Lecture on bond www.AssignmentPoint.com

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. www.AssignmentPoint.com

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). www.AssignmentPoint.com

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) www.AssignmentPoint.com

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. www.AssignmentPoint.com

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 www.AssignmentPoint.com

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. www.AssignmentPoint.com

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. www.AssignmentPoint.com

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% www.AssignmentPoint.com

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% www.AssignmentPoint.com

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% www.AssignmentPoint.com

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. www.AssignmentPoint.com

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. www.AssignmentPoint.com

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) www.AssignmentPoint.com

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) www.AssignmentPoint.com

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) = $754.16 + 57.00 = $811.16 www.AssignmentPoint.com

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 (11.4699) + $1,000 (0.3118) = $688.19 + 311.80 = $999.99 www.AssignmentPoint.com

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) = $368.68 + 385.50 = $754.18 www.AssignmentPoint.com

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 www.AssignmentPoint.com

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) www.AssignmentPoint.com

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 (15.3725) + $1,000 (0.2314) = $614.90 + 231.40 = $846.30 www.AssignmentPoint.com

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 (19.6004) + $1,000 (0.4120) = $588.01 + 412.00 = $1,000.01 www.AssignmentPoint.com

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) www.AssignmentPoint.com

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) www.AssignmentPoint.com

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 www.AssignmentPoint.com

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 www.AssignmentPoint.com

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 www.AssignmentPoint.com

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

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 www.AssignmentPoint.com

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 www.AssignmentPoint.com

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 www.AssignmentPoint.com

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 www.AssignmentPoint.com

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. www.AssignmentPoint.com

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? www.AssignmentPoint.com

YTM 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] www.AssignmentPoint.com

YTM 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] www.AssignmentPoint.com

YTM solution (interpolate) .07 $1,273 .02 IRR $1,250 $192 .09 $1,081 X $23 .02 $192 $23 X = www.AssignmentPoint.com

YTM solution (interpolate) .07 $1,273 .02 IRR $1,250 $192 .09 $1,081 X $23 .02 $192 $23 X = www.AssignmentPoint.com

YTM solution (interpolate) .07 $1,273 .02 YTM $1,250 $192 .09 $1,081 ($23)(0.02) $192 $23 X X = X = .0024 YTM = .07 + .0024 = .0724 or 7.24% www.AssignmentPoint.com

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? www.AssignmentPoint.com

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? www.AssignmentPoint.com

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. www.AssignmentPoint.com

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) www.AssignmentPoint.com

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 www.AssignmentPoint.com

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%. www.AssignmentPoint.com

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. www.AssignmentPoint.com

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. www.AssignmentPoint.com

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. www.AssignmentPoint.com

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 www.AssignmentPoint.com

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 + 160 b.p.). <- Floating rate bond www.AssignmentPoint.com