When a corporation or government wishes to borrow money from public it usually does so by issuing or selling bonds When investors buy a bond they lend money to the bond issuer the government or corporation ID: 740938
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Slide1
Bond ValuationSlide2
What is Bond?
When a corporation or government wishes to borrow money from public, it usually does so by issuing, or selling bonds
When investors buy a bond, they lend money to the bond issuer, the government or corporation
As a lender, investors expect to be paid back the original amount (principle) and interest over some specified period time
As a borrower, the bond issuer must repay principle and interest to buyers over some specified period time Slide3
Definition of Bond
A security that the government or corporation issue or sell to borrow money from investors today and pay promised payments later
A loan that the borrower (issuer) promises to repay the lender (investor) the amount borrowed (principle) plus interest over some specified period timeSlide4
Key Features
Par
value (face value,
F
)
Amount borrowed by issuers (sellers) from investors (buyers) at the beginning
Re-paid at
the end of loan
Assume $1,000 for corporate
bonds
Annual Coupon (
C
)
Annual interest payments to buyers
Coupon Rate
= Annual coupon/Par Value =
C/FSlide5
Key Features
Maturity (
T
)
:
Number of years
until
par value is
repaid
by issuers (sellers)
Yield to maturity (
YTM):
D
iscount
rate used to value a
bond
Quoted
as an
annual rate
Market rate
of return Slide6
Annual Coupon Bond Price
Consider a bond with a 10% annual coupon rate, 15 years to maturity and a par value of $1,000. If the yield to maturity is 11%, the current price is?
Par value:
Maturity:
years
Yield to maturity:
Coupon Rate
Annual coupon:
Price = ?
Slide7
Annual Coupon Bond Price
The cash flows from investing on this bond are 15 years $100 plus $1,000 in the end of year 15
How much will
investors
pay
to buy the bond?
Present value of this stream of cash flows
14
…
100
100
0
1
2
100
100
15
1,000
P=?Slide8
Annual Coupon Bond Price
The present value of 15 years $100 is the present value of the annuity that pays $100 at the end of each year for 15 years, so we can make use of annuity formula
Slide9
Annual Coupon Bond Price
The present value of $1,000 is the present value of one lump-sum future value at year 15, so we can make use of present value formula
Bond price is the present value of annual coupons plus the present value of face value
Slide10
Annual Coupon Bond Price
Slide11
Problem 6-3 Bond Prices
Lycan
, Inc., has 7.6% coupon bonds on the market that have 9 years left to maturity. The bonds make annual payments. If the YTM on these bonds is 9.6%, what is the current bond price? Slide12
Semiannual Coupon Bond Price
Bonds issued in US usually make coupon payments twice a year
Semiannual coupon bond price:
C
is the
annual
coupon
Slide13
Semiannual Coupon Bond Price
Consider a bond with a 10% annual coupon rate, 15 years to maturity and a par value of $1,000. This bond makes semiannual payments. If the yield to maturity is 11%, the current price is?
Slide14
Problem 6-6 Bond Prices
App Store Co. issued 20-year bonds one year ago at a coupon rate of 6.1%. The bonds make semiannual payments. If the YTM on these bonds is 5.3%, what is the current bond price?Slide15
Bond YTM
Suppose we have a bond with the following characteristics
. What is the YTM of the bond
?
Par value:
Maturity:
0
years
Coupon Rate
Annual
coupon:
Price:
If the bond make annual coupon payment,
If the bond make
semiannual
coupon payment,
Slide16
Annual Coupon
Annual coupon bond
Slide17
Problem 6-5 Coupon Rate
Merton Enterprises has bonds on the market making annual payments, with 14 years to maturity, and selling for $953. At this price, the bonds yield
9.4%.
