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3–1) California Coastal Sage, Chaparral, and Oak Woodlands; Sonoran Desert enforcement activity, and energy development and transmission Chapter 3 Chapter 3 Methodology Introduction The project's main purpose was concerned with the investigation of the use of transaction logs and other methods

Label Review Manual Chapter 3 General Labeling Requirements Table of Contents Table of Contents What's changed in this version? Chapter 3 Verifying Potential Errors and Taking Corrective Actions Table of Contents (Rev 853, 01 04 19) Transmittals for

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Chapter 03

- - Valuing Bonds

Chapter 03 Valuing Bonds Multiple Choice Questions

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

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

None of the above

face value of euros 100 and maturing in five years

- none of the above

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

II) Perpetuity,

III) Single payment A

I and III only D

- none of the above

- - Valuing Bonds

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

bonds issued in the following countries pay interest semi-annually

- & V) Japan A
- & IV only D

- then: A

interest is paid once a year B

interest is paid every six moths C

interest is paid every three months D

- none of the above

calculate the price of the bond

None of the above

- - Valuing Bonds

- 0% coupon rate and face value of $1000

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

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

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

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 III only C

II and III only D

None of the given statements are true

Chapter 03

- - Valuing Bonds

- a coupon rate of 6%,
- a yield to maturity of 8%,
- and ten years to maturity

This bond's duration is: A

7 years B

6 years C

1 years D

5 years

- yield to maturity of 10%,
- and twenty years to maturity

0 years B

4 years C

0 years D

6 years

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

- coupon rate of 0%,
- yield to maturity of 9%,
- and ten years to maturity

This bond's duration is: A

7 years B

5 years C

6 years D

0 years

- 7 years has yield to maturity of 9%

Chapter 03

- - Valuing Bonds

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

- 75% (points) then the price of the bond: A
- decreases by 10% B
- decreases by 7
- increases by 7
- increases by 0

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

- 5% (points) then the price of the bond: A
- changes by 5% B
- changes by 2
- changes by 7
- none of the above

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

Relationship between spot interest rates and stock prices C

None of the above

Chapter 03

- - Valuing Bonds

? 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

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

I and III only

If the 3-year spot rate is 10

- 5% and the 2-year spot rate is 10%,

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

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

- - Valuing Bonds

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 two-year investment (APR) C

? 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

II only C

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

- - Valuing Bonds

what is the real rate of interest

If the inflation rate is 4%,

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

- $1100 B
- $1000 C
- $1058 D

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

- ? Bond A: YTM = 4

Coupon = 6% or $60,

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

Cannot be determined

Chapter 03

- - Valuing Bonds

most bonds make coupon payments annually

True False

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

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

- - Valuing Bonds

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

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

- before 1997

True False

True False

Forward rates are always higher than spot rates

Defaulted bonds often pay some level of residual

- ? True False

Short Answer Questions

- - Valuing Bonds

Briefly explain the term "yield to maturity

- - Valuing Bonds

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

Briefly explain the expectations theory

Chapter 03

- - Valuing Bonds

- "real interest rate

- ? Briefly explain

What is the relationship between spot and forward rates

- - Valuing Bonds

Chapter 03 Valuing Bonds Answer Key

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

Individuals

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

Chapter 03

- - Valuing Bonds

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

face value of euros 100 and maturing in five years

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

- 05) = 5 euros Price = PV

FV = 100

- & N = 5

Compute: PV = 106

77 euros

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

II) Perpetuity,

II and III only C

- none of the above

Type: Easy

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

face value of euros 100 and maturing in five years

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

- 05) = 5 euros Using a financial Calculator: PMT = 5

- & N = 5
- -106 Compute: I = 3

Type: Medium

- - Valuing Bonds

Generally,

bonds issued in the following countries pay interest semi-annually

I) USA,

II) UK,

- & V) Japan A
- & IV only D

- then: A

interest is paid once a year B

interest is paid every six moths C

interest is paid every three months D

- none of the above

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

- 54 PV = (100/1
- 08) + (100/(1
- 08^2)) + (1100/(1
- 08^3)) = $1051

- - Valuing Bonds

08) = $80

A three-year bond has 8

- 0% coupon rate and face value of $1000

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

- 00 PV = (40/1
- 05) + (40/(1

05^2)) +

- + (1040/(1
- 05^6)) = $949

If the current price of the bond is $878

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

- 6% Use trial and error method
- 12) + (80/(1
- 12^2)) + (80/(1
- 12^3)) + (1080/(1
- 12^4)) = $870

