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Description

Chapter 03

Chapter 03 Valuing Bonds Multiple Choice Questions

The following entities issue bonds to raise long-term loans except: A

The federal government B

State and local governments C

Companies D

Individuals

The type of bonds where the identities of bonds' owners are recorded and the coupon interest payments are sent automatically are called: A

Bearer bonds B

Government bonds C

Registered bonds D

None of the above

A government bond issued in Germany has a coupon rate of 5%,

face value of euros 100 and maturing in five years

The interest payments are made annually

Calculate the price of the bond (in euros)if the yield to maturity is 3

Generally,

a bond can be valued as a package of: I) Annuity,

II) Perpetuity,

III) Single payment A

I and II only B

II and III only C

I and III only D

Chapter 03

A government bond issued in Germany has a coupon rate of 5%,

face value of euros 100 and maturing in five years

The interest payments are made annually

Calculate the yield to maturity of the bond (in euros) if the price of the bond is 106 euros

Generally,

bonds issued in the following countries pay interest semi-annually

I) USA,

II) UK,

III) Canada,

IV) Germany,

None of the above

If a bond is paying interest semi-annually,

interest is paid once a year B

interest is paid every six moths C

interest is paid every three months D

A 3-year bond with 10% coupon rate and $1000 face value yields 8% APR

Assuming annual coupon payment,

calculate the price of the bond

A 5-year treasury bond with a coupon rate of 8% has a face value of $1000

What is the semi-annual interest payment

None of the above

Chapter 03

A three-year bond has 8

If the yield to maturity on the bond is 10%,

calculate the price of the bond assuming that the bond makes semi-annual coupon interest payments

A four-year bond has an 8% coupon rate and a face value of $1000

If the current price of the bond is $878

calculate the yield to maturity of the bond (assuming annual interest payments)

A 5-year bond with 10% coupon rate and $1000 face value is selling for $1123

Calculate the yield to maturity on the bond assuming annual interest payments

None of the above

Which of the following statements about the relationship between interest rates and bond prices is true

? I) There is an inverse relationship between bond prices and interest rates

II) There is a direct relationship between bond prices and interest rates

III) The price of short-term bonds fluctuates more than the price of long-term bonds for a given change in interest rates

(Assuming that coupon rate is the same for both) IV) The price of long-term bonds fluctuates more than the price of short-term bonds for a given change in interest rates

(Assuming that the coupon rate is the same for both) A

I and IV only B

I and III only C

II and III only D

None of the given statements are true

Chapter 03

Consider a bond with a face value of $1,000,

This bond's duration is: A

7 years B

6 years C

1 years D

5 years

A bond with a face value of $1,000 has coupon rate of 7%,

The bond's duration is: A

0 years B

4 years C

0 years D

6 years

A bond with a face value of $1,000,

This bond's duration is: A

7 years B

5 years C

6 years D

0 years

A bond with duration of 10 years has yield to maturity of 10%

This bond's volatility is: A

A bond with duration of 5

The bond's volatility is: A

Chapter 03

If a bond's volatility is 10% and the interest rate goes down by 0

If a bond's volatility is 5% and the interest rate changes by 0

Volatility of a bond is given by: I) Duration/ (1 + yield) II) Slope of the curve relating the bond price to the interest rate III) Yield to maturity A

I only B

II only C

III only D

I and II only

The term structure of interest rates can be described as the: A

Relationship between the spot interest rates and the bond prices B

Relationship between spot interest rates and stock prices C

Relationship between spot interest rates and maturity of a bond D

None of the above

Chapter 03

Which of the following statements is true

? I) The spot interest rate is a weighted average of yields to maturity II) Yield to maturity is the weighted average of spot interest rates and estimated forward rates III) The yield to maturity is always higher than the spot rates A

I only B

II only C

III only D

I and III only

A forward rate prevailing from period three through to period four can be: I) readily observed in the market place II) extracted from spot interest rate with 3 and 4 years to maturity III) extracted from 1 and 2 year spot interest rates A