What must the coupon rate be on Merton’s bonds?Slide18
Annual Coupon
Semiannual
coupon
bond
Slide19
Problem 6-8 Coupon Rate
Volbeat
Corporation has bonds on the market with 12 years to maturity, a YTM of
9.7%,
and a current price of $948. The bonds make semiannual payments. What must the coupon rate be on the bonds?Slide20
Bond Sold at Par
Price = Par value
When are bonds sold at par?
30-year annual coupon bonds with $100 face value and 5% coupon rate
If YTM
is 5
%, how much is the bond?
Issuer promises $5 annual coupon (interest payment)
Bondholders expect $5 return
Actual interest payment = Expected return
Investors are willing to lend $100 to the issuer, so pay $100 to buy the bondSlide21
Discount Bond
Price < Par value
If
YTM is
10%,
how much is the bond?
Issuer promises $5 annual coupon (interest payment)
Bondholders expect
$10
return
Actual interest payment
< Expected returnInvestors are not willing to lend $100 to the issuerInvestors will pay less than $100 to buyBond price is $52.87 < $100 Slide22
Premium Bond
Price > Par value
If
YTM is 3
%,
how much is the bond?
Issuer promises
$5
annual coupon (interest payment)
Bondholders expect
$3
returnActual interest payment > Expected returnInvestors would like to pay more than $100 to buyInvestors will lend more than $100 to the issuer Bond price is $139.20 > $100Slide23
Current Yield
Coupon portion of bond return
Current Yield = Annual Coupon / Bond
Price
Discount bound
Current yield:
Current yield:
Premium bound
Current yield:
YTM
Current yield:
Slide24
Relations
Bond sold at par
Discount bond
Premium bond
Slide25
Interest Rate Risk
Interest rate movements affect investors’ expectation on
bond
return
, so do bond price
Interest rate risk refers to the sensitivity
of bond price
to
interest rate variations
Two features determine interest rate risk
MaturityCoupon Rate Slide26
Interest Rate Risk
The longer the maturity, the greater the interest rate risk
Bond with longer maturity has more distant cash flows, which are more adversely affected by the increasing of interest rate
The lower the coupon rate, the greater the interest rate risk
Bond with lower coupon rate proportionally depends more on the present value of par value, so its price is more adversely affected by the increasing of interest rateSlide27
Problem 6-16
Interest Rate Risk
Both Bond Bill and Bond Ted have
12.4%
coupons, make semiannual payments, and are priced at par value. Bond Bill has 5 years to maturity, whereas Bond Ted has 22 years to maturity. If interest rates suddenly rise by
3%,
what is the percentage change in the price of these bonds?Slide28
Interest Rates Rise by 3%
YTM
=
12.4%
Both Bond Bill and Ted are worth par value $1,000
YTM =
15.4%
Bond
Bill
is worth
$897.97
Bond Ted is worth $812.64% ChangeBond Bill: Bond Ted:
Slide29
Maturity
The only difference between Bond
Bill
and
Ted is coupon rate: Ted
has
a longer maturity
% decline in price for Bond Ted
is
greater
than % decline for
Bill, so Bond Ted price is more sensitive to interest rate changesSlide30
Problem 6-17 Interest Rate Risk
Bond J has a coupon rate of 4.5%. Bond S has a coupon rate of 14.5%. Both bonds have eight years to maturity, make semiannual payments, and have a YTM of 10%. If interest rates suddenly rise by 3%, what is the percentage change in the price of these bonds? What does this problem tell you about the interest rate risk of lower-coupon bonds?Slide31
Interest Rates Rise by 3%
YTM
=
10%
Bond J is worth $701.96
Bond S is worth $1,243.85
YTM =
13%
Bond J is worth
$584.87
Bond S is worth
$1,073.26% ChangeBond J: Bond S:
Slide32
Coupon Rate
The only difference between Bond
J
and
S
is
coupon rate: S
has
a greater coupon rate
% decline in price for Bond S
is
smaller than % decline for S, so Bond S price is less sensitive to interest rate changes