there are nine questions in total in excel, lecture slides attached
assignment__6.xlsx
lc6_bond_canvas.ppt
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#1
Consider a $1,000 par value bond with a 6% coupon rate paid semiannually, and has 9 years to maturity. What is the
#2
Cutler Co. issued 11-year bonds a year ago at a coupon rate of 7.8 percent. The bonds make semiannual payments. If
the current bond price?
#3
A $1000 bond with a coupon rate of 6.2% paid semiannually has eight years to maturity and a yield to maturity of 8.3
increases to 8.6%, what will happen to the price of the bond?
#4
Linebacker Co. has 7 percent coupon bonds on the market with 9 years left to maturity. The bonds make annual paym
is its YTM?
#5
Caribbean Reef Software has 8.4 percent coupon bonds on the market with 9 years to maturity. The bonds make sem
percent of par. What is the YTM?
#6
Suppose that General Motors Acceptance Corporation issued a bond with 10 years until maturity, a face value of $10
The yield to maturity on this bond when it was issued was 6%. Assuming the yield to maturity remains constant, wha
makes its first coupon payment?
o maturity. What is the price of the bond if it is priced to yield 7%?
emiannual payments. If the YTM on these bonds is 8.6 percent, what is
yield to maturity of 8.3%. If interest rates rise and the yield to maturity
onds make annual payments. If the bond currently sells for $1,080, what
. The bonds make semiannual payments and currently sell for 95.5
ity, a face value of $1000, and a coupon rate of 7% (annual payments).
remains constant, what is the price of the bond immediately after it
The following table summarizes prices of various default-free zero-coupon bonds (expressed as a
percentage of face value):
Maturity (years)
Price (per $100 face value)
1
2
3
4
$95.51
$91.05
$86.38
$81.65
a. Compute the yield to maturity for each bond.
Par value
Maturity (years)
Price (per $100 face value)
Yield to maturity
100
100
100
1
2
95.51
91.05
100
3
86.38
4
81.65
b. Plot the zero-coupon yield curve (for the first five years). Is it upward-sloping or downward-sloping?
onds (expressed as a
5
$76.51
100
5
76.51
oping or downward-sloping?
HMK Enterprises would like to raise $10 million to invest in capital expenditures. The company plans to i
year bonds with a face value of $1000 and a coupon rate of 6.5% (annual payments). The following table
summarizes the yield to maturity for five-year (annual-pay) coupon corporate bonds of various ratings:
Rating
Yield to maturity
Total Amount needed
Maturity
Face value
Coupon rate
Solve price of bonds with
various ratings
AAA
6.20%
A
BB
6.50%
7.50%
A
BB
10,000,000.00
5
1,000.00
6.50%
AAA
nditures. The company plans to issue fivepayments). The following table
ate bonds of various ratings:
Problem 6-23
Consider the following 4 bonds A B C D:
(a) What is the percentage change in the price of each bond if its yields to maturity falls
from 6% to 5%?
Par value
100.00
Yield to maturity
6.00%
Price at
Price at
Bond
Coupon Rate Maturity
6.00%
5.00%
A
0.00%
15
B
0.00%
10
C
4.00%
15
D
8.00%
10
(b) From your calculation, how does interest rate risk change with maturity (if bonds
have same coupon rate)? How does it change with coupon rate (if bonds have same
maturity)?
s yields to maturity falls
Percentage
Change
ith maturity (if bonds
(if bonds have same
Chapter 6
Bonds
The Bond Market
❑
❑
❑
❑
❑
Largest securities market
Daily trading volume: $814 billion in 2010 (vs. $105 billion
for stocks on 3 major exchanges)
All outstanding U.S. debt issue: $12 trillion (1996) to $36
trillion (2010)
More popular since the recent economic crisis as bank
lending became more stringent
Most widely traded bond in the world: 10-year Treasury
Bond Valuation
2
Bond Terminology
Bond
❑ Bond certificate
❑
Terms of the bond
❑ Amounts and dates of all payments to be made.
❑
Payments
❑ Maturity date
❑ Term
❑
Bond Valuation
3
Bond Terminology
❑
Face value (aka par value or principal amount)
Notional amount used to compute interest payments
❑ Usually standard increments, such as $1000
❑ Typically repaid at maturity
❑
❑
Coupons
Bond Valuation
4
Bond Terminology
❑
Coupon rate
Set by the issuer and stated on the bond certificate
❑ By convention, expressed as an APR, so the amount of each
coupon payment, CPN, is
❑
CPN =
Coupon Rate Face Value
Number of Coupon Payments per Year
Bond Valuation
(Eq. 6.1)
5
Bond Terminology
Bond Valuation
6
Types of Bond
❑
Zero-coupon bonds
❑
❑
❑
Pay face value at maturity
Treasury bills are zero-coupon U.S. government bonds with maturity
of up to one year.
