The price of the bond today. Introduction: Bond Price : It is supposed to be the present discounted value of future cash stream that is created by a bond. In simple words, it is sum of all the present value of coupon payments along with the present value of the par value of the time of maturity.

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Answer 1

Question

Chapter 16, Problem 11PS

a.

Summary Introduction

To calculate: The price of the bond today.

Introduction:

Bond Price: It is supposed to be the present discounted value of future cash stream that is created by a bond. In simple words, it is sum of all the present value of coupon payments along with the present value of the par value of the time of maturity.

a.

Expert Solution

Answer to Problem 11PS

The price of the bond today is $103.90.

Explanation of Solution

Given information:

1-year zero-coupon bonds yields 7%

2-year zero-coupon bonds yields 8%

3-year and longer maturity bonds yields 9%

Payment of coupons annually is 8%

Let us calculate the price of the bond as on today. The formulas to be used is as follows:

PV=C(1+y)t+FV(1+y)T

Where

C= periodic coupon payment

Y= YTM

FV= the bond’s par value or face value

t=time

T=the number of periods until the bond’s maturity date

Since the par value is given to us, let us assume the par value to be $100. Let us now calculate the coupon payment.

Calculation of coupon payment:

=$100×8%=$100×8100=$100×0.08=$8

The value of $8 has to be used for further calculations.

PV=$8(1+7%)1+$8(1+8%)2+$8(1+9%)3+$108(1+9%)3

Let us convert the percentages into decimals for easy calculations.

PV=$8 (1+0.07)1+$8 (1+0.08)2+$8 (1+0.09)3+$108 (1+0.09)3PV=$8(1+0.07)+$8(1+0.1664)+$8(1+0.295029)+$108(1+0.295029)PV=$8(1.07)+$8(1.1664)+$8(1.295029)+$108(1.295029)PV=7.4766+6.8587+6.1774+83.3958=$103.9086 or $103.90

Therefore, the price of the bond today is $103.90.

b.

Summary Introduction

To calculate: The price of each bond in one year if yield curve is flat at 9% at that time.

Introduction:

Bond Price: It is supposed to be the present discounted value of future cash stream that is created by a bond. In simple words, it is sum of all the present value of coupon payments along with the present value of the par value of the time of maturity.

b.

Expert Solution

Answer to Problem 11PS

The price of the bond when the yield is flat at 9% will be $103.64.

Explanation of Solution

Given information:

1-year zero-coupon bonds yields 7%

2-year zero-coupon bonds yields 8%

3-year and longer maturity bonds yields 9%

Payment of coupons annually is 8%

A yield curve is said to flat when the interest rates remain stable over a said period.

We are told that the yield curve is flat at 9%. So, in all the three bonds, we will consider the yield as 9%. Let us now calculate the price of bond.

Calculation of coupon payment:

=$100×8%=$100×8100=$100×0.08=$8

The value of $8 has to be used for further calculations.

PV=$8 (1+9%)1+$8 (1+9%)2+$8 (1+9%)3+$108 (1+9%)3PV=$8 (1+0.09)1+$8 (1+0.09)2+$8 (1+0.09)3+$108 (1+0.09)3PV=$8(1+0.09)+$8(1+0.1881)+$8(1+0.295029)+$108(1+0.295029)PV=$8(1.09)+$8(1.1881)+$8(1.295029)+$108(1.295029)PV=7.3394+6.7334+6.1774+83.3958=$103.64

Therefore, the price of the bond when the yield is flat at 9% will be $103.64.

c.

Summary Introduction

To calculate: Rate of return on each bond.

Introduction:

Bond Price: It is supposed to be the present discounted value of future cash stream that is created by a bond. In simple words, it is sum of all the present value of coupon payments along with the present value of the par value of the time of maturity.

c.

Expert Solution

Answer to Problem 11PS

The rate of return on 1-year bond will be 9.81% and on 2-year bond it will be 8%, and on 3-year bond it will be 4.76%

Explanation of Solution

Given information:

1-year zero-coupon bonds yields 7%

2-year zero-coupon bonds yields 8%

3-year and longer maturity bonds yields 9%

Payment of coupons annually is 8%

Calculation of rate of return on 1-year bond:

Rate of return= Current yield at purchase date+ capital gain

This formula can further be simplified.

Rate of return= Coupon paymentBond’s purchase price+Bond’s price when sold−Bond’s purchase priceBond’s purchase price=$8$100+Bond’s price when sold−$100$100

Since we are not aware of the bond’s price when it is sold, let us calculate it now.

Calculation of bond’s selling price:

Years to maturity =2

Coupon payment=$8

Interest=7%

Face value=$100

Since Excel application simplifies our calculations let us make use of it here.

=PV(rate,nper,pmt,fv)=PV(0.07,2,8,100)=−$101.81

If we ignore the ‘-‘ sign, our selling price of the bond will be $101.81.

Let us now calculate the rate of return.

Let us now substitute the required values in the formula.

=$8$100+$101.81−$100$100=$8$100+$1.81$100=0.08+0.0181=0.0981

or 9.81 % when converted into percentages.

Therefore, the rate of return on 1-year bond will be 9.81%.

Calculation of rate of return on 2-year bond:

Rate of return= Coupon paymentBond’s purchase price+Bond’s price when sold−Bond’s purchase priceBond’s purchase price=$8$100+Bond’s price when sold−$100$100

Since we are not aware of the bond’s price when it is sold, let us calculate it now.

Calculation of bond’s selling price:

Years to maturity =3

Coupon payment=$8

Interest=8%

Face value=$100

Since Excel application simplifies our calculations let us make use of it here.

=PV(rate,nper,pmt,fv)=PV(0.08,3,8,100)=−$100

If we ignore the ‘-‘ sign, our selling price of the bond will be $100

Let us now calculate the rate of return.

=$8$100+$100−$100$100=$8$100+$0$100=0.08+0=0.08

or 8%

Therefore, the rate of return on 2-year bond will be 8%.

