FM - 4. Bond Valuation

8/8/2019 FM - 4. Bond Valuation

1/35

Bond valuation

A bond has a $1,000 face value and provides an 8%annual coupon for 3030 years. The appropriate discount rate

is 10% . What is the value of the bond?

V = CP (PVIFA k d , nn) + MV (PVIF k d , nn)


2/35

Bond valuation

A bond has a $ 1,000 face value and provides an 8%annual coupon for 3030 years. The appropriate discount rate


VV = CP (PVIFA 10% , 3030) + MV (PVIF 10% , 3030)= $80 (9.427) + $1,000 (0.057)

= $754.16 + 57.00= $811.16$811.16


3/35

S ample problem #1

A bond has a $ 1,000 face value and provides a 6%annual coupon for 2020 years. The appropriate discount rate

is 6%. What is the value of the bond?


= $688.19 + 311.80= $999.99$999.99


4/35

S ample problem #2

A bond has a $ 1,000 face value and provides a 6%annual coupon for 1010 years. The appropriate discount rate



= $368.68 + 385.50= $754.18$754.18


5/35


6/35

S emi-annual compounding

A non-zero coupon bond adjusted for semi-annual

compounding:

V = CP/2 (PVIFAkd/2 , n*2n*2

) + MV (PVIFkd/2 , n*2n*2

)


7/35

S ample problem #1

A bond has a $ 1,000 face value and provides an 8%semi-annual coupon for 1515 years. The appropriate

discount rate is 10% (annual rate) . What is the value of the coupon bond?

VV = CP/2 (PVIFA 10%/2 , 15*215*2 ) + MV (PVIF 10%/2 , 15*215*2 )

= $40 (15.3725) + $1,000 (0.2314)= $614.90 + 231.40= $846.30$846.30


8/35

S ample problem #2

A bond has a $ 1,000 face value and provides a 6% semi-annual coupon for 1515 years. The appropriate discount rate

is 6% (annual rate) . What is the value of the coupon bond?

VV = CP/2 (PVIFA 6%/2 , 15*215*2 ) + MV (PVIF 6%/2 , 15*215*2 )

= $30 (19.6004) + $1,000 (0.4120)= $588.01 + 412.00= $1,000.01$1,000.01


9/35

Z ero-coupon bond valuation

A zero-coupon bond is a bond that pays no interest butsells at a deep discount from its face value.

V = MV (PVIF kd , nn )


10/35

Z ero-coupon bond example

A bond has a $1,000 face value and a 30-year life. Theappropriate discount rate is 10%. What is the value of the

zero-coupon bond?

V = MV (PVIF kd , nn )


11/35

Z ero-coupon bond example

A bond has a $1,000 face value and a 3030 -year life. Theappropriate discount rate is 10% . What is the value of the

zero-coupon bond?

VV = MV (PVIF 10% , 3030)

= $1,000 (0.057)= $57.00$57.00


12/35

Z ero-coupon bond example #2


zero-coupon bond?

VV = MV (PVIF 6% , 3030)

= $1,000 (0.1741)= $174.10$174.10


13/35

Z ero-coupon bond example #3


zero-coupon bond?

VV = MV (PVIF 6% , 1010)

= $1,000 (0.5584)= $558.40$558.40


14/35

Perpetual bond valuation

A perpetual bond is a bond that never matures. It has aninfinite life.

V = CP / kd


15/35

Perpetual bond example

A bond has a $1,000 face value and provides an 8%coupon. The appropriate discount rate is 10%. What is the

value of the perpetual bond?

V = CP / kd


16/35


17/35

Perpetual bond example #2

A bond has a $1,000 face value and provides a 6%coupon. The appropriate discount rate is 20% . What is thevalue of the perpetual bond?

CP = $1,000 * ( 6% ) = $60

k d = 20% = 0.20VV = CP / k d= $60 / 0.20= $300$300


18/35

Perpetual bond example #3

A bond has a $1,000 face value and provides a 5%coupon. The appropriate discount rate is 8% . What is thevalue of the perpetual bond?

CP = $1,000 * ( 5% ) = $50

k d = 8% = 0.08VV = CP / k d= $50 / 0.08= $625$625


19/35

Y ield to maturity ( YT M)

The yield to maturity ( YT M) of a bond is the discountrate which returns the market price of the bond.

YTM is often used to price a bond.

Bond prices are often quoted in terms of YT M .


20/35


21/35

YT M solution (9%)

$1,250 = $100 (PVIFA 9%, 15) +$1,000 (PVIF 9%, 15)

$1,250 = $100 (8.061) +$1,000 (.275)

$1,250 = $806.10 + $275.00= $1,081.10

[Rate is too high]


22/35

YT M solution (7%)

$1,250 = $100 (PVIFA 7% , 15) +$1,000 (PVIF 7% , 15)

$1,250 = $100 (9.108) +$1,000 (.362)

$1,250 = $910.80 + $362.00= $1,272.80

[Rate is too low]


23/35

YT M solution (interpolate)

.07 $1,273.02 IRR $1,250 $1 92

.09 $1,081

X $23.02 $192

$23X

=


24/35


.07 $1,273.02 IRR $1,250 $192

.09 $1,081

X $23.02 $192

$23X

=


25/35


.07 $1,273.02 YTMYTM $1,250$1,250 $192

.09 $1,081

($23) (0.02)

$192

$23X

X = X = .0024

YT MYT M = .07 + .0024 = .0724 or 7.24%7.24%


26/35

YT M problem #1

Your firm has an issue of 8% annual coupon bonds with10 years10 years left to maturity.

The bonds have a current market value of $1,100.

What is the YT M?


27/35

YT M problem #2

Your firm has an issue of 9% annual coupon bonds with12 years12 years left to maturity.

The bonds have a current market value of $1,310.

What is the YT M?


28/35


29/35

Current vs. coupon yield

The current yield is the coupon payment (CP) as a percentage of the current bond price (V ).

Current yield = CP / V

The coupon yield of a bond is the stated rate of interest.

Coupon yield = Annual coupon payments ( CP )

Maturity value (MV)


30/35

YT M, current & coupon yield

When a bond sells at a discountYTM > current yield > coupon yield

When a bond sells at a premiumCoupon yield > current yield > YT M

When a bond sells at par YTM = current yield = coupon yield


31/35

T he Bangladeshi bond market

Bangladeshs bond market is TINY.

It accounts for only 12% of the GDP.

In South Asian countries, bonds account for anaverage of 34% of the GDP.

In USA, the bond market accounts for 21% of theGDP, in Korea 2 9%, in Japan 16% and for selectOECD countries 16%.


32/35


The bond market is dominated by short and longterm government securities.

The Bangladesh Bank sells 28-day, 91-day, 182-dayand 364-day treasury bills and five, ten, fifteen andtwenty year treasury bonds.

The central bank holds auctions every week and anyinvestor can bid for bonds through any bank.


33/35


An auction committee fixes the coupon rate which isapplicable throughout the instruments life.

These government bonds pay interest or coupon payments every six months.

Generally, these bonds are of 100,000 (or 1 Lakh)Taka denomination or their multiples.


34/35


There is a secondary bond market; however, thetrading activity is very limited.

Government paper has been traded since 2005.

Corporate bonds are far and few in between.


35/35


The corporate bond market is highly under-developed and hasonly ten bonds.

All corporate bonds are issued through private placement.

Notable corporate bonds include the Islamic Bank BangladeshLimited (IBBL) M udaraba Perpetual bond.

FM - 4. Bond Valuation

Documents

Transcript of FM - 4. Bond Valuation