CY
yield to maturity
yield to call
current yield
YTM : current required rate of return on a bond. It is
same as kd, or promised return
Given P(current price), N, INT, M
P = INT PVIFAkd,N + M PVIFkd,N
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yield to call
YTC : rate of return earned on a bond if it is called
before its maturity date
If current YTM < kc (i.e. premium bond) and bond is
callable. then it is likely to be called
P= INT PVIFAk,TTC + Pc PVIFk,TTC
P is current market price of the bond
Pc is call price (usually M+INT)
Solve for k, it is YTC
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Current yield
Current yield: CYt:
Current yield relates the annual coupon interest to the
market price.
current yield 
annual dollar coupon
price
The current yield calculation takes into account only the
coupon interest and no other source of return that will
affect an investor’s yield. No consideration is given to
capital gain/loss. The time value of money is also ignored.
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What is YTM:
The yield-to-maturity on a bond is the single interest
rate that, if paid by a bank on the amount invested,
would enable the investor to obtain all the payments
promised by the security in question.
Equivalently, YTM is the discount rate that makes the
present value of the promised future cash flows equal
in sum to the current market price of the bond.
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YTM
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so YTM is a promised yield
but it is not the expected yield unless P(default)=0
it is an ex ante return
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YTM
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YTM calculations do not take into account any changes in the
market value of a security before maturity.
This fact might be interpreted as implying that the owner has no
interest in selling the instrument before maturity, no matter what
happens to his or her situation.
The calculation also fails to treat intermediate payments in a fully
satisfactory way.
An owner who does not wish to spend interest payments might
choose to buy more of these securities. But the number that can
be bought at any time depends on the price at that time, and
YTM calculations fail to take this consideration into account.
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Holding-Period Return
A measure that can be used for any investment is its holdingperiod return. The idea is to specify a holding period and then
assume that any payments received during that period will be
reinvested. Holding period is defined as the length of time over
which an investor is assumed to invest a given sum of money.
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Although assumptions may differ from case to case, the usual
procedure assumes that any payment received from a security
will be used to purchase more units of that security at the then
current market price.
When this procedure is applied, the performance of a security
can be measured by comparing the value obtained in this
manner at the end of the holding period with the value at the
beginning.
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Holding-Period Return
if there are N years in the holding period, rhp can be
converted into an equivalent annual rate:
(1+rhp,annual )N = rhp
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Example
Consider a 5% annual coupon bond
with $1,000 face value and 3 years
to maturity. Its current market price
is $922.69.
YTM is 8%. It is the interest rate that solves the following equation
YTM calculation assumes:
• that the owner will receive those 3 cash flows, i.e. bond will be
held until maturity.
• coupons will be reinvested
• the reinvested coupons will earn k percent return per year
(which is the current YTM we will find).
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Example
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It is easier to see this as follows:
Original investment: $922.69
at t=0
Final Value: $50(1+k1)2+$50(1+k2)+$1,050 at t=3
Our choice of k1 and k2 reflect our reinvestment rate
assumption
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Example
Question: What is the average annual rate earned from
this investment?
$922.69(1+kavg)3 = $50(1+k1)2+$50(1+k2)+$1,050
YTM concept solves this equation by assuming kavg = k1 = k2
Using bank analogy above:
Generates same cash flows
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Holding period return
does not make the above assumptions
 It does not assume bond will be held till maturity

It requires you to know in advance the reinvestment rate(s) for
your coupons
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But it is flexible about those rates i.e. it does not assume
kavg = k1 = k2
So compared to YTM calculation we need to know more:
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Our horizon: when we will sell the bond
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Reinvestment rates
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Selling price of the bond at the end of our horizon
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Holding period return
For example, assume we choose 2 years as our horizon.
i.e. we will sell the bond after 2 years
If we further assume that we will deposit coupons into a
bank account (one year time deposit)
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Holding period return
Original investment: $922.69
Final Value: $50(1+3%) +$50+$990.65 =$1,092.15
Question:
at t=0
at t=2
What is the average annual rate earned from this
investment?