Calculation of rate of return on 3-year bond:

Rate of return= Coupon paymentBond’s purchase price+Bond’s price when sold−Bond’s purchase priceBond’s purchase price=$8$100+Bond’s price when sold−$100$100

Since we are not aware of the bond’s price when it is sold, let us calculate it now.

Calculation of bond’s selling price:

Years to maturity =4

Coupon payment=$8

Interest=9%

Face value=$100

Since Excel application simplifies our calculations let us make use of it here.

=PV(rate,nper,pmt,fv)=PV(0.09,4,8,100)=−$96.76

If we ignore the ‘-‘ sign, our selling price of the bond will be $96.76.

Let us now calculate the rate of return.

=$8$100+$96.76−$100$100=$8$100+(−3.24)$100=0.08−0.0324=0.0476

or 4.76%

Therefore, the rate of return on 3-year bond will be 4.76%

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Students have asked these similar questions

What are the Modified Duration and Macaulay Duration of the following bond? Coupon Rate = 8% (Semi-annually paid) YTM = 9% Maturity = 2 Years Par Value = 1,000 (Hint: this question is similar to Example 1 and Example 2 on slides) ModD = 1.886 and MacD = 1.805 ModD = 1.784 and MacD = 1.954 ModD = 1.954 and MacD = 1.784 ModD = 1.805 and MacD = 1.886

There are three bonds that mature at the same time, have the same par value, and are expected to pay their first annual coupon 1 next year. The bonds are detailed in the below table. Bond A B с PV PV PV Present Value B ? ? ? PV B If ca r, then what can we say about the prices of the bonds today? (Enter >, <, or ?) PV C PV Yield to Maturity C r rb Coupon Rate ca с с

2. Consider a bond with a 7.5% annual coupon rate and a face value of $1,000. Calculate the bond price and duration & show your work. Years to Maturity Interest rate Bond Price Duration 4 6. 6. 9. What relationship do you observe between yield to maturity and the current market value? What is the relationship between YTM and duration?

Answer 2

Question

Chapter 16, Problem 11PS

a.

Summary Introduction

To calculate: The price of the bond today.

Introduction:

Bond Price: It is supposed to be the present discounted value of future cash stream that is created by a bond. In simple words, it is sum of all the present value of coupon payments along with the present value of the par value of the time of maturity.

a.

Expert Solution

Answer to Problem 11PS

The price of the bond today is $103.90.

Explanation of Solution

Given information:

1-year zero-coupon bonds yields 7%

2-year zero-coupon bonds yields 8%

3-year and longer maturity bonds yields 9%

Payment of coupons annually is 8%

Let us calculate the price of the bond as on today. The formulas to be used is as follows:

PV=C(1+y)t+FV(1+y)T

Where

C= periodic coupon payment

Y= YTM

FV= the bond’s par value or face value

t=time

T=the number of periods until the bond’s maturity date

Since the par value is given to us, let us assume the par value to be $100. Let us now calculate the coupon payment.

Calculation of coupon payment:

=$100×8%=$100×8100=$100×0.08=$8

The value of $8 has to be used for further calculations.

PV=$8(1+7%)1+$8(1+8%)2+$8(1+9%)3+$108(1+9%)3

Let us convert the percentages into decimals for easy calculations.

PV=$8 (1+0.07)1+$8 (1+0.08)2+$8 (1+0.09)3+$108 (1+0.09)3PV=$8(1+0.07)+$8(1+0.1664)+$8(1+0.295029)+$108(1+0.295029)PV=$8(1.07)+$8(1.1664)+$8(1.295029)+$108(1.295029)PV=7.4766+6.8587+6.1774+83.3958=$103.9086 or $103.90

Therefore, the price of the bond today is $103.90.

b.

Summary Introduction

To calculate: The price of each bond in one year if yield curve is flat at 9% at that time.

Introduction:

Bond Price: It is supposed to be the present discounted value of future cash stream that is created by a bond. In simple words, it is sum of all the present value of coupon payments along with the present value of the par value of the time of maturity.

b.

Expert Solution

Answer to Problem 11PS

The price of the bond when the yield is flat at 9% will be $103.64.

Explanation of Solution

Given information:

1-year zero-coupon bonds yields 7%

2-year zero-coupon bonds yields 8%

3-year and longer maturity bonds yields 9%

Payment of coupons annually is 8%

A yield curve is said to flat when the interest rates remain stable over a said period.

We are told that the yield curve is flat at 9%. So, in all the three bonds, we will consider the yield as 9%. Let us now calculate the price of bond.

Calculation of coupon payment:

=$100×8%=$100×8100=$100×0.08=$8

The value of $8 has to be used for further calculations.

PV=$8 (1+9%)1+$8 (1+9%)2+$8 (1+9%)3+$108 (1+9%)3PV=$8 (1+0.09)1+$8 (1+0.09)2+$8 (1+0.09)3+$108 (1+0.09)3PV=$8(1+0.09)+$8(1+0.1881)+$8(1+0.295029)+$108(1+0.295029)PV=$8(1.09)+$8(1.1881)+$8(1.295029)+$108(1.295029)PV=7.3394+6.7334+6.1774+83.3958=$103.64

Therefore, the price of the bond when the yield is flat at 9% will be $103.64.

c.

Summary Introduction

To calculate: Rate of return on each bond.

Introduction:

Bond Price: It is supposed to be the present discounted value of future cash stream that is created by a bond. In simple words, it is sum of all the present value of coupon payments along with the present value of the par value of the time of maturity.

c.

Expert Solution

Answer to Problem 11PS

The rate of return on 1-year bond will be 9.81% and on 2-year bond it will be 8%, and on 3-year bond it will be 4.76%

Explanation of Solution

Given information:

1-year zero-coupon bonds yields 7%

2-year zero-coupon bonds yields 8%

3-year and longer maturity bonds yields 9%

Payment of coupons annually is 8%

Calculation of rate of return on 1-year bond:

Rate of return= Current yield at purchase date+ capital gain

This formula can further be simplified.

Rate of return= Coupon paymentBond’s purchase price+Bond’s price when sold−Bond’s purchase priceBond’s purchase price=$8$100+Bond’s price when sold−$100$100

Since we are not aware of the bond’s price when it is sold, let us calculate it now.

