Connect 1-Semester Access Card for Essentials of Investments
Connect 1-Semester Access Card for Essentials of Investments
10th Edition
ISBN: 9781259354977
Author: Zvi Bodie, Alan Marcus, Alex Kane
Publisher: McGraw-Hill Education
Question
Book Icon
Chapter 10, Problem 44C
Summary Introduction

(a)

To calculate:

The rate of return for a one year investment if the bond is selling at a yield to maturity of7%by the end of the year where bond has5%coupon rate with8%yield to maturity and maturity life is20years.

Introduction:

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

Expert Solution
Check Mark

Answer to Problem 44C

The rate of return for holding one year is19.62%

Explanation of Solution

Given:

Coupon on bondPMTis$50

Maturity of bondnis20years

Yield to maturity of bondris8%

Face value of bondFVis$1000

Bond price ist=120PMT1+r1+FV1+r20

For starting year price is

For price for the next year is

  Price=t=119$501.071+$10001.0719=$501.07+$501.072+$501.073+$501.074+$501.075+$501.076+$501.077+$501.078+$501.079+$501.0710+  $501.0711+$501.0712+$501.0713+$501.0714+$501.0715+$501.0716+$501.0717+$501.0718+$501.0719+$10001.0719=$46.73+$43.67+$40.81+$38.14+$35.65+$33.31+$31.14+$29.10+$27.20+$25.42+$23.75+   $22.20+$20.75+$19.39+$18.12+$16.94+$15.83+$14.79+$13.83+$276.51=$793.28

The return on holding period is

  Return on Holding Period=Coupon income +End of year value - Beginning priceBeginning price×100=$50+$793.28$705.44$705.44=19.54%

Summary Introduction

(b)

To calculate:

The tax on income from bond and capital gain if the bond is selling at a yield to maturity of7%by the end of the year where bond has5%coupon rate with8%yield to maturity and maturity life is20years.

Introduction:

Tax to be levied on income of coupon bond as per regular rate of tax and capital gain shall be levied on change in price if there is change in yield to maturity from constant yield to maturity.

Expert Solution
Check Mark

Answer to Problem 44C

Total tax on income is$46.99

Explanation of Solution

Given:

Coupon on bondPMTis$50

Maturity of bondnis20years

Yield to maturity of bondris8%

Face value of bondFVis$1000

Tax rate on income is40%

Tax on capital gain is30%

For calculation income from bond if yield to maturity is8%

Price for initial year is$705.44

  as per calculated above

Price for first year is

  Price=t=119PMT1+r1+FV1+r19

  Price=t=119$501.081+$10001.0819=$501.08+$501.082+$501.083+$501.084+$501.085+$501.086+$501.087+$501.088+$501.089+$501.0810+  $501.0811+$501.0812+$501.0813+$501.0814+$501.0815+$501.0816+$501.0817+$501.0818+$501.0819+$10001.0819=$46.30+$42.87+$39.69+$36.75+$34.03+$31.51+$29.17+$27.01+$25.01+$23.16+$21.44+  $19.86+$18.38+$17.02+$15.76+$14.59+$13.51+$12.51+$11.59+$231.71=$711.87

Implicit interest for the first year is

  Interest Rate=$711.87705.44=$6.43

Tax on bond is

  Tax=interest income+Implicit Interest×tax rate=$50+$6.43×40%=$22.57

Tax on capital gain is as follows:

  Tax=Bond price under 7% YTM- price under 8% YTM×capital gain tax rate=$793.28$711.88×30%=$24.42

So total tax on income is

  Tax=$22.57+$24.42=$46.99

Summary Introduction

(c)

To calculate:

The rate of return after tax for a one year investment if the bond is selling at a yield to maturity of7%by the end of the year where bond has5%coupon rate with8%yield to maturity and maturity life is20years.