$922.69(1+kavg)2 = $1,092.15
kavg =8.80% is the holding period return
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different reinvestment rate
If we use a different reinvestment rate
assumption, for example reinvesting
coupons on the same bond, then we
need the following information
At time 1 we buy
=0.052 shares of the same bond
At time 2 we will get coupon =1.052*50=$52.60
Sell our 1.052 shares of the bond for
1.052*990.65=$1,042.16
Original investment: $922.69
Final Value: $52.60+$1,042.16=$1,094.76
$922.69(1+kavg)2 =$1,094.76
kavg = 8.93%
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Example
Assume that all coupons are reinvested
at the new YTM
Investor’s horizon i.e. when liquidation
occurs is important
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Example
Note that if your holding period is 5 years, your equivalent annual
holding period return is 9.00% which is equal to the YTM at the
time of purchase
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Example
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Example
Note that if your holding period is 5 years, your equivalent annual
holding period return is 9.00% which is equal to the YTM at the
time of purchase
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What does the example show:
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When you buy the bond you do not know if ytm is going to change
and if it is in what direction.
Note that 5 year horizon gives you 9% average annual holding period
return no matter if ytm falls or rises by 1 percent.
5 year is the value of another measure (which we will not discuss in
this course) called the duration. If your horizon is 5 years, then
reinvestment rate and price effects cancel each other and your
average annual holding period return equals ytm at the time of the
purchase.
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Yield to Call
Example:
10 year bond 10% semiannual coupon payment
selling for $1,133.9
Can be called after 4 years. If YTM stays at this rate (or falls) the
issuer may call it. (To buy it back at a price lower than the market price)
Find YTC
P=1,133.9= 50 PVIFAk,8 + 1,050PVIFk,8
what is YTM at this time
P=1133.9= 50 PVIFAk,20 + 1000PVIFk,20
As YTM decreases bond is more likely to be called
The company may use refunding strategy
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Yield to Call
note that in the example above kc>YTM>YTC
What happens to YTC as YTM decreases?
P increases so YTC has also to fall
Example: if we assume current price=$885.30
 YTC= 14%
 YTM= 12%
note that in this example kc<YTM<YTC
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Riskiness of a bond
Interest rate risk
Interest rate risk is the concern that rising kd will cause the value of
a bond to fall.
Means as kd  VB 
Exposure is higher on bonds with longer maturities ceteris paribus
Example: 10% annual coupon
bonds with 1 year and 10
years to maturity. When yield
to maturity changes
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Reinvestment rate risk
Reinvestment rate risk is the concern that kd will fall,
and future CFs will have to be reinvested at lower rates,
hence reducing income.
As kd  funds will be reinvested at a lower rate many
bonds will be called
Even if they are not called, funds will be reinvested at a
lower rate at maturity
Exposure is higher on bonds with shorter maturities
ceteris paribus
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Default Risk
Recall interest rate= k* + IP + DRP + LP + MRP
Types of corporate bonds
Bond ratings
Junk bonds
Bankruptcy and reorganization
Default risk depends on
financial strength of issuer
Terms of bond contract
Same corporation may have several types of bonds outstanding.
They may have different default risks due to differences in
seniority and collateralization.
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types of bonds
Mortgage bond: Represents debt that is secured by the pledge of
specific property. In the event of default, the bondholders are
entitled to obtain the property in question and sell it to satisfy their
claims on the firm.
Debenture: An unsecured debt backed only by the credit
worthiness of the borrower. There is no collateral, and the
agreement is documented by an indenture. To protect the holders
of such bonds, the indenture will usually limit the future issuance
of secured as well as any additional unsecured debt.
Subordinated debenture:
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Why are ratings important?
They affect cost of borrowing for firms
Institutional investors can only buy investment grade bonds
Individual issue ratings may change over time (up or downgrading
possible)
Junk bonds (speculative grade bonds)
Have high default risk and therefore have required return
Junk bond market was developed in early 1980s and it collapsed in early
1990s
These bonds are used by companies to finance:
a leveraged buyout
a merger
a troubled company
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Bankruptcy and reorganization
bankruptcy may lead to either liquidation or reorganization
reorganization calls for the restructuring of existing debt
interest rate 
maturity 
bond holders may get equity stake
decision depends on :
value of reorganized firm > or < liquidation value of firm’s assets
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