Calculation of bond’s selling price:

Years to maturity =2

Coupon payment=$8

Interest=7%

Face value=$100

Since Excel application simplifies our calculations let us make use of it here.

=PV(rate,nper,pmt,fv)=PV(0.07,2,8,100)=−$101.81

If we ignore the ‘-‘ sign, our selling price of the bond will be $101.81.

Let us now calculate the rate of return.

Let us now substitute the required values in the formula.

=$8$100+$101.81−$100$100=$8$100+$1.81$100=0.08+0.0181=0.0981

or 9.81 % when converted into percentages.

Therefore, the rate of return on 1-year bond will be 9.81%.

Calculation of rate of return on 2-year bond:

Rate of return= Coupon paymentBond’s purchase price+Bond’s price when sold−Bond’s purchase priceBond’s purchase price=$8$100+Bond’s price when sold−$100$100

Since we are not aware of the bond’s price when it is sold, let us calculate it now.

Calculation of bond’s selling price:

Years to maturity =3

Coupon payment=$8

Interest=8%

Face value=$100

Since Excel application simplifies our calculations let us make use of it here.

=PV(rate,nper,pmt,fv)=PV(0.08,3,8,100)=−$100

If we ignore the ‘-‘ sign, our selling price of the bond will be $100

Let us now calculate the rate of return.

=$8$100+$100−$100$100=$8$100+$0$100=0.08+0=0.08

or 8%

Therefore, the rate of return on 2-year bond will be 8%.

Calculation of rate of return on 3-year bond:

Rate of return= Coupon paymentBond’s purchase price+Bond’s price when sold−Bond’s purchase priceBond’s purchase price=$8$100+Bond’s price when sold−$100$100

Since we are not aware of the bond’s price when it is sold, let us calculate it now.

Calculation of bond’s selling price:

Years to maturity =4

Coupon payment=$8

Interest=9%

Face value=$100

Since Excel application simplifies our calculations let us make use of it here.

=PV(rate,nper,pmt,fv)=PV(0.09,4,8,100)=−$96.76

If we ignore the ‘-‘ sign, our selling price of the bond will be $96.76.

Let us now calculate the rate of return.

=$8$100+$96.76−$100$100=$8$100+(−3.24)$100=0.08−0.0324=0.0476

or 4.76%

Therefore, the rate of return on 3-year bond will be 4.76%

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Answer 3

Question

Chapter 16, Problem 11PS

a.

Summary Introduction

To calculate: The price of the bond today.

Introduction:

Bond Price: It is supposed to be the present discounted value of future cash stream that is created by a bond. In simple words, it is sum of all the present value of coupon payments along with the present value of the par value of the time of maturity.

a.

Expert Solution

Answer to Problem 11PS

The price of the bond today is $103.90.

Explanation of Solution

Given information:

1-year zero-coupon bonds yields 7%

2-year zero-coupon bonds yields 8%

3-year and longer maturity bonds yields 9%

Payment of coupons annually is 8%

Let us calculate the price of the bond as on today. The formulas to be used is as follows:

PV=C(1+y)t+FV(1+y)T

Where

C= periodic coupon payment

Y= YTM

FV= the bond’s par value or face value

t=time

T=the number of periods until the bond’s maturity date

Since the par value is given to us, let us assume the par value to be $100. Let us now calculate the coupon payment.

Calculation of coupon payment:

=$100×8%=$100×8100=$100×0.08=$8

The value of $8 has to be used for further calculations.

PV=$8(1+7%)1+$8(1+8%)2+$8(1+9%)3+$108(1+9%)3

Let us convert the percentages into decimals for easy calculations.

PV=$8 (1+0.07)1+$8 (1+0.08)2+$8 (1+0.09)3+$108 (1+0.09)3PV=$8(1+0.07)+$8(1+0.1664)+$8(1+0.295029)+$108(1+0.295029)PV=$8(1.07)+$8(1.1664)+$8(1.295029)+$108(1.295029)PV=7.4766+6.8587+6.1774+83.3958=$103.9086 or $103.90

Therefore, the price of the bond today is $103.90.

b.

Summary Introduction

To calculate: The price of each bond in one year if yield curve is flat at 9% at that time.

Introduction:

Bond Price: It is supposed to be the present discounted value of future cash stream that is created by a bond. In simple words, it is sum of all the present value of coupon payments along with the present value of the par value of the time of maturity.

b.

Expert Solution

Answer to Problem 11PS

The price of the bond when the yield is flat at 9% will be $103.64.

Explanation of Solution

Given information:

1-year zero-coupon bonds yields 7%

2-year zero-coupon bonds yields 8%

3-year and longer maturity bonds yields 9%

Payment of coupons annually is 8%

A yield curve is said to flat when the interest rates remain stable over a said period.

We are told that the yield curve is flat at 9%. So, in all the three bonds, we will consider the yield as 9%. Let us now calculate the price of bond.

Calculation of coupon payment:

=$100×8%=$100×8100=$100×0.08=$8

The value of $8 has to be used for further calculations.

PV=$8 (1+9%)1+$8 (1+9%)2+$8 (1+9%)3+$108 (1+9%)3PV=$8 (1+0.09)1+$8 (1+0.09)2+$8 (1+0.09)3+$108 (1+0.09)3PV=$8(1+0.09)+$8(1+0.1881)+$8(1+0.295029)+$108(1+0.295029)PV=$8(1.09)+$8(1.1881)+$8(1.295029)+$108(1.295029)PV=7.3394+6.7334+6.1774+83.3958=$103.64

Therefore, the price of the bond when the yield is flat at 9% will be $103.64.

c.

Summary Introduction

To calculate: Rate of return on each bond.

Introduction:

Bond Price: It is supposed to be the present discounted value of future cash stream that is created by a bond. In simple words, it is sum of all the present value of coupon payments along with the present value of the par value of the time of maturity.

c.

