Finance Final Exam

• Bond


  A long-term debt instrument in which a borrower agrees to make payments of principal and interest, on specific dates, to the holders of the bond
• Bond


  • Par value - face amount of the bond, which is paid at maturity
  • Coupon interest rate - stated interest rate (generally fixed) paid by the issuer
  • Maturity date - years until the bond must be repaid
  • Issue date - when the bond was issued
  • Yield to maturity - rate of return earned on a bond held until maturity
• Bond markets


  Primarily traded in the over-the-counter (OTC) market<|>Most bonds are owned by and traded among large financial institutions<|>The Wall Street Journal reports key developments in the Treasury, corporate, and municipal markets
• Call provision


  Allows issuer to refund the bond issue if rates decline (helps the issuer, but hurts the investor)<|>Borrowers are willing to pay more, and lenders require more, for callable bonds<|>Most bonds have a deferred call and a declining call premium
• Sinking fund


  Provision to pay off a loan over its life rather than all at maturity<|>Similar to amortization on a term loan<|>Reduces risk to investor, shortens average maturity<|>Not good for investors if rates decline after issuance
• How sinking funds are executed

  1. Call x% of the issue at par, for sinking fund purposes

  2. Buy bonds in the open market
• Convertible bond


  May be exchanged for common stock of the firm, at the holder's option
• Warrant


  Long-term option to buy a stated number of shares of common stock at a specified price
• Putable bond


  Allows holder to sell the bond back to the company prior to maturity
• Income bond


  Pays interest only when interest is earned by the firm
• Indexed bond


  Interest rate paid is based upon the rate of inflation
• Opportunity cost of debt capital

  The discount rate (ri) is the opportunity cost of capital, and is the rate that could be earned on alternative investments of equal risk
• Valuing a 10-year, 10% annual coupon bond with rd = 10%


  PV = $90.91 + $38.55 + ... + $1,000 / (1.10)^10
• Using a financial calculator to value a bond

  N=10, I/YR=10, PMT=100, PV=-1000, FV=1000
• Valuing a 10-year, 13% annual coupon bond with rd = 10%


  PV = $130 * (1 - (1+10%)^-10) / 10% + $1,000 / (1+10%)^10
• Valuing a 10-year, 7% annual coupon bond with rd = 10%


  PV = $70 * (1 - (1+10%)^-10) / 10% + $1,000 / (1+10%)^10
• At maturity, the value of any bond must equal its par value
• If rd remains constant: the value of a premium bond would decrease over time, the value of a discount bond would increase over time, and the value of a par bond stays at $1,000
• Finding the YTM on a 10-year, 9% annual coupon, $1,000 par value bond, selling for $887

  PV = $90 * (1 - (1+rd)^-10) / rd + $1,000 / (1+rd)^10 = $887
• Using a financial calculator to solve for the YTM

  N=10, I/YR=10.91, PMT=90, PV=-887, FV=1000
• Finding the YTM if the bond price is $1,134.20

  N=10, I/YR=7.08, PMT=90, PV=-1134.2, FV=1000
• Current yield (CY)


  Annual coupon payment / Beginning price
• Capital gains yield (CGY)


  Expected change in price / Beginning price
• Expected total return


  Current yield + Capital gains yield
• Interest rate risk is the concern that rising rd will cause the value of a bond to fall
• A 10-year bond has more interest rate risk than a 1-year bond


  The 10-year bond is more sensitive to interest rate changes
• CGY


  Change in price
• Capital


  Price
• Current yield (CY)


  Annual coupon payment
• Current yield


  10.15%
• An Example


  • Current and Capital Gains Yield
• Find the current yield and the capital gains yield

  For a 10-year, 9% annual coupon bond that sells for $887, and has a face value of $1,000
• Capital gains yield


  0.76%
• YTM


  Current yield + Capital gains yield
• Interest rate (or price) risk


  The concern that rising rd will cause the value of a bond to fall
• 1. year bond


  Has less interest rate risk than a 10-year bond
• 10-year bond


  Is more sensitive to interest rate changes, and hence has more interest rate risk
• Reinvestment rate risk


  The concern that rd will fall, and future CFs will have to be reinvested at lower rates, hence reducing income
• Reinvestment Rate Risk Example

  • Investing $500,000 in either a 10-year bond or a series of ten 1-year bonds, both currently yielding 10%
• Nothing is riskless!