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BONDS and BOND VALUATION (Students)Interest Rates or YieldsBasis Point:Prices:Treasury Securities(Bonds & Notes)Notes have a maturity of 1 yr10 yrs, Bonds have a maturity of 10 yrs30 yrs.Each point in price are divided into 32nd’s or 64th’s instead of 8ths or tenths.This implies that a quote in the WSJ of 90:05 means …Likewise, 85:31 = 85 31/32 = $859.69 on 1000 Par.So,prices proceed as follows: 89:31, 90:00,90:01, 90:02, 90:03…90:29, 90:30, 90:31, 91:00, etc.RateMaturityMo/YrBidAskedChgAskedYield1 5/8Feb 06 n99:3099:31+13.221 1/2Mar 06 n99:2299:23+14.182 1/4Apr 06 n99:1799:18....4.482May 06 n99:1399:14+14.454 5/8May 06 n100:00100:01....4.436 7/8May 06 n100:16100:17-14.382 1/2May 06 n99:1399:14+14.512 3/4Jun 06 n99:1199:12+14.5Corporate Bonds:Prices are quoted in fractions of a point in 1000th’s of a pointeg.98.203, 105.685, etc. and are based on a par of 1000, so these would be priced at$982.03 and $1056.85.Bonds Features1)Coupon Rate–1
The coupon rate quoted as a percent of par or face value, i.e., 5% of $1000 is $50per year and if paid semiannually would be two $25 payments per year, every 6months.2)Par or Face Value–3)Maturity–4)Yield to Maturity–5)Price or Present Value of a BondNote that the bond price consists of a Present Value of an Annuity and the PV of alump sumTherefore, for a constantannualcoupon bondwe have:)nyrsr%,FV(PVIF)nyrsr%,FACoupon(PVIPriceIn terms of the pricing equation, we have:icePrFor a Zero Coupon Bond:icePrExamples of Equations:10 year bond with 5% coupon and 7% ytm.2
Semiannual Interest Payments:as indicated above most bonds have semiannualcoupons, so now we receive 2 payments per year which implies that the discounting &compounding twice in one year.PriceRecall that the coupon payments of a bond are simply an annuity, so to find the price wefind the present value of the annuity and then the present value of the lump sum Par value:PriceThe Yield to Maturityassumes the following:1)The Investor will hold the bond until maturity.2)All intermediate cash flows will be reinvested at the same rate as the YTM.Note:YTM’s are market rates of interest determined by the supply and demand forloanable funds.Accrued Interest:Bonds are sold on an accrued interest basis and the current bond pricedoes not reflect that interest.For example, assume a bond with a 10% semiannual couponthat is paid in June and December sells in for $935 in March.Whoever buys the bond inMarch will receive the 50 dollar payment in June, but the previous owner of the bond isentitled to the interest earned from January through March.Therefore, at the settlementthe purchaser must pay the previous owner $25.Bond Prices & Interest RatesBond prices rarely sell at their Par or Face Value, and do so usually only at issue.Theysell at a Premium or Discount depending on market interest rates and the relationshipbetween the coupon, the YTM, the par and the price.