Coupon bonds
❑
❑
❑
Pay face value at maturity
Also make regular coupon interest payments
Two types of U.S. Treasury coupon securities are currently traded in
financial markets (treasury notes and bonds)
Bond Valuation
7
U.S. Treasury Securities
Bond Valuation
8
Bond Price Quotes
❑
❑
❑
❑
Prices and yields are often used interchangeably.
Bond traders usually quote yields rather than prices.
One advantage is that the yield is independent of the face
value of the bond.
When prices are quoted in the bond market, they are
conventionally quoted per $100 face value.
Bond Valuation
9
Treasury Bond Quotes
US Treasury Bonds Rates
Maturity
Yield
3 Month
0.02
6 Month
0.07
2 Year
0.31
3 Year
0.70
5 Year
1.53
10 Year
2.73
30 Year
3.70
Yesterday
0.03
0.07
0.31
0.70
1.54
2.75
3.72
Bond Valuation
Last Week
0.03
0.05
0.32
0.67
1.53
2.72
3.69
Last Month
0.02
0.05
0.40
0.85
1.70
2.87
3.76
10
Corporate Bond Quotes
Issuer Name
INTEL CORP
Symbol
INTC.GD
INTEL CORP INTC.GE
INTEL CORP
INTEL CORP
INTEL CORP
INTEL CORP
INTC.AB
INTC.AC
INTC3940192
INTC3940212
Callable Coupon Maturity
Moody S&P
Fitch Price
Yield
A-
A
111.25
2.291
1.625
No
2.95
12/15/2035
No
3.25
8/1/2039
A2
A-
A
133.75
Yes
1.95
10/1/2016
A1
A+
A+
102.981 0.788
Yes
4.8
10/1/2041
A1
A+
A+
100.694 4.754
Yes
1.35
12/15/2017 A1
A+
A+
98.865
1.659
Yes
4.25
12/15/2042 A1
A+
A+
92.486
4.73
Bond Valuation
11
Cash Flows of a Coupon Bond or Note
❑
Assume that it is May 15, 2010 and the U.S. Treasury has just
issued securities with May 2015 maturity, $1000 par value and a
2.2% coupon rate with semiannual coupons. Since the original
maturity is only 5 years, these would be called “notes” as
opposed to “bonds”. The first coupon payment will be paid on
November 15, 2010. What cash flows will you receive if you
hold this note until maturity?
❑
❑
Since a note is just a package of cash flows, we need to know those
cash flows in order to value the note.
The note contains all of the information we would need to construct its
cash flow timeline.
Bond Valuation
12
Cash Flows of a Coupon Bond or Note
❑
The face value of this note is $1000. Because this note pays
coupons semiannually, from Eq.(6.1) you will receive a coupon
payment every six months =$1,000 x 2.2%/2=$11. Here is the
timeline based on a six-month period and there are a total of
10 cash flows:
❑
Note that the last payment occurs five years (ten six-month
periods) from now and is composed of both a coupon
payment of $11 and the face value payment of $1000.
Bond Valuation
13
Finding Bond Price
❑
❑
Asset value or price = PV of expected future cash flows
Bond pricing:
1
1
(1 + r) t
Bond Value = C
r
r: yield (YTM); quoted like APR
❑ t: time to maturity
❑ C: coupon payment
❑ F: principal repayment
❑
Bond Valuation
F
+
t
(1 + r)
(Eq. 6.2)
14
Bond Yield
❑
Return on a coupon bond comes from:
❑
❑
❑
The difference between the purchase price and the principal value
Periodic coupon payments
Yield to maturity (YTM)
❑
❑
❑
overall return measure – reflects both coupon yield and capital
gain/loss
changes with bond’s market price
reflects the rate of return for bonds with similar features (e.g.,
comparable risk)
Bond Valuation
15
Calculating Bond Yield
❑
❑
It is the interest rate that equates PV (of bond’s future cash
flows) to the current bond price.
The solution of r in the equation:
1
1
(1 + r) t
Bond market price = C
r
❑
❑
❑
F
+
t
(1 + r)
(Eq. 6.3)
Solve: trial and error (not recommended)
Excel: use rate function; convert to annualized rate if coupon is paid
semi-annually.
Equivalent to solving IRR with the cash flows on the bond
Bond Valuation
16
Yields for Zero-Coupon Bond
of Different Maturities
❑
Yield to maturity of an n-year zero-coupon bond:
1/ n
Face Value
1 + YTM n =
Price
❑
(Eq. 6.4)
Determine the corresponding yield to maturity for the
following zero-coupon bond, with $100 face value.
Maturity
1 year
2 years
3 years
4 years
Price
$96.62
$92.45
$87.63
$83.06
Bond Valuation
17
Yields for Zero-Coupon Bond
of Different Maturities
YTM1 = (100 / 96.62)1/1 − 1 = 3.50%
YTM 2 = (100 / 92.45)1/ 2 − 1 = 4.00%
YTM 3 = (100 / 87.63)1/ 3 − 1 = 4.50%
YTM 4 = (100 / 83.06)1/ 4 − 1 = 4.75%
Excel:
= RATE(1,0,-96.62,100)
= RATE(2,0,-92.45,100)
= RATE(3,0,-87.63,100)
= RATE(4,0,-83.06,100)
Bond Valuation
18
Example of Zero-Coupon Yield Curve
Bond Valuation
19
Computing the Yield to Maturity
of Coupon Bonds
Calculate the YTM for a 10% annual coupon rate, with 15 years to
maturity, par value of $1,000, and a current price of $928.09.
