UB MGF 401 - chap005 (25 pages)

5 1 Chapter 5 Topics Covered Bond Characteristics reading the financial pages Interest Rates and Bond Prices Current Yield and Yield to Maturity Bond Rates and Returns Corporate Bonds and the Risk of Default The Yield Curve McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 5 2 Bonds Terminology Bond 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 McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 5 3 Bonds WARNING The 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 McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 5 4 Bond Pricing The 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 cpn cpn cpn par PV 1 2 t 1 r 1 r 1 r McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 5 5 Bond Pricing Example What 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 55 55 1 055 PV 1 2 1 035 1 035 1 035 3 PV 1 056 03 McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 5 6 Bond Cash Flows McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 5 7 Bond Pricing Example continued What is the price of the bond if the required rate of return is 5 5 55 55 1 055 PV 1 2 3 1 055 1 055 1 055 PV 1 000 McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 5 8 Bond Pricing Example continued What is the price of the bond if the required rate of return is 15 55 55 1 055 PV 1 2 1 15 1 15 1 15 3 PV 783 09 McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 5 9 Bond Pricing Example continued What is the price of the bond if the required rate of return is 3 5 AND the coupons are paid semi annually 27 50 27 50 27 50 1 027 50 PV 1 2 5 1 0175 1 0175 1 0175 1 0175 6 PV 1 056 49 McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 5 10 Bond Pricing Example continued Q How did the calculation change given semiannual coupons versus annual coupon payments McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 5 11 Bond Pricing Example continued Q How did the calculation change given semiannual coupons versus annual coupon payments Time Periods Discount Rate Paying coupons twice a year instead of once doubles the total number of cash flows to be discounted in the PV formula Since the time periods are now half years the discount rate is also changed from the annual rate to the half year rate McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 5 12 Bond Yields Current 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 McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 5 13 Bond Yields Calculating 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 cpn cpn cpn par PV 1 2 t 1 r 1 r 1 r McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 5 14 Bond Yields Example What 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 55 55 1 055 PV 1 2 3 1 r 1 r 1 r PV 1 056 03 McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 5 15 Bond Yields WARNING Calculating 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 McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 5 16 Bond Yields Rate of Return In general terms Earnings per period per dollar invested income per period Rate of returnall assets total investment Rate of returnbond McGraw Hill Irwin Coupon income price change investment Copyright 2007 by The McGraw Hill Companies Inc All rights 5 17 Bond Valuation Spreadsheet Esc and Double click on spreadsheet to access McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 5 18 Bond Yield Spreadsheet Esc and Double click on spreadsheet to access McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 5 19 Interest Rate Risk 1 080 Price path for Premium Bond 1 060 1 040 Bond Price 1 020 1 000 980 960 940 Today 900 Maturity Price path for Discount Bond 920 880 0 5 10 15 20 25 Time to Maturity McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 30 5 20 Interest Rate Risk 3 000 When the interest rate equals the 5 5 coupon rate both bonds sell at face value 2 500 30 yr bond Bond Price 2 000 1 500 3 yr bond 1 000 500 0 2 4 6 8 10 YTM McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 5 21 Nominal and Real rates Yield on UK nominal bonds Yield on UK bonds real rate McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 5 22 Default Risk Credit risk risk of default on obligation Default premium higher interest rate applied to loans with higher credit risk Rating Agencies Moody s Standard Poor s Assign ratings which reflect credit risk and associated default premium Investment grade Baa BBB or better Junk bonds Ba BB or lower McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 5 23 Default Risk Moody s Standard Poor s Aaa AAA Aa AA A A Baa BBB Ba B BB B Caa Ca C CCC CC C McGraw Hill Irwin Safety The strongest rating ability to repay interest and principal is very strong …