1. BBA, MBA(Finance), London, UK
Topic # 07
Bond Valuation
Zulfiqar Hasan
BBA, MBA(Finance), London, UK
Associate Professor

2. Contents
Bonds-its definition and types, Value a straight bond and a zero-coupon bond using present discounted value techniques; relationship between interest rates and bond prices; Determine the yield to maturity for a straight bond; relationships between zero coupon bonds and coupon bonds; Analyze bond price dynamics and predict how bond prices respond to changes in interest rates; Explain why coupon bonds and zero coupon bonds react differently to changes in interest rates; Explain the relationship between real and nominal interest rates
Zulfiqar Hasan

3. How does corporation raise capital?
Corporations raise capital in two Forms:
Debt: A type of Financing through the selling of a debt instrument is called Debt Financing.
Equity: Raising money for company activities by selling common or preferred stock to individual or institutional investors. No
Yes
Liquidation will result if not paid
Provides a tax Shield/Deduction
Grants ownership of the firm
Repayment is an obligation of the firm
EQUITY
FINANCING
DEBT
Issues
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4. Definition of Bond
In finance, a bond is a debt security, in which the authorized issuer owes the holders a debt and, depending on the terms of the bond, is obliged to pay interest (the coupon) and/or to repay the principal at a later date, termed maturity. A bond is a formal contract to repay borrowed money with interest at fixed intervals.
Bonds are long-term debt instruments sold by a company or government to raise money. It is a long-term promissory note.
A Bond is an instrument which pays fixed amounts (usually) of interest (called a coupon) on a regular basis, over its life and is redeemed at par value (usually) at maturity, by the issuer .
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5. Basics Terms of Bond/ Features of Bonds
Bond Valuation/FM
Basics Terms of Bond/ Features of Bonds
Par or Face Value: The par or face value of a bond is the amount of money that is paid to the bondholders at maturity.
Coupon Interest Rates: The stated annual rate of interest paid on a bond.
Coupon Payment: The coupon payments represent the periodic interest payments from the bond issuer to the bondholder.
Maturity Date: The maturity date represents the date on which the bond matures, i.e. the date on which the face value is repaid. The last coupon payment is also paid on the maturity date.
Original Maturity: The time remaining until the maturity date when the bond was issued.
Call Provision: A provision in a bond contract that gives the issuer the right to “recall” the bond and pay it off under specified terms prior to the stated maturity date.
Indenture: A legal document contains the details of the bond issue called the indenture.
Zulfiqar Hasan
Kazi Zulfiqar Hasan, Assistant Professor

6. 1.0 Classification of Bonds: By Issuer
Classifications of Bonds
1.0 Classification of Bonds: By Issuer
Government: Government issued treasury bond
Corporation: industrial, utility, financial, transportation
Foreign Bond: e.g. foreign government, foreign corporation, World Bank
2.0 Classification of Bonds: By security
Unsecured Bonds - backed by faith in the taxing power of the government, or the good name of the company (debenture)
Secured Bonds e.g. revenue bond, assessment bond, mortgage, collateral trust bond, equipment trust certificate
Bond security sometimes comes from non-traditional sources. Some rock stars floated bonds using their future earnings as backing.
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7. 3.0 Classification of Bonds: By Term
a. short-term ( a year) e.g. US Treasury bills
b. intermediate-term e.g. US Treasury notes
(2 to 10 years )
c. long-term e.g. US Treasury bonds ( 10 years)
d. open-ended e.g. corporate line of credit
e. serial bond - a portfolio of bonds with
staggered terms
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8. Bond Valuation Formula
Bond Valuation/FM
Bond Valuation Formula Or
Vd = Bond Value/Present Value of the Bond/ Current Price of the Bond
i = Kd = r =The average rate of return
n = The number of years before the bond matures.
INT=Amount of interest paid each year (Coupon payment) = Coupon rate X Par value
M = The par or face value of the bond.
NB: Some books use PMT or Cr instead of INT.
Zulfiqar Hasan
Kazi Zulfiqar Hasan, Assistant Professor

