FINMAN2 BOND VALUATION PRESENTATION

8/7/2019 FINMAN2 BOND VALUATION PRESENTATION

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!"!"

Characteristics of Bonds

###

00 11 2 . . .2 . . . nn

$I $I $I $I $I $I+$M$I $I $I $I $I $I+$M

!"#!$

$%#&#%

'#

(

%&'&(%&'&()) *+*+

,, --./0111./0111

--(23(23 ,0,0

.(2.(2 4.*+214.*+21 ,5,5

66 -+74+1*+5-+74+1*+5

8%&'&8%&'&

0 1 2 … 28

$32.50 $32.50 $32.50 $32.50 $32.50 $32.50+$1000

)*)*

99::;;

6<<6<<

== ,,

>>

?@?@ ,A ,A

,<>,<>

A#<A#<

)*)*

4A<,54A<,5

+,-&...+,-&.../)0/)01122



)*)*

4A<,54A<,5

./0111B&./0111B&C<C<<DE<DE

8A<AB8A<AB

&,<&,<

)*)*

&A&A

<<

FF

0,000,00

,,A,,A

<<

,,

@,,A@,,A

FF>>

G,G,

,A,,A,

6@,,,6@,,,

@>@>

8,,8,,

>,>,FFAA

8<08<0,,

--,,

AA

GG

,,

@,E@,E

-A,-A,

@ @ -,-,FFGG

-,-,

V =V = t = 1t = 1

nn

ΣΣΣΣΣΣΣΣ

$Ct

(1 + k)t

@ @

/'/'

34'334'3

)#()#( 55

))

++

)()(



FFAA

,,FFGG

&4&4

55

&,4<&,4<

55

Vb = $It (PVIFA kb, n) + $M (PVIF kb, n)

$It $M(1 + kb)

t (1 + kb)nVVbb = += +

nn

t = 1t = 1ΣΣΣΣΣΣΣΣ

-- *(#*(#

66 147)8&4147)8&4

##

197)8&9#197)8&9#

1:7)8&:#1:7)8&:#

;; !!

#<#<

7)87)8

!!

== !#!#

7)8!7)8!

H&6H&6

800

1000

1100

1200

1300

$1400

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

Discount Rate

Bond Value

6 3/8

When the YTM < coupon, the bond

trades at a premium.

When the YTM = coupon, the

bond trades at par.

When the YTM > coupon, the bond trades at a discount.

66

C

Consider two otherwise identical bonds.

The long-maturity bond will have much more

volatility with respect to changes in the

discount rate

Discount Rate

Bond Value

Par

Short Maturity Bond

Long Maturity

Bond



$$

Consider two otherwise identical bonds.

The low-coupon bond will have much morevolatility with respect to changes in the

discount rate

Discount Rate

Bond Value

High Coupon Bond

Low Coupon Bond

##

) ) 4848 >>

/# /# + +

T r

F PV

)1( +=

Present value of a pure discount bond at time 0:

0

0$

1

0$

2

0$

1−T

F $

T

6.6.

#,-&...#,-&...

))

((

-6<&-6<-6<&-6<

1212

6 6

-6&48B%-6&48B%@0@0 5IB48B5IB48B@0@0 55

-/+148B%-/+148B%/+0+1/+0+1 5I/11148B5I/11148B/+0+1/+0+1 55

//

-6&/-6&/ 4/I4/I55 IBJ4/IIBJ4/I55

//

-/+1/-/+1/ 4//+54//+5+1+1

II /111J4//+5/111J4//+5+1+1

-./111-./111/+/+

)?)?

(-.<1(-.<1

>>#2#2

Note: If the coupon rate > discount rate,

the bond will sell for a premium.

6 6

-6&48B%-6&48B%@0@0 5IB48B5IB48B@0@0 55

-/+148B%-/+148B%/10+1/10+1 5I/11148B5I/11148B/10+1/10+1 55

//

-6&/-6&/ 4/I4/I55 IBJ4/IIBJ4/I55

//

-/+1/-/+1/ 4//154//15+1+1 I/111J4//15I/111J4//15+1+1 --./0/1+./0/1+

/1/1



)?)?

(-=<1(-=<1>>#2#2

Note: If the coupon rate < discount rate,the bond will sell for a discount.

