Chapter 3 Prob Solutions

8/9/2019 Chapter 3 Prob Solutions

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Chapter 3: Valuation of Bonds and Shares

Problem 1

(1) 1-year government bond maturity value (Rs) 1,000

Market rate of interest 8%

PV of te bond! 1,000"1#08 (Rs) $$'() Purase rie of bond (Rs) $0*#$8

+mlied return! (1,000 $0*#$8)"$0*#$8 10#&0%

Problem 2

Peretual interest (Rs) 1*0

urrent yield 0#1'

Prie of bond (.) (Rs)! 1*0"0#1' 10/#$

Reuired rate 0#1&

2e3 rie of bond (.) (Rs) ! 1*0"0#1& $''#''

Problem 3

4ae value (Rs) 1000

5nnual interest (Rs) 1*0

Maturity (years) 10

Maturity value (Rs) 1000

Reuired rate 0#1 0#1* 0#1

PV54, 10 year &0 *#8''

PV4, 10 year 0#'0 0#$/ 0#/

PV of interest (Rs) /$1#0' /'0# /#&

PV of maturity value (Rs)! (d 6 g) '1#$/ $#/* #8

PV of 10-year debenture (Rs) 111'#00 1000#00 $0'#'*

7imilar alulations an be made if te reuired rate is 1*% or 1%#

Reuired rate 0#1 0#1* 0#1

PV54, & year '#0*8 '#*''1 '#/*'

PV4, & year 0#&/* 0#&1$* 0#*/1

PV of interest (Rs) &0*#/ *80#' *&8#*0PV of maturity value (Rs) &/#*' &1$#'/ */#11

PV of &-year debenture (Rs) 10/#10 1000#00 $'*#&1

Problem 4

4ae value (Rs) 1000

+nterest rate 0#1

+nterest (Rs)! (1,000 6 0#1) 10

800 1'00 1000

0#0 0#1' 0#1

Problem 5

at 3ould aen to te resent value of bond ifit ad a maturity of & years9 5 similar roedure an befollo3ed# PV of a &-year bond at 1%, 1*% and 1% resetively 3ill be as so3n belo3!

Prie of bond, .0(Rs)

PV of 10-year bond= t=1

n=10140t

(1.12)t+1,000(1.12)10

140PVAF. 12, 10+1,000PVF. 12, 101405.6502+1,0000 .3220=Rs 1,113. 00

Yield=I!

B0


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:a6o (tree-year maturity)! PV4 PV4

;ear as flo3 $% PV (Rs) 1%

1 10 0#$1/ 110#0$ 0#8$'

10 0#8* 101#00 0#/$/

' 110 0#// 8*#8& 0#/1

10/$*

Ma6o (tree-year maturity)!

;ear as flo3 PV4 $% PV (Rs) PV4 1%

1 0 0#$1/ && 0#8$'

0 0#8* &0#&0 0#/$/

' 100 0#// 818#&1 0#/1

$*#0

:a6o (eigt-year maturity)!

;ear as flo3 $% PV (Rs) 1%

1 10 0#$1/ 110#0$ 0#8$'

10 0#8* 101#00 0#/$/

' 10 0#// $# 0#/1

* 10 0#/08 8 0#'

& 10 0#&0 //#$$ 0#&/

10 0#&$ /1#&& 0#&0/

/ 10 0#&*/ * 0#*&

8 110 0#&0 $ 0#*0*

11#0*

Ma6o (eigt-year maturity)!