9. Problem 01: Bond price or Current Value
A bond has a coupon interest rate of 10% per year, a $1,000 par value, and 3 years remaining until maturity. The market rate of interest for this bond is 9%. If interest is paid annually, what is the current value of the bond?
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10. Problem 02: Multiple Compounding
A bond has a coupon interest rate of 10% per year, a $1,000 par value, and 3 years remaining until maturity. The market rate of interest for this bond is 8%. If interest is paid semi-annually, what is the current value & yield of the bond?
$1,052.41
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11. Practice 01
n = Your Age
What’s the value of a 10-year, 10% coupon bond if i = 10% and Face value is $1000?
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12. a. How much should you be willing to pay for the bonds?
Practice 01
You have a chance to buy a BB-rated bond that has a face value of $1,000. The bond has a 5% coupon rate of interest and matures in four years. Interest is paid semi-annually. The market rate of interest is currently 6% per year for similar bonds.
a. How much should you be willing to pay for the bonds?
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13. Practice 02: Current Value of Bond
A bond has a coupon interest rate of 10% per year, a $1,000 par value, and 2 years remaining until maturity. The market rate of interest for this bond is 9%. If interest is paid annually, what is the current value of the bond? $
Practice 03: Current Value of Bond
Complex Systems has an outstanding issue of $1000 par value bond with a 12% coupon interest rate. The issue pays interest annually and has 16 years remaining to its maturity date. If bonds of similar risk are currently earning a 10% rate of return, how much should the Complex System bond sell for today?
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14. Current Yield
It is the annual interest payment on a bond divided by its current market value.
Example: A bond has a coupon interest rate of 10% per year, a $1,000 par value, and 3 years remaining until maturity. The market rate of interest for this bond is 9%. If interest is paid annually, what is the current Yield of the bond?
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15. Yield to Maturity (YTM/Kd/IRR)
It is the average rate of return earned on a bond if it is held to maturity. The rate of return anticipated on a bond if it is held until the maturity date. YTM is considered a long-term bond yield expressed as an annual rate. The calculation of YTM takes into account the current market price, par value, coupon interest rate and time to maturity. It is also assumed that all coupons are reinvested at the same rate. Sometimes this is simply referred to as "yield" for short.
An approximate YTM can be found by using a bond yield table. However, because calculating a bond's YTM is complex and involves trial and error, it is usually done by using a programmable business calculator.
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16. Finding the YTM YTM at $829 is 15%
YTM 01: A bond has a coupon interest rate of 15% per year, a $1,000 par value, and 14 years remaining until maturity. The current value of this bond is $ What is the approximate YTM of the bond?
YTM 02: The Seven Company’s bonds have four years remaining to maturity. Interest is paid annually, the bonds have a $1000 par value, and the coupon interest rate is 9 percent.
Compute the Approximate yield to maturity for the bonds if the current market price is either $829 or $1104.
YTM at $829 is 15%
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17. Selling at Discount, Premium or Par Value
Practice: Lahey Industries has outstanding a $1000 par value bond with an 8% coupon interest rate. The bond has 12 years remaining to its maturity date.
If interest is paid annually, find the value of the bond when the required return is 7%, 8% and 10%.
Indicate for each case in part a whether the bond is selling at a discount, at a premium, or at its par value.
Using the 10% required return, find the bond’s value when interest is paid semiannually.
Result
$ , $1000, $863.73
Sells at premium, par value, Discount
$862.01
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18. Bond Duration
Duration is the average time to maturity of the bond i.e. the average time after which the cash flows on the bond will be received.
A bond with a YTM of 8% and a 10% coupon to be redeemed at par after 3 years.
Present value:
PV= 10/ (1.08) / (1.08) / (1.08) 3 =
Duration: 9.26 x x x 3
105.13
= years
Duration 02: A bond with a YTM of 10% and a 10% coupon to be redeemed at par ($100) after 3 years. Find out the duration of this bond.
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19. Factors that Affect Bond Prices Over Time
Factors that Affect the Risk-Free Rate
The Central Bank’s monetary policy
Impact of inflation
Impact of economic growth
Factors that Affect the Default Risk Premium:
Change in economic conditions
Change in a firm’s financial conditions
Bond Market Indicators
Indicators of inflation
Indicators of economic growth
Indicators of a firm’s financial condition
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20. Bond Investment Strategies
A passive strategy is a strategy in which investors establish a diversified portfolio of bonds and maintain the portfolio for a long period of time.
A matching strategy is a strategy in which investors estimate future cash outflows and choose bonds whose coupon or principal payments will cover the projected cash outflows.
A laddered strategy is a strategy in which investors evenly allocate funds invested in bonds in each of several different maturity classes to minimize interest rate sensitivity.
A barbell strategy is a strategy in which investors allocate funds into bonds with short-term and long-term, but few or no intermediate-term maturities.
An interest rate strategy is a strategy in which investors allocate funds to capitalize on interest rate forecasts and revise their portfolio in response to changes in interest rate expectations.
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21. Terms of Repayment on Bond
Interest Only: the periodic payments are entirely interest
Sinking Fund: periodically, a portion of the debt principal is set aside or certain number of the bonds is retired
Balloon Loan: the debt may be partially amortized with each payment
Income Bond: interest is payable only if it is earned
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22. Bond Principles: Bond Cash Flows
Annuities: most bonds are annuities plus an ultimate repayment of principal
Zero Coupon: only the par value is returned at maturity
Variable (Adjustable) Rate: the rate fluctuates in accordance with some market index or predetermined schedule
Consols: a level rate of interest is paid perpetually
Inflation-indexed Treasury Bonds: the principal value is adjusted based on the consumer price index
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23. Exchangeable Bond : may be exchanged for shares in another firm
Bond Options
Convertible Bond : may be exchanged for common stock in the company that issued the bond
Exchangeable Bond : may be exchanged for shares in another firm
Bond Registration
Bearer (Coupon) Bonds - belong to whomever legally hold them; no longer issued in the United States because of tax considerations
Registered Bonds : the bonds show the bondholder’s name
Book Entry Bonds : bond ownership is reflected only in the accounting records
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24. Bond Risks: Price Risks Bond Risks: Convenience Risks
default risk - the possibility that the issue of the bond is unable to pay; rated by agencies like Moody’s and Standard & Poor’s
interest rate risk - the chance of loss due to changing interest rates
Bond Risks: Convenience Risks
call risk: the possibility that the company will exercise a bond’s call feature
reinvestment rate risk: the chance that the interest received cannot be reinvested to earn as much as the bond’s original yield to maturity. The higher the coupon on a bond, the higher its reinvestment rate risk
marketability risk: The difficulty of selling a bond in the secondary market
Zulfiqar Hasan