6 6

-6&48B%-6&48B%@0@0 5IB48B5IB48B@0@0 55-/+148B%-/+148B%/K0+1/K0+1 5I/11148B5I/11148B/K0+1/K0+1 55

//

-6&/-6&/ 4/I4/I55 IBJ4/IIBJ4/I55

//

-/+1/-/+1/ 4//K54//K5+1+1 I/111J4//K5I/111J4//K5+1+1 --.7(2K.7(2K

/K/K

6 6

-6&48B%-6&48B%@0@0 5IB48B5IB48B@0@0 55

-(148B%-(148B%/K0+1/K0+1 5I/11148B5I/11148B/K0+1/K0+1 55

//

-6&/-6&/ 4/I4/I55 IBJ4/IIBJ4/I55

//

-(1/-(1/ 4/154/15K1K1

I/111J4/15I/111J4/15K1K1

--.7(((7.7(((711

/#;./#;.

,-&...#7)8@<,-&...#7)8@<

11.174$)06.1(

000,1$

)1( 30

==

+

=T

r

F PV

0

0$

1

0$

2

0$

29

000,1$

30

H&6H&6

&&

&,&,

H&6H&6

&&

&,&,

$It $M

(1 + kb)t (1 + kb)

nPP00 = += +

nn

t = 1t = 1ΣΣΣΣΣΣΣΣ



H&6H&6

,ABAB.,ABAB.

,-&...-.<,-&...-.<AA

11

22

6 6

-6&48B%-6&48B%@0@0 5IB48B5IB48B@0@0 557L7L1-2148B%7L7L1-2148B%@0/(@0/( 5I/11148B5I/11148B@0/(@0/( 55

//

-6&/-6&/ 4/I4/I55 IBJ4/IIBJ4/I55

//

7L7L1-21/7L7L1-21/ 4/I4/I 55/(/( II /111J4/I/111J4/I55/(/(

,< ,<

==

""

&&FF

,C.A,C.A

-.-.

1212

0 100 10

--$508 $1000$508 $1000

6 6

-B48B-B48B 00 55

217-/11148B217-/11148B 0/10/1 55

217-48B217-48B 0/10/1 55

-BJ4/I5-BJ4/I5/1/1

217-/111J4/I5217-/111J4/I5/1/1

/L(72-/L(72-4/I54/I5/1/1

--33

==

0 10

PV = -508 FV = 1000

'<<$G$'<<$G$

&<&<

A./111,/+&A./111,/+&

//3//3

-- 848B%0848B%0@0@05I648B05I648B0@0@055

B,GB,G

4/5//304+5/234*5734/5//304+5/234*573

&&

//3//3-.//14(KL+5I./01114+7(5-./011111-.//14(KL+5I./01114+7(5-./011111

/23/23-.//142K+/5I./01114/75-.7**/-.//142K+/5I./01114/75-.7**/

7373-.//142*(5I./01114*L5-./0++2L(-.//142*(5I./01114*L5-./0++2L(

,$G$,$G$

700

800

900

1,000

1,100

1,200

1,300

8% 10% 12% 14%



'&'&M M $G$$G$

6N6N :/2:/20/+30/+30./111,&G0./111,&G /K30A /K30A

/K3/2/K3/2

-- 84848B%@308B%@305I645I648B@308B@3055

%G/K30 %G/K30 ,A4/5/204+5L4*5*,A4/5/204+5L4*5* 4K5/4K5/

&&

//3//3-.//14(KL+5I./01114+7(5-./011111-.//14(KL+5I./01114+7(5-./011111

/23/23-.//142K+/5I./01114/75-.7**/-.//142K+/5I./01114/75-.7**/

7373-.//142*(5I./01114*L5-./0++2L(-.//142*(5I./01114*L5-./0++2L(

**4/254/25 4,-6.@-=6D,-&...-=.4,AEE.=4,-6.@-=6D,-&...-=.4,AEE.=

**4L54L5 4,-6.=B=@D,-&...;.A4,B.-C64,-6.=B=@D,-&...;.A4,B.-C6

** ;; 4,-6.6;66D,-&...@EC4,BC;@=4,-6.6;66D,-&...@EC4,BC;@=

**4/54/5 4,-6..AEED,-&...AEE4,BA66=4,-6..AEED,-&...AEE4,BA66=

1 0 0 0

98 2

95 4

90 1

87 7

86 0

88 0

90 0

92 0

94 0

96 0

98 0

1 0 0 0

1 0 2 0

0 2 4 6 8 1 0 1 2 1 4 1 6

BondValue

($)

Years to Maturity

H6H6

55

FF

$435 H&6435 6

! -... B A A6.

* -... -6 -@ -...

F C.. -6 -6 C@.

$$

((

,-&.=C..)-C,-&.=C..)-CE<E<

,-&...#,-&...#

(&(&

22

FINMAN2 BOND VALUATION PRESENTATION

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