I only B

II only C

III only D

I and III only

If the 3-year spot rate is 10

what is the one-year forward rate of interest two years from now

None of the above

If the 5-year spot rate is 10% and the 4-year spot rate is 9%,

what is the one-year forward rate of interest four years from now

Chapter 03

If the 4-year spot rate is 7% and the 3-year spot rate is 6%,

what is the one-year forward rate of interest three years from now

None of the above

Interest represented by "r2" is: A

Spot rate on a one-year investment (APR) B

Spot rate on a two-year investment (APR) C

Expected spot rate 2 years from today D

Expected spot rate one year from today

How can one invest today at the 2-year forward rate of interest

? I) By buying a 2-year bond and selling a 1-year bond with the same coupon II) By buying a 1-year bond and selling a 2-year bond with the same coupon III) By buying a 1-year bond and then after a year reinvesting in a further 1-year bond A

I only B

II only C

III only D

II and III only

The expectations hypothesis states that the forward interest rate is the: I) expected future spot rate II) always greater than the spot rate III) yield to maturity A

I only B

II only C

III only D

II and III only

Chapter 03

If the nominal interest rate per year is 10% and the inflation rate is 4%,

what is the real rate of interest

None of the above

X invests $1000 at 10% nominal rate for one year

If the inflation rate is 4%,

what is the real value of the investment at the end of one year

None of the above

What forward rate is embedded in a two year zero coupon bonds with a yield to maturity of 6% and a three year zero coupon bond and a yield to maturity of 6

? Assume both bonds are currently priced at par

Which bond is more sensitive to an interest rate change of 0

Maturity = 8 years,

Coupon = 6% or $60,

Par Value = $1,000 Bond B: YTM = 3

Maturity = 5 years,

Coupon = 7% or $70,

Par Value = $1,000 A

Both the same D

Cannot be determined

True / False Questions

Chapter 03

The yield to maturity on a bond is really its internal rate of return

True False

In the US,

most bonds make coupon payments annually

True False

The duration of any bond is the same as its maturity

True False

The duration of a zero coupon bond is the same as its maturity

True False

The longer a bond's duration greater is its volatility

True False

The term structure of interest rate is the relationship between yield to maturity and maturity

True False

If the term structure of interest rate is flat the nine-year interest rate is equal to the ten-year interest rate

True False

Short-term and long-term interest rates always move in parallel

True False

Chapter 03

The expectations theory implies that the only reason for a declining term structure is that investors expect spot interest rates to fall

True False

The relationship between nominal interest rate and real interest rate is given by: (1 + rnominal) = (1 + rreal)(1 + inflation rate) True False

Treasury bonds do not have default risk,

but are subject to inflation risk

True False

Indexed bonds were completely unknown in the U

True False

Treasury issues inflation-indexed bonds known as TIPs

True False

Forward rates are always higher than spot rates

True False

Defaulted bonds often pay some level of residual

Short Answer Questions

Chapter 03

Briefly explain the cash flows associated with a bond to the investor

Briefly explain the term "yield to maturity

What is the relationship between interest rates and bond prices

Discuss the concept of duration

Chapter 03

Briefly discuss the concept of volatility

Briefly explain what is meant by "the term structure of interest rates

Briefly explain the expectations theory

What is the relationship between real and nominal rates of interest

Chapter 03

Define the term,

What are TIPs

What is the relationship between spot and forward rates

Chapter 03

Chapter 03 Valuing Bonds Answer Key

Multiple Choice Questions

The following entities issue bonds to raise long-term loans except: A

The federal government B

State and local governments C

Companies D

Individuals

Type: Easy

The type of bonds where the identities of bonds' owners are recorded and the coupon interest payments are sent automatically are called: A