Expert Solution

Answer to Problem 11PS

The rate of return on 1-year bond will be 9.81% and on 2-year bond it will be 8%, and on 3-year bond it will be 4.76%

Explanation of Solution

Given information:

1-year zero-coupon bonds yields 7%

2-year zero-coupon bonds yields 8%

3-year and longer maturity bonds yields 9%

Payment of coupons annually is 8%

Calculation of rate of return on 1-year bond:

Rate of return= Current yield at purchase date+ capital gain

This formula can further be simplified.

Rate of return= Coupon paymentBond’s purchase price+Bond’s price when sold−Bond’s purchase priceBond’s purchase price=$8$100+Bond’s price when sold−$100$100

Since we are not aware of the bond’s price when it is sold, let us calculate it now.

Calculation of bond’s selling price:

Years to maturity =2

Coupon payment=$8

Interest=7%

Face value=$100

Since Excel application simplifies our calculations let us make use of it here.

=PV(rate,nper,pmt,fv)=PV(0.07,2,8,100)=−$101.81

If we ignore the ‘-‘ sign, our selling price of the bond will be $101.81.

Let us now calculate the rate of return.

Let us now substitute the required values in the formula.

=$8$100+$101.81−$100$100=$8$100+$1.81$100=0.08+0.0181=0.0981

or 9.81 % when converted into percentages.

Therefore, the rate of return on 1-year bond will be 9.81%.

Calculation of rate of return on 2-year bond:

Rate of return= Coupon paymentBond’s purchase price+Bond’s price when sold−Bond’s purchase priceBond’s purchase price=$8$100+Bond’s price when sold−$100$100

Since we are not aware of the bond’s price when it is sold, let us calculate it now.

Calculation of bond’s selling price:

Years to maturity =3

Coupon payment=$8

Interest=8%

Face value=$100

Since Excel application simplifies our calculations let us make use of it here.

=PV(rate,nper,pmt,fv)=PV(0.08,3,8,100)=−$100

If we ignore the ‘-‘ sign, our selling price of the bond will be $100

Let us now calculate the rate of return.

=$8$100+$100−$100$100=$8$100+$0$100=0.08+0=0.08

or 8%

Therefore, the rate of return on 2-year bond will be 8%.

Calculation of rate of return on 3-year bond:

Rate of return= Coupon paymentBond’s purchase price+Bond’s price when sold−Bond’s purchase priceBond’s purchase price=$8$100+Bond’s price when sold−$100$100

Since we are not aware of the bond’s price when it is sold, let us calculate it now.

Calculation of bond’s selling price:

Years to maturity =4

Coupon payment=$8

Interest=9%

Face value=$100

Since Excel application simplifies our calculations let us make use of it here.

=PV(rate,nper,pmt,fv)=PV(0.09,4,8,100)=−$96.76

If we ignore the ‘-‘ sign, our selling price of the bond will be $96.76.

Let us now calculate the rate of return.

=$8$100+$96.76−$100$100=$8$100+(−3.24)$100=0.08−0.0324=0.0476

or 4.76%

Therefore, the rate of return on 3-year bond will be 4.76%

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Answer 4

Question

Chapter 16, Problem 11PS

a.

Summary Introduction

To calculate: The price of the bond today.

Introduction:

Bond Price: It is supposed to be the present discounted value of future cash stream that is created by a bond. In simple words, it is sum of all the present value of coupon payments along with the present value of the par value of the time of maturity.

a.

Expert Solution

Answer to Problem 11PS

The price of the bond today is $103.90.

Explanation of Solution

Given information:

1-year zero-coupon bonds yields 7%

2-year zero-coupon bonds yields 8%

3-year and longer maturity bonds yields 9%

Payment of coupons annually is 8%

Let us calculate the price of the bond as on today. The formulas to be used is as follows:

PV=C(1+y)t+FV(1+y)T

Where

C= periodic coupon payment

Y= YTM

FV= the bond’s par value or face value

t=time

T=the number of periods until the bond’s maturity date

Since the par value is given to us, let us assume the par value to be $100. Let us now calculate the coupon payment.

Calculation of coupon payment:

=$100×8%=$100×8100=$100×0.08=$8

The value of $8 has to be used for further calculations.

PV=$8(1+7%)1+$8(1+8%)2+$8(1+9%)3+$108(1+9%)3

Let us convert the percentages into decimals for easy calculations.

PV=$8 (1+0.07)1+$8 (1+0.08)2+$8 (1+0.09)3+$108 (1+0.09)3PV=$8(1+0.07)+$8(1+0.1664)+$8(1+0.295029)+$108(1+0.295029)PV=$8(1.07)+$8(1.1664)+$8(1.295029)+$108(1.295029)PV=7.4766+6.8587+6.1774+83.3958=$103.9086 or $103.90

Therefore, the price of the bond today is $103.90.

b.

Summary Introduction

To calculate: The price of each bond in one year if yield curve is flat at 9% at that time.

Introduction:

Bond Price: It is supposed to be the present discounted value of future cash stream that is created by a bond. In simple words, it is sum of all the present value of coupon payments along with the present value of the par value of the time of maturity.

b.

Expert Solution

Answer to Problem 11PS

The price of the bond when the yield is flat at 9% will be $103.64.

Explanation of Solution

Given information:

1-year zero-coupon bonds yields 7%

2-year zero-coupon bonds yields 8%

3-year and longer maturity bonds yields 9%

Payment of coupons annually is 8%

A yield curve is said to flat when the interest rates remain stable over a said period.

We are told that the yield curve is flat at 9%. So, in all the three bonds, we will consider the yield as 9%. Let us now calculate the price of bond.

Calculation of coupon payment:

=$100×8%=$100×8100=$100×0.08=$8

The value of $8 has to be used for further calculations.

PV=$8 (1+9%)1+$8 (1+9%)2+$8 (1+9%)3+$108 (1+9%)3PV=$8 (1+0.09)1+$8 (1+0.09)2+$8 (1+0.09)3+$108 (1+0.09)3PV=$8(1+0.09)+$8(1+0.1881)+$8(1+0.295029)+$108(1+0.295029)PV=$8(1.09)+$8(1.1881)+$8(1.295029)+$108(1.295029)PV=7.3394+6.7334+6.1774+83.3958=$103.64

Therefore, the price of the bond when the yield is flat at 9% will be $103.64.

c.

