Fundamentals of Corporate Finance Chapter Valuing Bonds Fifth Edition Slides by Matthew Will McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc All rights 5- Topics Covered  Bond Characteristics reading the financial pages  Interest Rates and Bond Prices  Current Yield and Yield to Maturity  Bond Rates and Returns  The Yield Curve  Corporate Bonds and the Risk of Default McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc All rights 5- Bonds Terminology  Bond - Security that obligates the issuer to make specified payments to the bondholder  Coupon - The interest payments made to the bondholder  Face Value (Par Value or Principal Value) - Payment at the maturity of the bond  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- 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- 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 = + + + t (1 + r ) (1 + r ) (1 + r ) McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc All rights 5- Bond Pricing Example What is the price of a 5.5 % annual coupon bond, with a $1,000 face value, which matures in years? Assume a required return of 3.5% 55 55 1,055 PV = + + (1.035) (1.035) (1.035) PV = $1,056.03 McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc All rights 5- Bond Cash Flows McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc All rights 5- 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 = + + (1.055) (1.055) (1.055) PV = $1,000 McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc All rights 5- Bond Pricing Example (continued) What is the price of the bond if the required rate of return is 15 %? 55 55 1,055 PV = + + (1.15) (1.15) (1.15) PV = $783.09 McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc All rights 5- 10 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 = + + + + (1.0175) (1.0175) (1.0175) (1.0175) PV = $1,056.49 McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc All rights 5- 12 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- 13 Bond Yields  Current Yield - Annual coupon payments divided by bond price  Yield To Maturity - Interest rate for which the present value of the bond’s payments equal the price McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc All rights 5- 14 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 = + + + t (1 + r ) (1 + r ) (1 + r ) McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc All rights 5- 15 Bond Yields Example What is the YTM of a 5.5 % annual coupon bond, with a $1,000 face value, which matures in years? The market price of the bond is $1,056.03 55 55 1,055 PV = + + (1 + r ) (1 + r ) (1 + r ) PV = $1,056.03 McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc All rights 5- 16 Bond Yields WARNING Calculating YTM by hand can be very tedious It is highly recommended that you learn to use the “IRR” or “YTM” or “i” functions on a financial calculator McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc All rights 5- 17 Bond Yields Rate of Return - Earnings per period per dollar invested total income Rate of return = investment Coupon income + price change Rate of return = investment McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc All rights 5- 18 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- 19 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- 20 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 10 15 20 25 Time to Maturity McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc All rights 30 5- 21 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 1,000 yr bond 500 - YTM McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc All rights 5- 22 Nominal and Real rates Yield on UK nominal bonds Yield on UK indexed bonds McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc All rights 5- 23 Default Risk  Credit risk  Default premium  Investment grade  Junk bonds McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc All rights 5- 24 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 Very strong likelihood that interest and principal will be repaid Strong ability to repay, but some vulnerability to changes in circumstances Adequate capacity to repay; more vulnerability to changes in economic circumstances Considerable uncertainty about ability to repay Likelihood of interest and principal payments over sustained periods is questionable Bonds in the Caa/CCC and Ca/CC classes may already be in default or in danger of imminent default C-rated bonds offer little prospect for interest or principal on the debt ever to be repaid Copyright © 2007 by The McGraw-Hill Companies, Inc All rights 5- 25 Corporate Bonds  Zero coupons  Floating rate bonds  Convertible bonds McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc All rights 5- 26 The Yield Curve Term Structure of Interest Rates - A listing of bond maturity dates and the interest rates that correspond with each date Yield Curve - Graph of the term structure McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc All rights [...]... of imminent default C-rated bonds offer little prospect for interest or principal on the debt ever to be repaid Copyright © 2007 by The McGraw- Hill Companies, Inc All rights 5- 25 Corporate Bonds  Zero coupons  Floating rate bonds  Convertible bonds McGraw- Hill/Irwin Copyright © 2007 by The McGraw- Hill Companies, Inc All rights 5- 26 The Yield Curve Term Structure of Interest Rates - A listing of. .. rights 5- 17 Bond Yields Rate of Return - Earnings per period per dollar invested total income Rate of return = investment Coupon income + price change Rate of return = investment McGraw- Hill/Irwin Copyright © 2007 by The McGraw- Hill Companies, Inc All rights 5- 18 Bond Valuation Spreadsheet Esc and Double click on spreadsheet to access McGraw- Hill/Irwin Copyright © 2007 by The McGraw- Hill Companies, Inc... 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- 15 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... yr bond 500 - YTM McGraw- Hill/Irwin Copyright © 2007 by The McGraw- Hill Companies, Inc All rights 5- 22 Nominal and Real rates Yield on UK nominal bonds Yield on UK indexed bonds McGraw- Hill/Irwin Copyright © 2007 by The McGraw- Hill Companies, Inc All rights 5- 23 Default Risk  Credit risk  Default premium  Investment grade  Junk bonds McGraw- Hill/Irwin Copyright © 2007 by The McGraw- Hill Companies,... is $1 ,056 .03 55 55 1 ,055 PV = + + 1 2 (1 + r ) (1 + r ) (1 + r ) 3 PV = $1 ,056 .03 McGraw- Hill/Irwin Copyright © 2007 by The McGraw- Hill Companies, Inc All rights 5- 16 Bond Yields WARNING Calculating YTM by hand can be very tedious It is highly recommended that you learn to use the “IRR” or “YTM” or “i” functions on a financial calculator McGraw- Hill/Irwin Copyright © 2007 by The McGraw- Hill Companies,... changed from the annual rate to the half year rate McGraw- Hill/Irwin Copyright © 2007 by The McGraw- Hill Companies, Inc All rights 5- 13 Bond Yields  Current Yield - Annual coupon payments divided by bond price  Yield To Maturity - Interest rate for which the present value of the bond’s payments equal the price McGraw- Hill/Irwin Copyright © 2007 by The McGraw- Hill Companies, Inc All rights 5- 14 Bond... semiannual coupons versus annual coupon payments? McGraw- Hill/Irwin Copyright © 2007 by The McGraw- Hill Companies, Inc All rights 5- 12 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... and Double click on spreadsheet to access McGraw- Hill/Irwin Copyright © 2007 by The McGraw- Hill Companies, Inc All rights 5- 20 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-... rights 5- 26 The Yield Curve Term Structure of Interest Rates - A listing of bond maturity dates and the interest rates that correspond with each date Yield Curve - Graph of the term structure McGraw- Hill/Irwin Copyright © 2007 by The McGraw- Hill Companies, Inc All rights ... CCC CC C McGraw- Hill/Irwin Safety The strongest rating; ability to repay interest and principal is very strong Very strong likelihood that interest and principal will be repaid Strong ability to repay, but some vulnerability to changes in circumstances Adequate capacity to repay; more vulnerability to changes in economic circumstances Considerable uncertainty about ability to repay Likelihood of interest