;ear as flo3 PV4 $% PV (Rs) PV4 1%

1 0 0#$1/ && 0#8$'

0 0#8* &0#&0 0#/$/

' 0 0#// *#'' 0#/1

* 0 0#/08 *#&1 0#'

& 0 0#&0 '$#00 0#&/

0 0#&$ '/8 0#&0/

/ 0 0#&*/ '#8 0#*&

8 100 0#&0 &'1#$8 0#*0*

8''#$

Problem 6

(1) 5nnual omounding! 5nnual interest rate 1%

alf-yearly omounding! >alf-yearly interest rate %


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Period as flo3 PV4 PV PV4

1 to 0 0 1&8$ $''& 1*#8//

0 1,000 0#10 10#/ 0#&&*

1,&*

* Annuity factor

Problem 7

4ae value (Rs) 1,000

Maturity eriods (alf-yearly) 0

>alf-yearly interest rate %

+nterest ayment eriod 10

Maturity value (Rs) 1,0&0

Reuired rate (alf-yearly) /%

+nterest ayment, 11 to 0 years (Rs) 0#00Value of interest (Rs) 1*#'

Value of maturity value (Rs) /1#'*

Value of bond (Rs) *8&/

Problem 8

.ond 1 .ond .ond ' .ond *

+nterest rate 1% 1*% 1% 1%

Reuired rate of return 1&% 1'% 8% 8%

Maturity eriod (years) & 1& 0 10Par"maturity value (Rs) 100 100 100 100

7emi-annual interest rate 8#00% /#00% #00% #00%

Reuired rate of return (alf-yearly) /#&0% #&0% *#00% *#00%

omounding eriods &0 '0 *0 0

PV54 (annuity) 1#$/*8 1'#0&8/ 1$#/$8 1'#&$0'

>alf-yearly interest (Rs) 8 /

PV of interest (Rs) 10'#80 $1#*1 118#/ 81#&*

PV4 (lum sum) 0#0$ 0#1&1 0#08' 0#*&*

PV of maturity value (Rs) #$ 1 0#8' **

.ond value (Rs) 10#*$ 10#&' 1'$#&$ 1/#18

urrent market rie of bonds (Rs) $& 100 110 11&

5nnual yields (by trial @ error) 1#8% 1*#00% 10#/% $#0%7emi-annual yield (by trial @ error) 8#*'% /#00% '$% *#8%

Value of a bond tat ays interest alf-yearly an be alulated by te follo3ing euation!

Problem

Value of bond=t=11

20 60t

(1.0" )t+

1,050

(1.0" )n

60(PVAF20 ,7PVAF10 ,7)+1,050PVF20,760 (10.5#40".0236 )+1,0500.25$4=Rs 4$5. 5"

B0=

t=1

2n 1

2(INT

t)

(1+kd

2)t+

Bn

(1+kd

2 )2n


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Problem 1!

Problem 11

5nnual interest rate 1&%

?uarterly interest rate '#/&%

Market rie (Rs) 8/&

Maturity value (Rs) 1000

?uarterly eriods 0

2e3 interest rate 1#00%

2e3 uarterly interest rate '#00%

Stated yield

?uarterly interest (Rs) '/#&Market rie (Rs) 8/&

?uarterly yield *#'*%

Expected yield

?uarterly interest (Rs) '0

Market rie (Rs) 8/&

?uarterly yield '#&0%

Quarterly yields can be found by trial and error. You can also use the Excel formula for rate to calculate yield:

A R5:B(ner,mt,v,CfvD,CtyeD,guess)

Problem 12

Value of eretual referene sare A1"0#10 A Rs 10 10

20year bond redee%able in 12 years& 'alf-yearly in(eres( 5)* +eriods 24

1,000=t=1

24 50t

(1+YTC)t+

1,150

(1+YTC)n

YTC=5.32

1,000=t=1

24 50t

(1+YTC)t+1,100

(1+YTC)n

YTC=5.2220year bond redee%able in $ years& 'alf-yearly in(eres( 5)* +eriods 16

1,000=t=1

16 50t

(1+YTC)t+

1,150

(1+YTC)n

YTC=5.60

20year bond redee%able in 12 years& 'alf-yearly in(eres( 5)* +eriods 241,000=

t=1

24 50t

(1+YTC)t+

1,150

(1+YTC)n

YTC=5.32

1,000=t=1

24 50t

(1+YTC)t+

1,100

(1+YTC)n

YTC=5.2220year bond redee%able in $ years& 'alf-yearly in(eres( 5)* +eriods 16

1,000=t=1

16 50t

(1+YTC)t+

1,150

(1+YTC)n

YTC=5.60


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;ou an use te B6el formula to alulate value of redeemable referene sare! APV(rate,ner,mt,CfvD,CtyeD)