Summary Introduction

To calculate: Rate of return on each bond.

Introduction:

Bond Price: It is supposed to be the present discounted value of future cash stream that is created by a bond. In simple words, it is sum of all the present value of coupon payments along with the present value of the par value of the time of maturity.

c.

Expert Solution

Answer to Problem 11PS

The rate of return on 1-year bond will be 9.81% and on 2-year bond it will be 8%, and on 3-year bond it will be 4.76%

Explanation of Solution

Given information:

1-year zero-coupon bonds yields 7%

2-year zero-coupon bonds yields 8%

3-year and longer maturity bonds yields 9%

Payment of coupons annually is 8%

Calculation of rate of return on 1-year bond:

Rate of return= Current yield at purchase date+ capital gain

This formula can further be simplified.

Rate of return= Coupon paymentBond’s purchase price+Bond’s price when sold−Bond’s purchase priceBond’s purchase price=$8$100+Bond’s price when sold−$100$100

Since we are not aware of the bond’s price when it is sold, let us calculate it now.

Calculation of bond’s selling price:

Years to maturity =2

Coupon payment=$8

Interest=7%

Face value=$100

Since Excel application simplifies our calculations let us make use of it here.

=PV(rate,nper,pmt,fv)=PV(0.07,2,8,100)=−$101.81

If we ignore the ‘-‘ sign, our selling price of the bond will be $101.81.

Let us now calculate the rate of return.

Let us now substitute the required values in the formula.

=$8$100+$101.81−$100$100=$8$100+$1.81$100=0.08+0.0181=0.0981

or 9.81 % when converted into percentages.

Therefore, the rate of return on 1-year bond will be 9.81%.

Calculation of rate of return on 2-year bond:

Rate of return= Coupon paymentBond’s purchase price+Bond’s price when sold−Bond’s purchase priceBond’s purchase price=$8$100+Bond’s price when sold−$100$100

Since we are not aware of the bond’s price when it is sold, let us calculate it now.

Calculation of bond’s selling price:

Years to maturity =3

Coupon payment=$8

Interest=8%

Face value=$100

Since Excel application simplifies our calculations let us make use of it here.

=PV(rate,nper,pmt,fv)=PV(0.08,3,8,100)=−$100

If we ignore the ‘-‘ sign, our selling price of the bond will be $100

Let us now calculate the rate of return.

=$8$100+$100−$100$100=$8$100+$0$100=0.08+0=0.08

or 8%

Therefore, the rate of return on 2-year bond will be 8%.

Calculation of rate of return on 3-year bond:

Rate of return= Coupon paymentBond’s purchase price+Bond’s price when sold−Bond’s purchase priceBond’s purchase price=$8$100+Bond’s price when sold−$100$100

Since we are not aware of the bond’s price when it is sold, let us calculate it now.

Calculation of bond’s selling price:

Years to maturity =4

Coupon payment=$8

Interest=9%

Face value=$100

Since Excel application simplifies our calculations let us make use of it here.

=PV(rate,nper,pmt,fv)=PV(0.09,4,8,100)=−$96.76

If we ignore the ‘-‘ sign, our selling price of the bond will be $96.76.

Let us now calculate the rate of return.

=$8$100+$96.76−$100$100=$8$100+(−3.24)$100=0.08−0.0324=0.0476

or 4.76%

Therefore, the rate of return on 3-year bond will be 4.76%

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Answer 5

Chapter 16, Problem 11PS

a.

Summary Introduction

To calculate: The price of the bond today.

Introduction:

Bond Price: It is supposed to be the present discounted value of future cash stream that is created by a bond. In simple words, it is sum of all the present value of coupon payments along with the present value of the par value of the time of maturity.

a.

Expert Solution

Answer to Problem 11PS

The price of the bond today is $103.90.

Explanation of Solution

Given information:

1-year zero-coupon bonds yields 7%

2-year zero-coupon bonds yields 8%

3-year and longer maturity bonds yields 9%

Payment of coupons annually is 8%

Let us calculate the price of the bond as on today. The formulas to be used is as follows:

PV=C(1+y)t+FV(1+y)T

Where

C= periodic coupon payment

Y= YTM

FV= the bond’s par value or face value

t=time

T=the number of periods until the bond’s maturity date

Since the par value is given to us, let us assume the par value to be $100. Let us now calculate the coupon payment.

Calculation of coupon payment:

=$100×8%=$100×8100=$100×0.08=$8

The value of $8 has to be used for further calculations.

PV=$8(1+7%)1+$8(1+8%)2+$8(1+9%)3+$108(1+9%)3

Let us convert the percentages into decimals for easy calculations.

PV=$8 (1+0.07)1+$8 (1+0.08)2+$8 (1+0.09)3+$108 (1+0.09)3PV=$8(1+0.07)+$8(1+0.1664)+$8(1+0.295029)+$108(1+0.295029)PV=$8(1.07)+$8(1.1664)+$8(1.295029)+$108(1.295029)PV=7.4766+6.8587+6.1774+83.3958=$103.9086 or $103.90

Therefore, the price of the bond today is $103.90.

b.

Summary Introduction

To calculate: The price of each bond in one year if yield curve is flat at 9% at that time.

Introduction:

Bond Price: It is supposed to be the present discounted value of future cash stream that is created by a bond. In simple words, it is sum of all the present value of coupon payments along with the present value of the par value of the time of maturity.

b.

Expert Solution

Answer to Problem 11PS

The price of the bond when the yield is flat at 9% will be $103.64.

Explanation of Solution

Given information:

1-year zero-coupon bonds yields 7%

2-year zero-coupon bonds yields 8%

3-year and longer maturity bonds yields 9%

Payment of coupons annually is 8%

A yield curve is said to flat when the interest rates remain stable over a said period.

We are told that the yield curve is flat at 9%. So, in all the three bonds, we will consider the yield as 9%. Let us now calculate the price of bond.