Bearer bonds B

Government bonds C

Registered bonds D

None of the above

Type: Medium

Chapter 03

A government bond issued in Germany has a coupon rate of 5%,

face value of euros 100 and maturing in five years

The interest payments are made annually

Calculate the price of the bond (in euros)if the yield to maturity is 3

none of the above The annual interest payment = (100) × (0

Using a financial Calculator: PMT = 5

FV = 100

Compute: PV = 106

77 euros

Type: Medium

Generally,

a bond can be valued as a package of: I) Annuity,

II) Perpetuity,

III) Single payment A

I and II only B

II and III only C

I and III only D

Type: Easy

A government bond issued in Germany has a coupon rate of 5%,

face value of euros 100 and maturing in five years

The interest payments are made annually

Calculate the yield to maturity of the bond (in euros) if the price of the bond is 106 euros

none of the above The annual interest payment = (100) × (0

FV = 100

Type: Medium

Chapter 03

Generally,

bonds issued in the following countries pay interest semi-annually

I) USA,

II) UK,

III) Canada,

IV) Germany,

None of the above

Type: Medium

If a bond is paying interest semi-annually,

interest is paid once a year B

interest is paid every six moths C

interest is paid every three months D

Type: Easy

A 3-year bond with 10% coupon rate and $1000 face value yields 8% APR

Assuming annual coupon payment,

calculate the price of the bond

Type: Medium

Chapter 03

A 5-year treasury bond with a coupon rate of 8% has a face value of $1000

What is the semi-annual interest payment

None of the above Annual interest payment = 1000(0

08) = $80

Semi-annual payment = 80/2 = $40

Type: Easy

A three-year bond has 8

If the yield to maturity on the bond is 10%,

calculate the price of the bond assuming that the bond makes semi-annual coupon interest payments

05^2)) +

Type: Difficult

A four-year bond has an 8% coupon rate and a face value of $1000

If the current price of the bond is $878

calculate the yield to maturity of the bond (assuming annual interest payments)

Therefore,

Or use a financial calculator: PV =

PMT = 80

FV = 1000

COMPUTE: I = 12%

Type: Difficult

Chapter 03

A 5-year bond with 10% coupon rate and $1000 face value is selling for $1123

Calculate the yield to maturity on the bond assuming annual interest payments

None of the above Use a financial calculator: PV =

FV = 1000

PMT = 100 and N = 5 and compute I = 7

Type: Medium

Which of the following statements about the relationship between interest rates and bond prices is true

? I) There is an inverse relationship between bond prices and interest rates

II) There is a direct relationship between bond prices and interest rates

III) The price of short-term bonds fluctuates more than the price of long-term bonds for a given change in interest rates

(Assuming that coupon rate is the same for both) IV) The price of long-term bonds fluctuates more than the price of short-term bonds for a given change in interest rates

(Assuming that the coupon rate is the same for both) A

I and IV only B

I and III only C

II and III only D

None of the given statements are true

Type: Difficult

Consider a bond with a face value of $1,000,

This bond's duration is: A

7 years B

6 years C

1 years D

Duration = [(55

56) + 2(51

44) + 3(47

63) + 4(44

10) + 5(40

83) + 6(37

42) + 9(30

99)]/(865

80) = 7

6 years

Type: Difficult

Chapter 03

A bond with a face value of $1,000 has coupon rate of 7%,

The bond's duration is: A

0 years B

4 years C

0 years D

PMT = 70

FV = 1,000

Compute PV = 744

1^20)]/744

Type: Difficult

A bond with a face value of $1,000,

This bond's duration is: A

7 years B

5 years C

6 years D

0 years

Type: Difficult

A bond with duration of 10 years has yield to maturity of 10%

This bond's volatility is: A

Type: Difficult

Chapter 03

A bond with duration of 5

The bond's volatility is: A

Type: Difficult

If a bond's volatility is 10% and the interest rate goes down by 0

Type: Difficult

If a bond's volatility is 5% and the interest rate changes by 0

Type: Medium

Chapter 03

Volatility of a bond is given by: I) Duration/ (1 + yield) II) Slope of the curve relating the bond price to the interest rate III) Yield to maturity A

