EBK INVESTMENTS
EBK INVESTMENTS
11th Edition
ISBN: 9781259357480
Author: Bodie
Publisher: MCGRAW HILL BOOK COMPANY
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Chapter 14, Problem 31PS
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 31PS

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 31PS

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 31PS

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 31PS

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 31PS

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%

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