Calculation of coupon payment:

=$100×8%=$100×8100=$100×0.08=$8

The value of $8 has to be used for further calculations.

PV=$8 (1+9%)1+$8 (1+9%)2+$8 (1+9%)3+$108 (1+9%)3PV=$8 (1+0.09)1+$8 (1+0.09)2+$8 (1+0.09)3+$108 (1+0.09)3PV=$8(1+0.09)+$8(1+0.1881)+$8(1+0.295029)+$108(1+0.295029)PV=$8(1.09)+$8(1.1881)+$8(1.295029)+$108(1.295029)PV=7.3394+6.7334+6.1774+83.3958=$103.64

Therefore, the price of the bond when the yield is flat at 9% will be $103.64.

c.

Summary Introduction

To calculate: Rate of return on each bond.

Introduction:

Bond Price: It is supposed to be the present discounted value of future cash stream that is created by a bond. In simple words, it is sum of all the present value of coupon payments along with the present value of the par value of the time of maturity.

c.

Expert Solution

Answer to Problem 11PS

The rate of return on 1-year bond will be 9.81% and on 2-year bond it will be 8%, and on 3-year bond it will be 4.76%

Explanation of Solution

Given information:

1-year zero-coupon bonds yields 7%

2-year zero-coupon bonds yields 8%

3-year and longer maturity bonds yields 9%

Payment of coupons annually is 8%

Calculation of rate of return on 1-year bond:

Rate of return= Current yield at purchase date+ capital gain

This formula can further be simplified.

Rate of return= Coupon paymentBond’s purchase price+Bond’s price when sold−Bond’s purchase priceBond’s purchase price=$8$100+Bond’s price when sold−$100$100

Since we are not aware of the bond’s price when it is sold, let us calculate it now.

Calculation of bond’s selling price:

Years to maturity =2

Coupon payment=$8

Interest=7%

Face value=$100

Since Excel application simplifies our calculations let us make use of it here.

=PV(rate,nper,pmt,fv)=PV(0.07,2,8,100)=−$101.81

If we ignore the ‘-‘ sign, our selling price of the bond will be $101.81.

Let us now calculate the rate of return.

Let us now substitute the required values in the formula.

=$8$100+$101.81−$100$100=$8$100+$1.81$100=0.08+0.0181=0.0981

or 9.81 % when converted into percentages.

Therefore, the rate of return on 1-year bond will be 9.81%.

Calculation of rate of return on 2-year bond:

Rate of return= Coupon paymentBond’s purchase price+Bond’s price when sold−Bond’s purchase priceBond’s purchase price=$8$100+Bond’s price when sold−$100$100

Since we are not aware of the bond’s price when it is sold, let us calculate it now.

Calculation of bond’s selling price:

Years to maturity =3

Coupon payment=$8

Interest=8%

Face value=$100

Since Excel application simplifies our calculations let us make use of it here.

=PV(rate,nper,pmt,fv)=PV(0.08,3,8,100)=−$100

If we ignore the ‘-‘ sign, our selling price of the bond will be $100

Let us now calculate the rate of return.

=$8$100+$100−$100$100=$8$100+$0$100=0.08+0=0.08

or 8%

Therefore, the rate of return on 2-year bond will be 8%.

Calculation of rate of return on 3-year bond:

Rate of return= Coupon paymentBond’s purchase price+Bond’s price when sold−Bond’s purchase priceBond’s purchase price=$8$100+Bond’s price when sold−$100$100

Since we are not aware of the bond’s price when it is sold, let us calculate it now.

Calculation of bond’s selling price:

Years to maturity =4

Coupon payment=$8

Interest=9%

Face value=$100

Since Excel application simplifies our calculations let us make use of it here.

=PV(rate,nper,pmt,fv)=PV(0.09,4,8,100)=−$96.76

If we ignore the ‘-‘ sign, our selling price of the bond will be $96.76.

Let us now calculate the rate of return.

=$8$100+$96.76−$100$100=$8$100+(−3.24)$100=0.08−0.0324=0.0476

or 4.76%

Therefore, the rate of return on 3-year bond will be 4.76%

Answer 6

Chapter 16, Problem 11PS

a.

Summary Introduction

To calculate: The price of the bond today.

Introduction:

Bond Price: It is supposed to be the present discounted value of future cash stream that is created by a bond. In simple words, it is sum of all the present value of coupon payments along with the present value of the par value of the time of maturity.

a.

Expert Solution

Answer to Problem 11PS

The price of the bond today is $103.90.

Explanation of Solution

Given information:

1-year zero-coupon bonds yields 7%

2-year zero-coupon bonds yields 8%

3-year and longer maturity bonds yields 9%

Payment of coupons annually is 8%

Let us calculate the price of the bond as on today. The formulas to be used is as follows:

PV=C(1+y)t+FV(1+y)T

Where

C= periodic coupon payment

Y= YTM

FV= the bond’s par value or face value

t=time

T=the number of periods until the bond’s maturity date

Since the par value is given to us, let us assume the par value to be $100. Let us now calculate the coupon payment.

Calculation of coupon payment:

=$100×8%=$100×8100=$100×0.08=$8

The value of $8 has to be used for further calculations.

PV=$8(1+7%)1+$8(1+8%)2+$8(1+9%)3+$108(1+9%)3

Let us convert the percentages into decimals for easy calculations.

PV=$8 (1+0.07)1+$8 (1+0.08)2+$8 (1+0.09)3+$108 (1+0.09)3PV=$8(1+0.07)+$8(1+0.1664)+$8(1+0.295029)+$108(1+0.295029)PV=$8(1.07)+$8(1.1664)+$8(1.295029)+$108(1.295029)PV=7.4766+6.8587+6.1774+83.3958=$103.9086 or $103.90

Therefore, the price of the bond today is $103.90.

Answer 7

Chapter 16, Problem 11PS

a.

Summary Introduction

To calculate: The price of the bond today.

Introduction:

Bond Price: It is supposed to be the present discounted value of future cash stream that is created by a bond. In simple words, it is sum of all the present value of coupon payments along with the present value of the par value of the time of maturity.