Therefore,

- yield to maturity is 12%

PMT = 80

FV = 1000

Type: Difficult

Chapter 03

- - Valuing Bonds

None of the above Use a financial calculator: PV =

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

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 III only C

II and III only D

None of the given statements are true

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

- a coupon rate of 6%,
- a yield to maturity of 8%,
- and ten years to maturity

7 years B

6 years C

1 years D

- 5 years PV = $865

56) + 2(51

44) + 3(47

63) + 4(44

10) + 5(40

83) + 6(37

- 81) + 7(35) + 8(32

42) + 9(30

- 01) + 10(490

99)]/(865

80) = 7

6 years

- - Valuing Bonds

- yield to maturity of 10%,
- and twenty years to maturity

0 years B

4 years C

0 years D

- 6 years Step 1: N = 20

PMT = 70

Compute PV = 744

- 59 Step 2: Duration = [((1)(70)/1
- 1) + ((2)(70)/1
- + ((20)(1070)/1

1^20)]/744

- 59 = 10 years

- coupon rate of 0%,
- yield to maturity of 9%,
- and ten years to maturity

7 years B

5 years C

6 years D

0 years

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

- 0% Volatility (%) = Duration/(1 + yield) = 10/1

Type: Difficult

- - Valuing Bonds

A bond with duration of 5

- 7 years has yield to maturity of 9%

The bond's volatility is: A

- 0% Volatility = 5

- 75% (points) then the price of the bond: A
- decreases by 10% B
- decreases by 7
- increases by 7
- increases by 0
- 75% Change in bond price = (Volatility) * (change in interest rates) = 10 * 0

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

- 5% (points) then the price of the bond: A
- changes by 5% B
- changes by 2
- changes by 7
- none of the above 5 * 0

Type: Medium

- - Valuing Bonds

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

II only C

III only D

I and II only

Type: Difficult

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

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

II only C

Type: Difficult

Chapter 03

- - Valuing Bonds

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

II only C

- 5% and the 2-year spot rate is 10%,

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

105^3)/(1

-1 = 11

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

- 0% forward rate = [(1

1^5)/(1

-1 = 14

- - Valuing Bonds

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

07^4)/(1

-1 = 10%

Type: Difficult

Expected spot rate one year from today

? 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

II and III only

- - Valuing Bonds

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

II only C

what is the real rate of interest

- r real = 5

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

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

- $1100 B
- $1000 C
- $1058 D

None of the above Real investment = (1000 * 1

- 04) = $1058

Chapter 03

- - Valuing Bonds

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

- 50% First calculate the future value of $1 at each YTM

You get 1

- 1236 for the 2 year bond and 1
- 1910 for the 3 year bond

Now determine the IRR over between years 2 and 3

- ? Bond A: YTM = 4

Maturity = 5 years,

Par Value = $1,000 A

Bond B decreases in price from 1158 to 1121

A drops by 4

- 67% and B drops by 3

Chapter 03

- - Valuing Bonds

most bonds make coupon payments annually

Type: Easy

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

The longer a bond's duration greater is its volatility

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

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

- - Valuing Bonds

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

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

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

but are subject to inflation risk

Type: Medium

Indexed bonds were completely unknown in the U

- before 1997

Type: Medium

Treasury issues inflation-indexed bonds known as TIPs

Chapter 03

- - Valuing Bonds

Type: Difficult

Short Answer Questions

usually annually or semi-annually

Periodic interest payments are also called coupon payments

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

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

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

- - Valuing Bonds

What is the relationship between interest rates and bond prices

? Interest rates and bond prices are inversely related

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

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

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 an important concept for two reasons

the volatility of a bond is directly related to its duration

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

Type: Difficult

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

Type: Medium

" 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

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

Chapter 03

- - Valuing Bonds

Briefly explain the expectations theory

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

? 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)

- "real interest rate

" Real interest rate is the inflation adjusted nominal interest rate

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

- ? Briefly explain

Treasury

- but the nominal cash flows,

which includes interest and principal,

are increased as the Consumer Price Index (CPI) increases

Thus the buying power of the lender in protected

- - Valuing Bonds

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