I only B

II only C

III only D

I and II only

Type: Difficult

The term structure of interest rates can be described as the: A

Relationship between the spot interest rates and the bond prices B

Relationship between spot interest rates and stock prices C

Relationship between spot interest rates and maturity of a bond D

None of the above

Type: Difficult

Which of the following statements is true

? I) The spot interest rate is a weighted average of yields to maturity II) Yield to maturity is the weighted average of spot interest rates and estimated forward rates III) The yield to maturity is always higher than the spot rates A

I only B

II only C

III only D

I and III only

Type: Difficult

Chapter 03

A forward rate prevailing from period three through to period four can be: I) readily observed in the market place II) extracted from spot interest rate with 3 and 4 years to maturity III) extracted from 1 and 2 year spot interest rates A

I only B

II only C

III only D

I and III only

Type: Difficult

If the 3-year spot rate is 10

what is the one-year forward rate of interest two years from now

None of the above forward rate = [(1

105^3)/(1

-1 = 11

Type: Difficult

If the 5-year spot rate is 10% and the 4-year spot rate is 9%,

what is the one-year forward rate of interest four years from now

1^5)/(1

-1 = 14

Type: Difficult

Chapter 03

If the 4-year spot rate is 7% and the 3-year spot rate is 6%,

what is the one-year forward rate of interest three years from now

None of the above f = [(1

07^4)/(1

-1 = 10%

Type: Difficult

Interest represented by "r2" is: A

Spot rate on a one-year investment (APR) B

Spot rate on a two-year investment (APR) C

Expected spot rate 2 years from today D

Expected spot rate one year from today

Type: Easy

How can one invest today at the 2-year forward rate of interest

? I) By buying a 2-year bond and selling a 1-year bond with the same coupon II) By buying a 1-year bond and selling a 2-year bond with the same coupon III) By buying a 1-year bond and then after a year reinvesting in a further 1-year bond A

I only B

II only C

III only D

II and III only

Type: Difficult

Chapter 03

The expectations hypothesis states that the forward interest rate is the: I) expected future spot rate II) always greater than the spot rate III) yield to maturity A

I only B

II only C

III only D

II and III only

Type: Difficult

If the nominal interest rate per year is 10% and the inflation rate is 4%,

what is the real rate of interest

None of the above 1 + rreal = (1 + rnominal)/(1 + rinflation) = 1

Type: Easy

X invests $1000 at 10% nominal rate for one year

If the inflation rate is 4%,

what is the real value of the investment at the end of one year

None of the above Real investment = (1000 * 1

Type: Medium

Chapter 03

What forward rate is embedded in a two year zero coupon bonds with a yield to maturity of 6% and a three year zero coupon bond and a yield to maturity of 6

? Assume both bonds are currently priced at par

You get 1

Now determine the IRR over between years 2 and 3

Type: Difficult

Which bond is more sensitive to an interest rate change of 0

Maturity = 8 years,

Coupon = 6% or $60,

Par Value = $1,000 Bond B: YTM = 3

Maturity = 5 years,

Coupon = 7% or $70,

Par Value = $1,000 A

Both the same D

Cannot be determined The price of bond A decreases from 1134 to 1108

Bond B decreases in price from 1158 to 1121

A drops by 4

Type: Difficult

True / False Questions

The yield to maturity on a bond is really its internal rate of return

Type: Easy

Chapter 03

In the US,

most bonds make coupon payments annually

Type: Easy

The duration of any bond is the same as its maturity

Type: Difficult

The duration of a zero coupon bond is the same as its maturity

Type: Medium

The longer a bond's duration greater is its volatility

Type: Medium

The term structure of interest rate is the relationship between yield to maturity and maturity

Type: Medium

If the term structure of interest rate is flat the nine-year interest rate is equal to the ten-year interest rate

