1. Lecture on bond

2. What’s a bond?
A bond is a long-term debt instrument issued by a corporation or a government. It is a fixed-income security.

3. What’s a bond?
A bond is a formal contract to repay borrowed money with interest at fixed intervals.
A bond provides the borrower with external funds to:
finance long term investments (for corporations)
finance current expenditures (for municipal, state or national governments).

4. Difference between stocks and bonds
Shares of stock Bond
Equity stake in the firm Creditor stake in the firm
[i.e. owners] [.i.e. lenders]
Undefined term Defined term (maturity)
(outstanding indefinitely)

5. Types of bonds
A non-zero coupon-paying bond is a coupon-paying bond with a finite life.
A zero-coupon bond is a bond that pays no interest but sells at a deep discount from face value.
A perpetual bond is a bond that never matures. It has an infinite life.

6. Types of bonds
A fixed rate bond is a bond whose coupon rate remains constant throughout the life of the bond.
A floating rate bond is a bond with a variable coupon that is linked to a reference rate of interest, such as the LIBOR. [LIBOR + 20 b.p.]
An inflation-linked bond is a bond whose coupon payments and principal are indexed to inflation.
Gilts in the UK
TIPS in the US

7. Types of bonds
A Municipal bond (or muni) is a bond issued by a municipality, city, state or their agencies and is usually tax exempt.
A lottery bond is a bond with coupon payments like fixed-rate bonds, but the issuer will redeem randomly selected individual bonds for a higher value than the bond’s face value.
An asset-backed security (e.g. CDOs, CMOs, MBSs) is a bond whose interest and principal payments are backed by underlying cash flows from other assets.

8. The maturity value
The maturity value (MV) [or face value] of a bond is the stated value.
In the case of a U.S. bond, the MV is usually $1,000.
In the case of a Bangladeshi prize bond, the MV is usually 100 Taka.

9. Coupon rate
The coupon rate [or coupon yield] of a bond is the stated rate of interest.
Annual coupon payments (CP)
Coupon rate =
Maturity value (MV)
For example:
Annual coupon payments = $80
Face value = $1,000
Coupon rate = $80/$1,000
= 0.08 = 8%

10. Sample problem #1
If the annual coupon payments are $70 and the face value of a bond is $1,000, what is its coupon rate?
Annual coupon payments (CP)
Coupon rate =
Maturity value (MV)
Annual coupon payments = $70
Face value = $1,000
Coupon rate = $70/$1,000
= 0.07 = 7%

11. Sample problem #2
If the annual coupon payments are $100 and the face value of a bond is $1,000, what is its coupon rate?
Annual coupon payments (CP)
Coupon rate =
Maturity value (MV)
Annual coupon payments = $100
Face value = $1,000
Coupon rate = $100/$1,000
= 0.10 = 10%

12. The discount rate
The discount rate [or capitalization rate] of a bond is dependent on the risk of the bond.
The discount rate (kd) is composed of the risk-free rate plus a premium for risk.

13. Bond valuation Bond value = PV of coupons + PV of MV
Bond value = PV annuity + PV of lump sum
Remember: as interest rates increase, the PVs decrease.
So, as interest rates increase, bond prices decrease.

14. Bond valuation V = CP (PVIFA kd, n) + MV (PVIF kd, n)
Bond value = PV of coupons + PV of MV
Bond value = PV annuity + PV of lump sum
V = CP (PVIFA kd, n) + MV (PVIF kd, n)

15. Bond valuation V = CP (PVIFA kd, n) + MV (PVIF kd, n)
A bond has a $1,000 face value and provides an 8% annual coupon for 30 years. The appropriate discount rate is 10%. What is the value of the bond?
V = CP (PVIFA kd, n) + MV (PVIF kd, n)

16. Bond valuation V = CP (PVIFA 10%, 30) + MV (PVIF 10%, 30)
A bond has a $ 1,000 face value and provides an 8% annual coupon for 30 years. The appropriate discount rate is 10%. What is the value of the bond?
V = CP (PVIFA 10%, 30) + MV (PVIF 10%, 30)
= $80 (9.427) + $1,000 (0.057)
= $
= $811.16

