Essay About Bond Maturity And Bond Valuation Reviewbond Terminologya Bond

Bonds and Bond Valuation Review
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Bonds and Bond Valuation ReviewBond TerminologyA bond is a debt instrument that is commonly traded in financial markets.  The borrower agrees to pay scheduled cash flows (i.e., coupon payments) to the bondholder during the life (or term) of the bond and then a lump sum payment equal to the face (or par) value of the bond when it matures.  The contract that specifies the cash flows and their timing is called the bond “indenture”.  Prospective bond investors evaluate the financial health of the issuer, the size and timing of the cash flows and determine a price that reflects the present value of those cash flows.Bond Pricing Formula[pic 1]Face (Par) – Cash flow paid at bond maturity.$CPN – (Coupon Rate* Face Value)/kCoupon rate – (annual coupon)/(face value)k – Number of coupon payments per yearMaturity – Number of years until the face value is paid.t – Maturity * kytm – rate (APR) that makes the promised cash flows equal to the bond’s price.Assumes reinvestment at the YTM;Holding the bond until maturity;The probability of call is zero;The probability of default is zero.ExamplesUnless otherwise stated, we will always assume that the face or par value of a bond is $1,000 and that all bond cash flows occur semi-annually with semi-annual compounding.1.  Calculate the price of a semi-annual coupon bond with a coupon rate of 7.5%, 9.5 years to maturity and a yield to maturity of 8.5%.Semi-annual Coupon = $1000*7.5%*0.5 = $37.50Number of Periods = 9.5*2 = 19Face Value of Bond = $1,000.00Yield to Maturity = 8.5% (annual) or 4.25% (semi-annual)Price = (37.50/0.0425)[1 – (1/(1+0.0425)^19)] + $1,000/((1+0.0425)^19)         = $482.22661 + $453.47650Price = $935.70312 or it will be quoted as 93.5703122.  Calculate the yield to maturity on a bond that is selling for $1045.12 has a coupon rate of 5.25% and matures in 7 years.$1045.12 = [(.0525/2)*$1,000][1 – (1/(1 + YTM/2)^14)]YTM = 4.49164%Bond Price Quotation RulesUS Treasury bills – quoted at a discount from face value, with the discount expressed as an annual rate based on a 360 day year.US Government bonds – quoted as a percent of par. Trade on 32’nds.Corporate bonds – quoted as a percent of par.  Trade on 16ths.Investors sell at the bid price and buy at the ask (or offered) price.T-Bill Example:IssueBidAskChangeYield12/3/155.085.06-0.035.26 [pic 2]Assume Face value: $10,000 and 169 days until maturity$9,761.46 = $10,000 – $10,000((0.0508*169)/360)9,762.46 = $10,000 – $10,000((0.0506*169)/360)Treasury Bond Example:Note that the dealer buys at the Bid price and sells at the Ask price.MaturityBidAskChangeYield6 ½, 8/15/19105.0812+35.57Before considering the bond price table above, keep two things in mind:Bond prices are quoted as a percent of par andTreasury bonds trade in 32s.So, the bid price means that the dealer is willing to pay 105 plus 8/32 percent of par for the bond issued on 8/15/11 that’s offering a coupon of 6.5%.  How do we convert that into a price?Bond’s face value*(1.05 + (8/32)*(1/100))$1,000*(1.05+0.0025) = $1,052.50 = Bid PriceSo, what’s the dealer’s Ask Price? The 12 indicates that the dealer will sell the bond for 105 + 12/32 of par.  So,$1,000*(1.05+(12/32)*(1/100)) = $1,053.75 = Ask PriceExample: Calculating the realized return. What happens if you sell a bond before it matures? 3. You purchased US government 5-1/2’s of 09/15/16 at a price of 94.15 on 09/15/05.  You sell the bond today at its current bid price of 100.22.  (Assume today is 09/15/11).  Calculate your realized annualized return. How does this realized return compare with your required return at the time you purchased the bond?Coupon rate = 5.5% annual or 2.75% semi-annualCoupon Payment = $27.50 (semi-annual)Bond Price at Purchase = $941.50Face Value of Bond = $1,000Original Maturity of Bond = 11 yearsBond Price at Sale = $1002.20Time till Sale = 6 yearsYTM at Purchase = 6.243.11%Realized Return = 6.73158%Bond TypesTreasury Bill – maturity of less than a yearTreasury Note – maturity from 1 -10 yearsTreasury Bond – maturity from 10-30 yearsCorporate Bond – a bond issued by a corporationCallable Bond – a bond that can be purchased by issuer.Convertible Bond – the bondholder can exchange the bond for a set number of equity shares.Puttable Bond – the bondholder has the option to force the issuer to buy back the bond.Call options and bondsThe vast of majority of bonds with a maturity of 10 years or greater include a call option in the indenture.The call option gives the issuer the right the repurchase the bond at a pre-specified price after a stated number of periods (i.e., the “lockout period”).Is the Call option free?  Who pays for the option and how do they pay?4. Suppose you bought a 12% coupon Treasury bond with a term to maturity of exactly 10 years for $1,283.59.  The government has the right to call at $1,100 in five years.  What is the yield to call?