Chapter 5 - Topics CoveredBondsSlide 3Bond PricingSlide 5Bond Cash FlowsSlide 7Slide 8Slide 9Slide 10Slide 11Bond YieldsSlide 13Slide 14Slide 15Slide 16Bond Valuation SpreadsheetBond Yield SpreadsheetInterest Rate RiskSlide 20Nominal and Real ratesDefault RiskSlide 23Corporate BondsThe Yield CurveCopyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin5- 1Chapter 5 - Topics CoveredBond Characteristicsreading the financial pagesInterest Rates and Bond PricesCurrent Yield and Yield to MaturityBond Rates and ReturnsCorporate Bonds and the Risk of DefaultThe Yield CurveCopyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin5- 2BondsTerminologyBond – Legal Agreement that obligates the issuer to make specified payments to the bondholder.Coupon - The interest payments made to the bondholder (usually due every six months).Face Value (Par Value or Principal Value) - Payment at the maturity of the bond (usually $1,000).Coupon Rate - Annual interest payment, as a percentage of face value.Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin5- 3BondsWARNINGWARNINGThe coupon rate IS NOT the discount rate used in the Present Value calculations. The coupon rate merely tells us what cash flow the bond will produce. Since the coupon rate is listed as a %, this misconception is quite common.Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin5- 4Bond PricingThe price of a bond is the Present Value of all cash flows generated by the bond (i.e. coupons and face value) discounted at the required rate of return.PVcpnrcpnrcpn parrt ( ) ( )....( )( )1 1 11 2Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin5- 5Bond PricingExampleWhat is the price of a 5.5 % annual coupon bond, with a $1,000 face value, which matures in 3 years? Assume a required return of 3.5%. 03.056,1$)035.1(055,1)035.1(55)035.1(55321PVPVCopyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin5- 6Bond Cash FlowsCopyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin5- 7Bond PricingExample (continued)What is the price of the bond if the required rate of return is 5.5 %?000,1$)055.1(055,1)055.1(55)055.1(55321PVPVCopyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin5- 8Bond PricingExample (continued)What is the price of the bond if the required rate of return is 15 %?09.783$)15.1(055,1)15.1(55)15.1(55321PVPVCopyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin5- 9Bond PricingExample (continued)What is the price of the bond if the required rate of return is 3.5% AND the coupons are paid semi-annually?49.056,1$)0175.1(50.027,1)0175.1(50.27...)0175.1(50.27)0175.1(50.276521PVPVCopyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin5- 10Bond PricingExample (continued)Q: How did the calculation change, given semi-annual coupons versus annual coupon payments?Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin5- 11Bond PricingExample (continued)Q: How did the calculation change, given semi-annual coupons versus annual coupon payments?Time PeriodsPaying coupons twice a year, instead of once doubles the total number of cash flows to be discounted in the PV formula.Discount RateSince the time periods are now half years, the discount rate is also changed from the annual rate to the half year rate.Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin5- 12Bond YieldsCurrent Yield - Coupon payments for next year divided by bond price.Yield To Maturity - Interest rate for which the present value of the bond’s payments equal today’s price.Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin5- 13Bond YieldsCalculating Yield to Maturity (YTM=r)If you are given the price of a bond (PV) and the coupon rate, the yield to maturity can be found by solving for r.PVcpnrcpnrcpn parrt ( ) ( )....( )( )1 1 11 2Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin5- 14Bond YieldsExampleWhat is the YTM of a 5.5 % annual coupon bond, with a $1,000 face value, which matures in 3 years? The market price of the bond is $1,056.03.03.056,1$)1(055,1)1(55)1(55321PVrrrPVCopyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin5- 15Bond YieldsWARNINGWARNINGCalculating YTM by hand can be very tedious because it requires a trial and error approach. Solution: Use the “=Yield( )” function in Excel or solve for r using a financial calculator (make sure to include the face value as a FV at time t).Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin5- 16Bond YieldsRate of Return – In general terms = Earnings per period per dollar invested.investmentchange price+incomeCoupon =return of Rateinvestment totalperiodper income=return of Ratebondassets allCopyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin5- 17Bond Valuation SpreadsheetEsc and Double click on spreadsheet to accessCopyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin5- 18Bond Yield SpreadsheetEsc and Double click on spreadsheet to accessCopyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin5- 19Interest Rate Risk8809009209409609801,0001,0201,0401,0601,0800 5 10 15 20 25 30Time to MaturityBond PricePrice path for Premium BondPrice path for Discount BondTodayMaturityCopyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin5- 20Interest Rate Risk-5001,0001,5002,0002,5003,0000246810YTM$ Bond Price30 yr bond3 yr bondWhen the interest rate equals the 5.5% coupon rate, both bonds sell at face valueCopyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin5- 21Nominal and Real ratesYield on UK nominal bondsYield on UK bonds (real rate)Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin5- 22Default RiskCredit risk = risk of default on obligationDefault premium =
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