17. Sample problem #1 V = CP (PVIFA 6%, 20) + MV (PVIF 6%, 20)
A bond has a $ 1,000 face value and provides a 6% annual coupon for 20 years. The appropriate discount rate is 6%. What is the value of the bond?
V = CP (PVIFA 6%, 20) + MV (PVIF 6%, 20)
= $60 ( ) + $1,000 (0.3118)
= $
= $999.99

18. Sample problem #2 V = CP (PVIFA 10%, 10) + MV (PVIF 10%, 10)
A bond has a $ 1,000 face value and provides a 6% annual coupon for 10 years. The appropriate discount rate is 10%. What is the value of the bond?
V = CP (PVIFA 10%, 10) + MV (PVIF 10%, 10)
= $60 (6.1446) + $1,000 (0.3855)
= $
= $754.18

19. Semi-annual compounding
Most bonds pay coupon payments twice a year.
They pay ½ of the annual coupon payments.
Adjustments needed for semi-annual compounding:
(1) Divide kd by 2
(2) Multiply n by 2
(3) Divide CP by 2

20. Semi-annual compounding
A non-zero coupon bond adjusted for semi-annual compounding:
V = CP/2 (PVIFA kd/2, n*2) + MV (PVIF kd/2, n*2)

21. Sample problem #1 = $40 (15.3725) + $1,000 (0.2314) = $614.90 + 231.40
A bond has a $ 1,000 face value and provides an 8% semi-annual coupon for 15 years. The appropriate discount rate is 10% (annual rate). What is the value of the coupon bond?
V = CP/2 (PVIFA 10%/2, 15*2) + MV (PVIF 10%/2, 15*2)
= $40 ( ) + $1,000 (0.2314)
= $
= $846.30

22. Sample problem #2 = $30 (19.6004) + $1,000 (0.4120) = $588.01 + 412.00
A bond has a $ 1,000 face value and provides a 6% semi-annual coupon for 15 years. The appropriate discount rate is 6% (annual rate). What is the value of the coupon bond?
V = CP/2 (PVIFA 6%/2, 15*2) + MV (PVIF 6%/2, 15*2)
= $30 ( ) + $1,000 (0.4120)
= $
= $1,000.01

23. Zero-coupon bond valuation
A zero-coupon bond is a bond that pays no interest but sells at a deep discount from its face value.
V = MV (PVIF kd, n)

24. Zero-coupon bond example
A bond has a $1,000 face value and a 30-year life. The appropriate discount rate is 10%. What is the value of the zero-coupon bond?
V = MV (PVIF kd, n)

25. Zero-coupon bond example
A bond has a $1,000 face value and a 30-year life. The appropriate discount rate is 10%. What is the value of the zero-coupon bond?
V = MV (PVIF 10%, 30)
= $1,000 (0.057)
= $57.00

26. Zero-coupon bond example #2
A bond has a $1,000 face value and a 30-year life. The appropriate discount rate is 6%. What is the value of the zero-coupon bond?
V = MV (PVIF 6%, 30)
= $1,000 (0.1741)
= $174.10

27. Zero-coupon bond example #3
A bond has a $1,000 face value and a 10-year life. The appropriate discount rate is 6%. What is the value of the zero-coupon bond?
V = MV (PVIF 6%, 10)
= $1,000 (0.5584)
= $558.40

28. Perpetual bond valuation
A perpetual bond is a bond that never matures. It has an infinite life.
V = CP / kd

29. 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

30. 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?
CP = $1,000 * (8%) = $80
kd = 10% = 0.10
V = CP / kd
= $80 / 0.10
= $800

31. 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 the value of the perpetual bond?
CP = $1,000 * (6%) = $60
kd = 20% = 0.20
V = CP / kd
= $60 / 0.20
= $300

32. 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 the value of the perpetual bond?
CP = $1,000 * (5%) = $50
kd = 8% = 0.08
V = CP / kd
= $50 / 0.08
= $625

33. Yield to maturity (YTM)
The yield to maturity (YTM) of a bond is the discount rate which returns the market price of the bond.
YTM is often used to price a bond.
Bond prices are often quoted in terms of YTM.

