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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