Type: Medium

Chapter 03

Short-term and long-term interest rates always move in parallel

Type: Difficult

The expectations theory implies that the only reason for a declining term structure is that investors expect spot interest rates to fall

Type: Difficult

The relationship between nominal interest rate and real interest rate is given by: (1 + rnominal) = (1 + rreal)(1 + inflation rate) TRUE

Type: Medium

Treasury bonds do not have default risk,

but are subject to inflation risk

Type: Medium

Indexed bonds were completely unknown in the U

Type: Medium

Treasury issues inflation-indexed bonds known as TIPs

Type: Medium

Chapter 03

Forward rates are always higher than spot rates

Type: Difficult

Defaulted bonds often pay some level of residual

Type: Difficult

Short Answer Questions

Briefly explain the cash flows associated with a bond to the investor

Bonds provide two types of cash flows: interest payments and the principal payment

Interest payments occur each period,

usually annually or semi-annually

Periodic interest payments are also called coupon payments

Thus this forms an annuity

Principal payment occurs at the time of maturity of the bond and is a lump sum payment

Type: Easy

Briefly explain the term "yield to maturity

" The yield to maturity is the single discount rate that is used to calculate the present value of cash flows received from buying a bond

It is used for calculating the bond value

Conceptually it is the same as the internal rate of return (IRR)

It is also stock-in-trade of any bond dealer

Type: Medium

Chapter 03

What is the relationship between interest rates and bond prices

? Interest rates and bond prices are inversely related

High interest rates cause bond prices to fall and vice-versa

For a given change in interest rates,

prices of long-term bonds fluctuate more than for short-term bonds

Similarly,

for a given change in interest rates low coupon bond prices fluctuate more than for high coupon bonds

Type: Medium

Discuss the concept of duration

Duration can be thought of as the weighted average time of a bond's cash flow

The weights are determined by the present value factors

Duration is expressed in units of time

Duration is an important concept for two reasons

the volatility of a bond is directly related to its duration

Second,

one way to hedge interest rate risk is through a strategy of duration matching

Type: Difficult

Briefly discuss the concept of volatility

Volatility is calculated as Duration/ (1 + yield)

Bonds with longer duration also have greater volatility

Bond's volatility is directly related to duration

Volatility is also the slope of the curve relating the bond price to the interest rate

Type: Medium

Briefly explain what is meant by "the term structure of interest rates

" The term structure of interest rates is the plot of interest rates on the y-axis and the maturity on the x-axis

It is also called the yield curve

It shows how interest rates and maturity are related

Economists have developed several theories to explain the shape of the yield curve

Type: Medium

Chapter 03

Briefly explain the expectations theory

This theory postulates that the current forward rates are the expected value of the corresponding future spot rates

Type: Medium

What is the relationship between real and nominal rates of interest

? The exact relationship is given by: (1 + nominal rate ) = (1 + real rate) * (1 + expected Inflation rate)

It can also be written as: nominal rate = real rate + Inflation rate + (real rate) * (Inflation rate)

Type: Easy

Define the term,

" Real interest rate is the inflation adjusted nominal interest rate

We do not observe it directly

The relationship between the two is given by: 1 + rnominal = (1 + rreal rate)(1 + inflation rate)

(An approximate formula that works for low values is: rnominal = rreal rate + Inflation rate)

Type: Medium

What are TIPs

TIPs(Treasury Inflation-Protected Securities) are issued by the U

Treasury

Treasury began issuing TIPs in 1997

These are also known as Inflation-indexed bonds

The real cash flows on TIPs are fixed,

which includes interest and principal,

are increased as the Consumer Price Index (CPI) increases

Thus the buying power of the lender in protected

Type: Medium

Chapter 03

What is the relationship between spot and forward rates

? A forward rate is the internal rate of return derived from the future value of bonds given spot rates from two different maturity bonds

Type: Difficult