Problem 13

B6eted


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8#&

7are sould be bougt

Problem 16

Barnings gro3t u to / years 0#1&

Peretual gro3t after / years 0#0$

Reuired rate for / years 0#1

Reuired rate after / years 0#10

BP7 *#00


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1#&8

Problem 18

:otal assets (Rs) 80,000

Buity (Rs) 80,000

2umber of sares 10,000

Buity er sare! 80,000"10,000 8

+nternal rate of return, r 10%

Barnings! 10% H 80,000 8000

BP7 0#8

aitalisation rate, k 1%

Retention ratio, b /0%


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7are rie (Rs) if g A 10%, C&(1#1)"(0#1&-0#1)D 110

Problem 21

4ae value (Rs) 10

BP7 (Rs) onda 10# 0# 1' #

Lineti 1#0 0#& 1//#& #&

Maarastra# 7ooters 0#1 0#& 0 #&

Problem 22


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+nterest or dividend rate 1% 1*% 1&%

Payment freueny annual alf-yearly annual annual

Maturity (years) 1 10

omounding eriods 1 0

Maturity value (Rs) 1000 1000

Prinial amount (Rs rore) &0 '0 100 00

Reuired rate of return 0#100 0#00 0#1'& 0#1&0PV54 (annuity) #81'/ 11#*$$

PV4 (lum sum) 0#'18 0#'118

+nterest"dividend amount (Rs) 10 /0 1& 1

Peretual gro3t rate 0#08

Market value of ea debenture or sare (Rs) 10 6 #81'/ /0 6 11#*$$

G 1000 6 #'18 G 1000 6 #'118 1&"#1'& 1"(#1& - #08)

11'#/ 111*#/0 111#11 1/1#*'

:otal market value (Rs rore) Q ''#** 111#11 '*#8

Problem 25

2et rofit (Rs rore) &02umber of sares (rore)

BP7! &0" &

RNB &%

aitalisation rate, k 1%

Payout 0%

Retention ratio, b *0%


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Barnings from roKet after one year (Rs rore) 0

BP7 from roKet! 0"& *

Ero3t in earnings from roKet after one year 8%

Reuired rate of return 1#&0%

Value of gro3t oortunities! *"(0#1& 0#08) 88#8$

7are value 3it roKet! 18 G 88#8$ 1#8$

BP7 after roKet 0P"B ratio! 1#8$"0 10#8*

Problem 28

2umber of sares (million) 10

2et as rofits (Rs million) 80

as BP7! 80"10 8

Nortunity ost of aital 0%

(a) (i) Retention ratio *0%

Return on retained earnings 0%

Ero3t! *0% H 0% 8%

7are rie! "(0#0 0#08) *'#0

(a) (ii) Retention ratio 0%

Return on retained earnings 0%

Ero3t! 0% H 0% 1%

'#&8

7are rie! '#&8"(0#0 0#1) **#80

(b) (i) Retention ratio *0%

Return on retained earnings *%

Ero3t! *0% H *% $#0%

7are rie! "(0#0 0#0$) &0#&8(b) (ii) Retention ratio 0%

Return on retained earnings *%

Ero3t! 0% H *% 1*#*0%

'#

7are rie! '#"(0#0 0#1**) '/

Problem 2

;ear BP7


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'/#8

1&/#80

'$#01

:otal sare rie 3it gro3t oortunity! '/#8 G '$#01 /#$

Value after gro3t oortunity! (101#0$10"0#1&)

PV after gro3t oortunity! 1&/#80 "1"1#1&10

V=DIV1[1kg {1(1+g1+k)

n

}]5. 45[10.150.0#{1(1.0#1.15)

10

}]5. 4516.6"0.414$=Rs 3".6$


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PV4

PV (Rs) % PV (Rs)

