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Bond Valuation
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Bond Valuation

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  • 1. Bond Valuation Harish Narula Rajesh Bangera Shiva Pillai
  • 2. Contents
    • Bond Fundamentals
    • Bond Terminologies
    • Characteristics of Bond Prices
    • Basics of Bond Valuation
    • Yield to Maturity
    • YTM and Coupon Rates
    • Durations
    • Risks Bondholders face
    • Inflation & Interest Rate
    • Valuation of a Bond
    • Treasury STRIPS
    Rajesh Bangera Harish Narula Shiva Pillai
  • 3. Bond Fundamentals
    • What is a bond?
      • Loans to corporations and governments
      • Borrowers get cash; lenders earn interest
    • Different Issuers
      • Government, Municipal, Corporations
    • Different Maturities
      • Short Term, Long Term
    • Different Styles
      • Coupon bonds, Zero Coupon bonds
  • 4. Bond Terminologies
    • Par Value = The payment at maturity that is not part of a regular coupon payment
    • Indenture = It’s a Legal Stuff. Basically a written Agreement between the Entity & Bond holder.
    • Covenants = They are clauses of such an Indenture. Covenants specify the rights of bondholders and the duties of issuers, such as actions that the issuer is obligated to perform or is prohibited from performing
    • Discount Bond = A bond that promises a single payment at a future date.
    • Level Coupon Bond = A bond that pays equal coupon payments periodically prior to bond maturity. Bonds typically pay coupons semi-annually.
  • 5. Bond Terminologies
    • Coupon Rate = Annual Coupon Payment / Par Value
        • Note: A coupon rate of 8% on a $1,000 par value bond paying semi-annual coupons implies semi-annual coupons of $40
          • Coupon Payment = .08*$1000/2 = $40
    • Yield to Maturity = Its an important number in bond valuation
  • 6. Characteristics of Bond Prices
    • The cash flows on a bond are constant (“fixed income”)
    • A bond’s market price changes in response to the market interest rate.
      • When market rates increase, the fixed payments from the bond are worth less so the price falls.
      • If rates decrease, the fixed payments are now worth more.
  • 7. Basics of Bond Valuation
    • The bond pricing equation consists of two components
      • PV of Coupons
      • PV of Face Value
    • Th e price of a bond (these PVs) depends on:
      • Discount Rate (r)
      • Number of Periods (N)
      • Size of Cash Flows (C and P N )
  • 8. Yield To Maturity
    • The yield to maturity is an important number in bond valuation
    • It is the rate which equates the market price of the bond with the value of the discounted cash flows
    • That is, YTM is the r such that the bond equation holds
    • Finding the YTM requires a financial calculator, a goal-seeking solver, or trial and error
  • 9. YTM and the Coupon Rate
    • Relationship between YTM and Coupon Rate
      • YTM = Coupon  bond is selling at par (P 0 = P N ).
      • YTM > Coupon  bond is at a discount (P 0 < P N ).
      • YTM < Coupon  bond is at a premium (P 0 > P N ).
    • Why does the YTM differ from the coupon?
      • The coupon is set when the bond is issued.
      • The YTM is the market’s required interest rate. It may change as economic fundamentals shift.
  • 10. Duration
    • As we have seen, bonds have value from two sources: coupons and return of principal
    • Intuitively, bonds with high coupon rates or short maturities will return value more quickly than those with low coupons or long maturities
    • At the extreme is a zero coupon bond, which returns all value at maturity.
    • Duration is a measure of how quickly the (present) value of a bond is returned.
  • 11. Duration (cont…)
    • To calculate duration:
      • Find the present value of each cash flow individually
      • Sum these to get the present value of all cash flows (price)
      • Calculate the proportion of the total value from each individual cash flow
      • Multiply each proportion by the corresponding number of periods and sum
    • The answer will give a measure of the average life of the bond in a present value sense
    • Bonds with a low duration gets most of its value from cash flows occurring early
  • 12. Types of Risk Bondholders face
    • Interest Rate Risk
      • The risk of a bond changing in value when interest rates change. This affects all bonds regardless of credit quality, but is more severe for longer maturity bonds
    • Reinvestment Risk
      • The risk that investors will be unable to reinvest the coupon payments at the coupon rate. This is more important for high coupon bonds
    • Default (Credit) Risk
      • The risk that the firm will go bankrupt and not make all payments to bondholders
  • 13. Inflation & Interest Rates
    • Inflation is the increase in the nominal (or cash) cost of goods and services over time
    • Put differently, it is the decrease in purchasing power over time
    • In the end, we are generally concerned with consumption in finance (and in life). The amount of dollars you have is really much less important than their purchasing power
    • Nominal rates are the rates observed in the market and quoted in contracts
    • Real rates are actually very illusive since measuring inflation accurately is difficult.
  • 14. in MS Excel
    • PV & YTM in excel
    • Yield Curve
    • Duration
    • Excel Spreadsheet
  • 15. Treasury STRIPS
    • S eparate
    • T rading of
    • R egistered
    • I nterest and
    • P rincipal
    • S ecurities
  • 16.
    • Thank You