Introduction:

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

Expert Solution
Check Mark

Answer to Problem 44C

Total return on income after tax for holding period is

  =12.88%

Explanation of Solution

Given:

Coupon on bondPMTis$50

Total tax on income is$46.99

End of period value is$793.28

Initial year price is$705.44

Holding period return is

  Holding Period Return=Coupon Income+Value at End of period-Initial priceTaxInitial price=$50+$793.28$705.44$46.99$705.44=12.88%

Summary Introduction

(d)

To calculate:

The realized compound yield before taxes for two-years holding period where bond is selling after two years and having7%YTM at the end of second year and coupon amount is reinvested at3%interest rate for one-year.

Introduction:

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

Expert Solution
Check Mark

Answer to Problem 44C

The realized compound yield is12.95%

Explanation of Solution

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

Initial price of bond8%YTM=$705.44

Price on end of second year under7%YTMis

  Price=t=118PMT1+r1+FV1+r18=t=118$501.071+$10001.0718=$798.82

We invest coupon amount for one-year so total income including coupon amount in end of second year is

  Total Income=$50+$50×1.03=$101.15

So, total fund after two year including coupon income is

  Total Fund=$798.82+$101.15=$899.97

So, realized yield is

  Yield=Total proceedsInital price1=$899.97$705.441=12.95%

Summary Introduction

(e)

To calculate:

The realized compound yield after taxes for two-years where bond is selling after two years and having7%YTM at the end of second year and coupon amount is reinvested at3%interest rate for one-year

Introduction:

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

Expert Solution
Check Mark

Answer to Problem 44C

The realized compound yield after tax is8.47%

Explanation of Solution

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

Price for second year is

  Price=t=118$501.081+$10001.0818=$501.08+$501.082+$501.083+$501.084+$501.085+$501.086+$501.087+$501.088+$501.089+$501.0810+  $501.0811+$501.0812+$501.0813+$501.0814+$501.0815+$501.0816+$501.0817+$501.0818+$10001.0818=$46.30+$42.87+$39.69+$36.75+$34.03+$31.51+$29.17+$27.01+$25.01+$23.16+$21.44+  $19.86+$18.38+$17.02+$15.76+$14.59+$13.51+$12.51+$250.25=$718.82

So implicit interest for second year is

  Interest=$718.82$711.88=$6.94

Total income after tax in first year after considering tax on imlicit interest is

  Income after tax=coupon income1tax ratetax on implicit interesrt=$500.6$6.430.4=$27.43

We invested it for one-year then total proceed after tax is

  Proceeds after tax=$27.43×1.018=$27.92

So total proceeds up to the second year is

Price of bond in second year is $798.82

Tax on imputed interest in second year is

  Tax=$6.95×0.4=$2.78

Coupon amount after tax in second year is

  Coupon=$50×0.6=$30

Capital gain tax on second year sale price

  Capital Gain Tax=$798.82$718.82×30%=$24

So total cash flow in second year is

  Cash Flow=$798.82+$30$2.78$24+$27.92=$829.96

Realized coupon yield in second year is

  Coupon Yield=Total proceedsInital price1=$829.96$705.441=8.47%

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Knowledge Booster
Background pattern image
Recommended textbooks for you
Text book image
Essentials Of Investments
Finance
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Mcgraw-hill Education,
Text book image
FUNDAMENTALS OF CORPORATE FINANCE
Finance
ISBN:9781260013962
Author:BREALEY
Publisher:RENT MCG
Text book image
Financial Management: Theory & Practice
Finance
ISBN:9781337909730
Author:Brigham
Publisher:Cengage
Text book image
Foundations Of Finance
Finance
ISBN:9780134897264
Author:KEOWN, Arthur J., Martin, John D., PETTY, J. William
Publisher:Pearson,
Text book image
Fundamentals of Financial Management (MindTap Cou...
Finance
ISBN:9781337395250
Author:Eugene F. Brigham, Joel F. Houston
Publisher:Cengage Learning
Text book image
Corporate Finance (The Mcgraw-hill/Irwin Series i...
Finance
ISBN:9780077861759
Author:Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Jeffrey Jaffe, Bradford D Jordan Professor
Publisher:McGraw-Hill Education