Essentials Of Investments
Essentials Of Investments
11th Edition
ISBN: 9781260316193
Author: Bodie
Publisher: MCG
Question
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Chapter 10, Problem 38PS

a(i)

Summary Introduction

To calculate:

The bond price if yield to maturity is8%on zero coupon bonds where bond pays$1000at maturity.

Introduction:

Price at which investor can be purchased a bond, that be called bond price or the price at which the bond can be redeemed on maturity.

a(i)

Expert Solution
Check Mark

Answer to Problem 38PS

Price of Zero coupon bond having yield to maturity is8%which is equal to$463.19.

Explanation of Solution

Given:

Coupon rateris0%

Face valueFVis$1000

Price of the bond

  PV=t=1nPMT1+rt+FV1+rn

Where,

PV is present value on which bond can be purchased,

PMT is coupon payment,

nis no. of year i.e.10 years,

  PV=t=110$01.081+$10001.0810=$463.19

a(ii)

Summary Introduction

To calculate:

The bond price if yield to maturity is8%on 8% coupon bond where bond pays$1000and$80coupon once per year at maturity.

Introduction:

Price at which investor can be purchased a bond, that be called bond price or the price at which the bond can be redeemed on maturity.

a(ii)

Expert Solution
Check Mark

Answer to Problem 38PS

Price of8%coupon bond having yield to maturity is8%which is equal to$1000

Explanation of Solution

Given:

Coupon rateris8%

Face valueFVis$1000

Price of the bond

  PV=t=1nPMT1+rt+FV1+rn

Where

PV is present value on which bond can be purchased

PMT is coupon payment i.e. $80

nis no. of year i.e.10 years

  PV=t=110$801.081+$10001.0810=$801.081+$801.082+$801.083+$801.084+$801.085+$801.086+$801.087+$801.088+$801.089+$801.0810+$10001.0810=$74.07+$68.58+$63.51+$58.80+$54.45+$50.41+$46.68+$43.22+$40.02+$37.06+$463.19=$1000

a(iii)

Summary Introduction

To calculate:

The bond price if yield to maturity is8%on10%coupon bond where bond pays$1000and$100coupon once per year at maturity.

Introduction:

Price at which investor can be purchased a bond, that be called bond price or the price at which the bond can be redeemed on maturity.

a(iii)

Expert Solution
Check Mark

Answer to Problem 38PS

Price of10%coupon bond having yield to maturity is8%which is equal to$1134.19

Explanation of Solution

Given:

Coupon rateris10%

Face valueFVis$1000

Price of the bond

  PV=t=1nPMT1+rt+FV1+rn

Where,

PV is present value on which bond can be purchased

PMT is coupon payment i.e. $100

nis no. of year i.e.10 years

  PV=t=110$1001.081+$10001.0810=$1001.081+$1001.082+$1001.083+$1001.084+$1001.085+$1001.086+$1001.087+$1001.088+$1001.089+$1001.0810+$10001.0810=$92.59+$85.73+$79.38+$73.50+$68.06+$63.02+$58.35+$54.03+$50.02+$46.32+$463.19=$1134.19

b(i)

Summary Introduction

To calculate:

The bond price if yield to maturity is8%in beginning of next year on zero coupon bond where bond pays$1000.

Introduction:

Price at which investor can be purchased a bond, that be called bond price or the price at which the bond can be redeemed on maturity.

b(i)

Expert Solution
Check Mark

Answer to Problem 38PS

Price of zero coupon bonds having yield to maturity is8%in beginning of next year which is equal to$500.25

Explanation of Solution

Given:

Coupon rateris0%

Face valueFVis$1000

We stand on next year so total year of maturity on the beginning of next year is9years

Price of the bond

  PV=t=1nPMT1+rt+FV1+rn

Where,

PV is present value on which bond can be purchased

PMT is coupon payment i.e. $100

nis no. of year i.e.10 years

  PV=t=19$01.081+$10001.089=$500.25

b(ii)

Summary Introduction

To calculate:

The bond price if yield to maturity is8%in beginning of next year on8%coupon bond where bond pays$1000and$80coupon once per year at maturity.

Introduction:

Price at which investor can be purchased a bond, that be called bond price or the price at which the bond can be redeemed on maturity.

b(ii)

Expert Solution
Check Mark

Answer to Problem 38PS

Price of8%zero coupon bonds having yield to maturity is8%in beginning of next year which is equal to$1000.