Answer 8

a.

Expert Solution

Answer to Problem 11PS

The price of the bond today is $103.90.

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given information:

1-year zero-coupon bonds yields 7%

2-year zero-coupon bonds yields 8%

3-year and longer maturity bonds yields 9%

Payment of coupons annually is 8%

Let us calculate the price of the bond as on today. The formulas to be used is as follows:

PV=C(1+y)t+FV(1+y)T

Where

C= periodic coupon payment

Y= YTM

FV= the bond’s par value or face value

t=time

T=the number of periods until the bond’s maturity date

Since the par value is given to us, let us assume the par value to be $100. Let us now calculate the coupon payment.

Calculation of coupon payment:

=$100×8%=$100×8100=$100×0.08=$8

The value of $8 has to be used for further calculations.

PV=$8(1+7%)1+$8(1+8%)2+$8(1+9%)3+$108(1+9%)3

Let us convert the percentages into decimals for easy calculations.

PV=$8 (1+0.07)1+$8 (1+0.08)2+$8 (1+0.09)3+$108 (1+0.09)3PV=$8(1+0.07)+$8(1+0.1664)+$8(1+0.295029)+$108(1+0.295029)PV=$8(1.07)+$8(1.1664)+$8(1.295029)+$108(1.295029)PV=7.4766+6.8587+6.1774+83.3958=$103.9086 or $103.90

Therefore, the price of the bond today is $103.90.

Answer 13

b.

Summary Introduction

To calculate: The price of each bond in one year if yield curve is flat at 9% at that time.

Introduction:

Bond Price: It is supposed to be the present discounted value of future cash stream that is created by a bond. In simple words, it is sum of all the present value of coupon payments along with the present value of the par value of the time of maturity.

b.

Expert Solution

Answer to Problem 11PS

The price of the bond when the yield is flat at 9% will be $103.64.

Explanation of Solution

Given information:

1-year zero-coupon bonds yields 7%

2-year zero-coupon bonds yields 8%

3-year and longer maturity bonds yields 9%

Payment of coupons annually is 8%

A yield curve is said to flat when the interest rates remain stable over a said period.

We are told that the yield curve is flat at 9%. So, in all the three bonds, we will consider the yield as 9%. Let us now calculate the price of bond.

Calculation of coupon payment:

=$100×8%=$100×8100=$100×0.08=$8

The value of $8 has to be used for further calculations.

PV=$8 (1+9%)1+$8 (1+9%)2+$8 (1+9%)3+$108 (1+9%)3PV=$8 (1+0.09)1+$8 (1+0.09)2+$8 (1+0.09)3+$108 (1+0.09)3PV=$8(1+0.09)+$8(1+0.1881)+$8(1+0.295029)+$108(1+0.295029)PV=$8(1.09)+$8(1.1881)+$8(1.295029)+$108(1.295029)PV=7.3394+6.7334+6.1774+83.3958=$103.64

Therefore, the price of the bond when the yield is flat at 9% will be $103.64.

Answer 14

b.

Summary Introduction

To calculate: The price of each bond in one year if yield curve is flat at 9% at that time.

Introduction:

Bond Price: It is supposed to be the present discounted value of future cash stream that is created by a bond. In simple words, it is sum of all the present value of coupon payments along with the present value of the par value of the time of maturity.

Answer 15

b.

Expert Solution

Answer to Problem 11PS

The price of the bond when the yield is flat at 9% will be $103.64.

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given information:

1-year zero-coupon bonds yields 7%

2-year zero-coupon bonds yields 8%

3-year and longer maturity bonds yields 9%

Payment of coupons annually is 8%

A yield curve is said to flat when the interest rates remain stable over a said period.

We are told that the yield curve is flat at 9%. So, in all the three bonds, we will consider the yield as 9%. Let us now calculate the price of bond.

Calculation of coupon payment:

=$100×8%=$100×8100=$100×0.08=$8

The value of $8 has to be used for further calculations.

PV=$8 (1+9%)1+$8 (1+9%)2+$8 (1+9%)3+$108 (1+9%)3PV=$8 (1+0.09)1+$8 (1+0.09)2+$8 (1+0.09)3+$108 (1+0.09)3PV=$8(1+0.09)+$8(1+0.1881)+$8(1+0.295029)+$108(1+0.295029)PV=$8(1.09)+$8(1.1881)+$8(1.295029)+$108(1.295029)PV=7.3394+6.7334+6.1774+83.3958=$103.64

Therefore, the price of the bond when the yield is flat at 9% will be $103.64.

Answer 20

c.

Summary Introduction

To calculate: Rate of return on each bond.

Introduction:

Bond Price: It is supposed to be the present discounted value of future cash stream that is created by a bond. In simple words, it is sum of all the present value of coupon payments along with the present value of the par value of the time of maturity.

c.

Expert Solution

Answer to Problem 11PS

The rate of return on 1-year bond will be 9.81% and on 2-year bond it will be 8%, and on 3-year bond it will be 4.76%

Explanation of Solution

Given information:

1-year zero-coupon bonds yields 7%

2-year zero-coupon bonds yields 8%

3-year and longer maturity bonds yields 9%

Payment of coupons annually is 8%

Calculation of rate of return on 1-year bond:

Rate of return= Current yield at purchase date+ capital gain

This formula can further be simplified.

Rate of return= Coupon paymentBond’s purchase price+Bond’s price when sold−Bond’s purchase priceBond’s purchase price=$8$100+Bond’s price when sold−$100$100

Since we are not aware of the bond’s price when it is sold, let us calculate it now.

Calculation of bond’s selling price:

Years to maturity =2

Coupon payment=$8

Interest=7%

Face value=$100

Since Excel application simplifies our calculations let us make use of it here.

=PV(rate,nper,pmt,fv)=PV(0.07,2,8,100)=−$101.81

If we ignore the ‘-‘ sign, our selling price of the bond will be $101.81.

Let us now calculate the rate of return.

Let us now substitute the required values in the formula.

=$8$100+$101.81−$100$100=$8$100+$1.81$100=0.08+0.0181=0.0981

or 9.81 % when converted into percentages.