10/#1* 0#$*' 11'#1

$ 0#8$0 10#80

/$/#1$ 0#8*0 $*0#'/

1000#00 110#'8

PV (Rs) PV4 % PV (Rs)

&'#&/ 0#$*'

*/#8' 0#8$0 &'#*0

/&*#*$ 0#8*0 8$0#00

8&$ 1000#00

PV (Rs) % PV (Rs)

10/#1* 0#$*' 11'#1

$ 0#8$0 10#80

8*1 0#8*0 100#/&

/# 0#/$ $&

8#0$ 0#/*/ 8$#/

0#80 0#/0& 8*#0

&*#8 0#& /$#81

*'& 0#/ /0#/0

1000#00 1'/#&$

PV (Rs) PV4 % PV (Rs)

&'#&/ 0#$*'

*/#8' 0#8$0 &'#*0

*#/1 0#8*0 &0#'8

'8#1' 0#/$ */#&'

'*#0& 0#/*/ **#8*

'0#*0 0#/0& *#'0

/#1* 0#& '$#$0

*8#1 0#/

/01#$* 1000#00

1%

PV PV4 PV*'#&/ '#/* '$#$

&/#*' 0#*/ */#11

1000#00 8$#0'

8%

PV PV4 PV

**1#1 #/10 *0#0

&&8#'$ 0#*' *'#1$

1,000#00 8P

*%


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PV PV4 PV

8$#& 1'#&$0 81*

&&'#8 0#*& *'$

1,**#' 1,/1#81


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1-year bond

( )Annal yield

#5=10+1001+y

=15

( ) 'alf-yearly yield

#5=5

1+y+

5+100

(1+y )2=" .

2year bond( )Annal yield

100=10

1+y+

10+100

(1+y )2=


100=5

1+y+

5

(1+y )2+

5

(3year bond( )Annal yield

110=10

1+y +10

(1+y )2+1

(( ) 'alf-yearly yield

110=5

1+y+

5

(1+y )2+

5


10 10 1


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11*#8/

100=5

1+y+

5

(1+y )2+

5


110=10

1+y+

10

(1+y )2+

1


110=5

1+y+

5

(1+y )2+

5

(4year bond

( )Annal yield

115=10

1+y+

10

(1+y )2+

1


115=5

1+y+

5

(1+y )2+

5

(


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PV (Rs)

'#0&

'#11

'#1/

'#08

'#00

#$1

18#'

8$#&0

&0#&

8#8*


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Payout

0#*0 0#0*'' 0#018

0#1 0#0/& 0#01'

0#08 0#0/ 0#01*1

0#1* 0#0$80 0#01

Barningsyield


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1-year bond

( )Annal yield

#5=10+1001+y

=15


#5=5

1+y+

5+100

(1+y )2=" .$


100=10

1+y+

10+100

(1+y )2=10


100=5

1+y+

5

(1+y )2+

5

(1+y )3+

5+100

(1+y )4=5


110=10

1+y +10

(1+y )2+10+100

(1+y )3 =6.24


110=5

1+y+

5

(1+y )2+

5

(1+y )3+

5

(1+y )4+

5

(1+y )5+

5+100

(1+y )6=3.15


10 10 10 10+100


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100=5

1+y+

5

(1+y )2+

5

(1+y )3+

5+100

(1+y )4=5


110=10

1+y+

10

(1+y )2+

10+100

(1+y )3=6.24


110=5

1+y+

5

(1+y )2+

5

(1+y )3+

5

(1+y )4+

5

(1+y )5+

5+100

(1+y )6=3.15

4year bond

( )Annal yield

115=10

1+y+

10

(1+y )2+

10

(1+y )3+

10+100

(1+y )4=5."0


115=5

1+y+

5

(1+y )2+

5

(1+y )3+

5

(1+y )4+

5

(1+y )5+

5

(1+y )6+

5

(1+y )"+

5+100

(1+y )$=2.$"


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Chapter 3 Prob Solutions

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