34. YTM calculations
You want to determine the YTM for an issue of outstanding bonds at your firm.
Your firm has an issue of 10% annual coupon bonds with 15 years left to maturity.
The bonds have a current market value of $1,250.
What is the YTM?

35. YTM solution (9%) $1,250 = $100 (PVIFA 9%, 15) + $1,000 (PVIF 9%, 15)
$1,250 = $100 (8.061) +
$1,000 (.275)
$1,250 = $ $275.00
= $1,081.10
[Rate is too high]

36. YTM solution (7%) $1,250 = $100 (PVIFA 7%, 15) + $1,000 (PVIF 7%, 15)
$1,250 = $100 (9.108) +
$1,000 (.362)
$1,250 = $ $362.00
= $1,272.80
[Rate is too low]

37. YTM solution (interpolate)
.07 $1,273
.02 IRR $1, $192
.09 $1,081
X $ $192
$23 X =

38. YTM solution (interpolate)
.07 $1,273
.02 IRR $1, $192
.09 $1,081
X $ $192
$23 X =

39. YTM solution (interpolate)
.07 $1,273
.02 YTM $1, $192
.09 $1,081
($23)(0.02) $192
$23 X
X =
X = .0024
YTM = = or 7.24%

40. YTM problem #1
Your firm has an issue of 8% annual coupon bonds with 10 years left to maturity.
The bonds have a current market value of $1,100.
What is the YTM?

41. YTM problem #2
Your firm has an issue of 9% annual coupon bonds with 12 years left to maturity.
The bonds have a current market value of $1,310.
What is the YTM?

42. Premium vs. discount bond
A bond selling for more than its face value is called a premium bond.
A bond selling for less than its face value is called a discount bond.

43. Current vs. coupon yield
The current yield is the coupon payment (CP) as a percentage of the current bond price (P0).
Current yield = CP / P0
The coupon yield of a bond is the stated rate of interest.
Annual coupon payments (CP)
Coupon yield =
Maturity value (MV)

44. YTM, current & coupon yield
When a bond sells at a discount
YTM > current yield > coupon yield
When a bond sells at a premium
Coupon yield > current yield > YTM
When a bond sells at par
YTM = current yield = coupon yield

45. The Bangladeshi bond market
Bangladesh’s bond market is TINY.
It accounts for only 12% of the GDP.
In South Asian countries, bonds account for an average of 34% of the GDP.
In USA, the bond market accounts for 21% of the GDP, in Korea 29%, in Japan 16% and for select OECD countries 16%.

46. The Bangladeshi bond market
The bond market is dominated by short and long term government securities.
The Bangladesh Bank sells 28-day, 91-day, 182-day and 364-day treasury bills and five, ten, fifteen and twenty year treasury bonds.
The central bank holds auctions every week and any investor can bid for bonds through any bank.

47. The Bangladeshi bond market
An auction committee fixes the coupon rate which is applicable throughout the instrument’s 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.

48. The Bangladeshi bond market
There is a secondary bond market; however, the trading activity is very limited.
Government paper has been traded since 2005.
Corporate bonds are far and few in between.

49. The Bangladeshi bond market
The corporate bond market is highly under-developed and has only nine bonds.
All corporate bonds are issued through private placement.
Notable corporate bonds include the Islamic Bank Bangladesh Limited (IBBL) Mudaraba Perpetual bond. <- Perpetual bond

50. The Bangladeshi bond market
Grameenphone issued 540-day and 720-day bonds worth US $62 million via Citi. (coupon: 14.5%) <- Fixed rate bond
Bangladesh Petroleum (BPC) closed a US $250 million 360-day facility via Standard Chartered. (coupon: LIBOR b.p.). <- Floating rate bond