Therefore, the rate of return on 1-year bond will be 9.81%.

Calculation of rate of return on 2-year bond:

Rate of return= Coupon paymentBond’s purchase price+Bond’s price when sold−Bond’s purchase priceBond’s purchase price=$8$100+Bond’s price when sold−$100$100

Since we are not aware of the bond’s price when it is sold, let us calculate it now.

Calculation of bond’s selling price:

Years to maturity =3

Coupon payment=$8

Interest=8%

Face value=$100

Since Excel application simplifies our calculations let us make use of it here.

=PV(rate,nper,pmt,fv)=PV(0.08,3,8,100)=−$100

If we ignore the ‘-‘ sign, our selling price of the bond will be $100

Let us now calculate the rate of return.

=$8$100+$100−$100$100=$8$100+$0$100=0.08+0=0.08

or 8%

Therefore, the rate of return on 2-year bond will be 8%.

Calculation of rate of return on 3-year bond:

Rate of return= Coupon paymentBond’s purchase price+Bond’s price when sold−Bond’s purchase priceBond’s purchase price=$8$100+Bond’s price when sold−$100$100

Since we are not aware of the bond’s price when it is sold, let us calculate it now.

Calculation of bond’s selling price:

Years to maturity =4

Coupon payment=$8

Interest=9%

Face value=$100

Since Excel application simplifies our calculations let us make use of it here.

=PV(rate,nper,pmt,fv)=PV(0.09,4,8,100)=−$96.76

If we ignore the ‘-‘ sign, our selling price of the bond will be $96.76.

Let us now calculate the rate of return.

=$8$100+$96.76−$100$100=$8$100+(−3.24)$100=0.08−0.0324=0.0476

or 4.76%

Therefore, the rate of return on 3-year bond will be 4.76%

Answer 21

c.

Summary Introduction

To calculate: Rate of return on each bond.

Introduction:

Bond Price: It is supposed to be the present discounted value of future cash stream that is created by a bond. In simple words, it is sum of all the present value of coupon payments along with the present value of the par value of the time of maturity.

Answer 22

c.

Expert Solution

Answer to Problem 11PS

The rate of return on 1-year bond will be 9.81% and on 2-year bond it will be 8%, and on 3-year bond it will be 4.76%

Answer 23

c.

Expert Solution

Answer 24

c.

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Given information:

1-year zero-coupon bonds yields 7%

2-year zero-coupon bonds yields 8%

3-year and longer maturity bonds yields 9%

Payment of coupons annually is 8%

Calculation of rate of return on 1-year bond:

Rate of return= Current yield at purchase date+ capital gain

This formula can further be simplified.

Rate of return= Coupon paymentBond’s purchase price+Bond’s price when sold−Bond’s purchase priceBond’s purchase price=$8$100+Bond’s price when sold−$100$100

Since we are not aware of the bond’s price when it is sold, let us calculate it now.

Calculation of bond’s selling price:

Years to maturity =2

Coupon payment=$8

Interest=7%

Face value=$100

Since Excel application simplifies our calculations let us make use of it here.

=PV(rate,nper,pmt,fv)=PV(0.07,2,8,100)=−$101.81

If we ignore the ‘-‘ sign, our selling price of the bond will be $101.81.

Let us now calculate the rate of return.

Let us now substitute the required values in the formula.

=$8$100+$101.81−$100$100=$8$100+$1.81$100=0.08+0.0181=0.0981

or 9.81 % when converted into percentages.

Therefore, the rate of return on 1-year bond will be 9.81%.

Calculation of rate of return on 2-year bond:

Rate of return= Coupon paymentBond’s purchase price+Bond’s price when sold−Bond’s purchase priceBond’s purchase price=$8$100+Bond’s price when sold−$100$100

Since we are not aware of the bond’s price when it is sold, let us calculate it now.

Calculation of bond’s selling price:

Years to maturity =3

Coupon payment=$8

Interest=8%

Face value=$100

Since Excel application simplifies our calculations let us make use of it here.

=PV(rate,nper,pmt,fv)=PV(0.08,3,8,100)=−$100

If we ignore the ‘-‘ sign, our selling price of the bond will be $100

Let us now calculate the rate of return.

=$8$100+$100−$100$100=$8$100+$0$100=0.08+0=0.08

or 8%

Therefore, the rate of return on 2-year bond will be 8%.

Calculation of rate of return on 3-year bond:

Rate of return= Coupon paymentBond’s purchase price+Bond’s price when sold−Bond’s purchase priceBond’s purchase price=$8$100+Bond’s price when sold−$100$100

Since we are not aware of the bond’s price when it is sold, let us calculate it now.

Calculation of bond’s selling price:

Years to maturity =4

Coupon payment=$8

Interest=9%

Face value=$100

Since Excel application simplifies our calculations let us make use of it here.

=PV(rate,nper,pmt,fv)=PV(0.09,4,8,100)=−$96.76

If we ignore the ‘-‘ sign, our selling price of the bond will be $96.76.

Let us now calculate the rate of return.

=$8$100+$96.76−$100$100=$8$100+(−3.24)$100=0.08−0.0324=0.0476

or 4.76%

Therefore, the rate of return on 3-year bond will be 4.76%

Answer 27

Ch. 16 - Prob. 1PS Ch. 16 - Prob. 2PS Ch. 16 - Prob. 3PS Ch. 16 - Prob. 4PS Ch. 16 - Prob. 5PS Ch. 16 - Prob. 6PS Ch. 16 - Prob. 7PS Ch. 16 - Prob. 8PS Ch. 16 - Prob. 9PS Ch. 16 - Prob. 10PS

The price of the bond today. Introduction: Bond Price : It is supposed to be the present discounted value of future cash stream that is created by a bond. In simple words, it is sum of all the present value of coupon payments along with the present value of the par value of the time of maturity.

Concept explainers

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Answer to Problem 11PS

Explanation of Solution

Answer to Problem 11PS

Explanation of Solution

Answer to Problem 11PS

Explanation of Solution

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Chapter 16 Solutions