Explanation of Solution

Given:

Coupon rateris0%

Face valueFVis$1000

We stand on next year so total year of maturity on the beginning of next year is9years

Price of the bond

  PV=t=1nPMT1+rt+FV1+rn

Where,

PV is present value on which bond can be purchased

PMT is coupon payment i.e.$80

nis no. of year i.e.10 years

  PV=t=19$801.081+$10001.089=$801.081+$801.082+$801.083+$801.084+$801.085+$801.086+$801.087+$801.088+$801.089+$10001.089=$74.07+$68.58+$63.51+$58.80+$54.45+$50.41+$46.68+$43.22+$40.02+$500.25=$1000

b(iii)

Summary Introduction

To calculate:

The bond price if yield to maturity is8%in beginning of next year on8%coupon bond where bond pays$1000and$100coupon once per year at maturity.

Introduction:

Price at which investor can be purchased a bond, that be called bond price or the price at which the bond can be redeemed on maturity.

b(iii)

Expert Solution
Check Mark

Answer to Problem 38PS

Price of10%coupon bond having yield to maturity is8%in beginning of next year which is equal to$1124.93

Explanation of Solution

Given:

Coupon rateris0%

Face valueFVis$1000

We stand on next year so total year of maturity on the beginning of next year is9years

Price of the bond

  PV=t=1nPMT1+rt+FV1+rn

Where,

PV is present value on which bond can be purchased

PMT is coupon payment i.e.$100

nis no. of year i.e.10 years

  PV=t=19$1001.081+$10001.089=$1001.081+$1001.082+$1001.083+$1001.084+$1001.085+$1001.086+$1001.087+$1001.088+$1001.089+$10001.089=$92.59+$85.73+$79.38+$73.50+$68.06+$63.02+$58.35+$54.03+$50.02+$500.25=$1124.93

c(i)

Summary Introduction

To calculate:

The rate of return on zero coupon bond during one year holding period where yield to maturity is8%.

Introduction:

Return is a profit on an investment. So rate of return is a profit over a period of time of investment. It expressed as percentage of the original investment.

c(i)

Expert Solution
Check Mark

Answer to Problem 38PS

Rate of return on zero coupon bonds having yield to maturity is8%if it is holding for1year is which is equal to8%

Explanation of Solution

Given:

Coupon rateris0%

Face valueFVis$1000

PV as per10thyear is$463.19[as per a(i)]

PV as per9thyear is$500.25[as per b(i)]

Total Income on bond including coupon income is

  Total Income=$500.25$463.19+$0=$37.06

Rate of return on the bond

  Rate of Return= Total IncomePV for 10thyear×100=$37.06$463.19×100=8%

c(ii)

Summary Introduction

To calculate:

The rate of return on8%coupon bond during one year holding period where yield to maturity is8%.

Introduction:

Return is a profit on an investment. So rate of return is a profit over a period of time of investment. It expressed as percentage of the original investment.

c(ii)

Expert Solution
Check Mark

Answer to Problem 38PS

Rate of return on8%coupon bond having yield to maturity is8%if it is holding for1year is nil.

Explanation of Solution

Given:

Coupon rateris8%

Face valueFVis$1000

PV as per10thyear is$1000[as per a(ii)]

PV as per9thyear is$1000[as per b(ii)]

Here, formula to calculate and given are added followed by a detailed explanation / working out the complete problem.

Total Income on bond including coupon income is

  Total Income=$1000$1000+$80=$80

Rate of return on the bond

  Rate of Return= Total IncomePV for 10thyear×100=$80$1000×100=8%

c(iii)

Summary Introduction

To calculate:

The rate of return on10%coupon bond having one-year holding period where yield to maturity is8%.

Introduction:

Return is a profit on an investment. So rate of return is a profit over a period of time of investment. It expressed as a percentage of the original investment.

c(iii)

Expert Solution
Check Mark

Answer to Problem 38PS

Rate of return on10%coupon bond having yield to maturity is8%if it is holding for1year is nil.

Explanation of Solution

Given,

Coupon rateris10%

Face valueFVis$1000

PV as per10thyear is$1134.19[as per a(iii)]

PV as per9thyear is$1124.93[as per b(iii)]

Total Income on bond including coupon income is

  Total Income=$1124.93$1134.19+$100=$90.74

Rate of return on the bond

  Rate of Return= Total IncomePV for 10thyear×100=$90.74$1134.19×100=8%

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