❑ This bond pays an annual coupon payment of 10%* $1000 =
$100; the cash flow consists of an annuity of 15 payments of
$100, and one lump-sum payment of $1000 in 15 years.
❑ Excel: =rate(15,100,-928.09,1000)
❑ Or, IRR for the bond cash flows is also equivalent to its yield to
maturity.
Bond Valuation
20
Computing the Yield to Maturity
of Coupon Bonds
Calculate the YTM for a 10% coupon rate with semiannual
coupons, 20 years to maturity and is selling for $1,197.93 (par
value $1000).
❑ This bond pays a semi-annual coupon payment of 10%*
$1000/2 = $50; the cash flow consists of an annuity of 40
payments of $50 each, and one lump-sum payment of $1000
in 40 6-month periods.
❑ Excel: =rate(40,50,-1197.93,1000) = 4%
❑ 4% is the return based on half year. Since YTM is quoted like
APR, YTM = 4%*2 = 8%
Bond Valuation
21
Calculating Bond Price
of a Zero-coupon Bond
What is the price of a 5-year zero-coupon bond with a face value
of $100, if the YTM is 5%?
❑ The only expected cash flow is the lump-sum payment of $100
at the end of 5 years.
❑ Price = 100/1.05^5 = 78.35
❑ Excel: = PV(0.05,5,0,100)
Bond Valuation
22
Calculating Bond Price
of a Semiannual Coupon Bond
Bond issued in the U.S. usually make coupon payments twice a
year. An ordinary bond has a coupon rate of 14% (the owner get
two payments of $70 each, with $1000 face value). YTM is
quoted at 16% and the bond matures in 7 years.
❑ Bond yields are quoted like APRs; period rate =16%/2 = 8%
❑ PV = 70[1 – 1/(1.08)14]/.08 + 1,000/(1.08)14 = $917.56
❑ Excel: = PV(0.08,14,70,1000)
Bond Valuation
23
Why Bond Prices Change
❑
❑
❑
Zero-coupon bonds always trade for a discount.
Coupon bonds may trade at a discount or at a premium
Most issuers of coupon bonds choose a coupon rate so that
the bonds will initially trade at, or very close to, par.
❑
❑
If a bond sells at par the only return investors will earn is from the
coupons that the bond pays. (so the bond’s coupon rate will exactly
equal its YTM)
After the issue date, as interest rates in the economy fluctuate,
the yields that investors demand and the market price of a
bond also change over time.
Bond Valuation
24
Bond Prices:
Premium, Par, and Discount Bonds
Bond Valuation
25
Relationship Between YTM and Bond Price
Coupon rate = 8% with annual coupons; Par value = $1,000; Maturity = 10 years
1500
1400
Bond Price
1300
1200
1100
1000
900
800
700
600
0%
2%
4%
6%
8%
10%
12%
14%
Yield-to-maturity (YTM)
Bond Valuation
26
Bond Characteristics Affect
Interest Rate Risk
❑
❑
Interest rate risk: sensitivity of the price of a bond to interest
rate changes.
Bonds with different characteristics will respond differently
to changes in interest rates.
❑
❑
Investors view long-term bonds to be riskier than short-term bonds.
The lower the coupon payments, the more sensitive its price is to
fluctuations in market interest rates.
Bond Valuation
27
Maturity and Interest Rate Risk
Bond Valuation
28
Example:
Coupon Rates and Interest Rate Sensitivity
❑
Consider two bonds, each pays semi-annual coupons and 5
years left until maturity. One has a coupon rate of 5% and the
other has a coupon rate of 10%, but both currently have a
yield to maturity of 8%. How much will the price of each
bond change if its yield to maturity decreases from 8% to 7%?
Bond Valuation
29
Evaluating Bond’s Credit Risk
❑
❑
❑
❑
U.S. Treasuries are widely regarded to be (default) risk-free
(although still subject to interest rate risk and inflation risk).
Bond rating help investors assess the creditworthiness of the
issuer; concern only with the possibility of default, so that
bond’s cash flows are not known with certainty.
Corporations with higher default risk will need to pay higher
coupons to attract buyers to their bonds.
The rating depends on:
❑
❑
the risk of bankruptcy
bondholders’ claim to assets in the event of bankruptcy.
Bond Valuation
30
Bond Ratings of U.S. Public Firms (2009)
(cont.)
Bond Valuation
31
Bond Ratings of U.S. Public Firms (2009)
Bond Valuation
32
Corporate Yield Curves for Various Ratings,
March 2010
Bond Valuation
33
Yield Spreads and the Financial Crisis
Bond Valuation
34
…
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