1. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. ■ explain how bonds are priced ■ identify the factors that affect bond prices ■ explain how the sensitivity of bond prices to interest rates is dependent on particular bond characteristics ■ explain the risk of international bonds 8 Bond Valuation and Risk Chapter Objectives 1

2. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Bond Valuation Process ■Bonds are debt obligations with long-term maturities that are commonly issued by governments or corporations to obtain long-term funds. ■The price of a bond is the present value of the cash flows that will be generated by the bond, namely periodic interest or coupon payments and the principal at maturity. 2

3. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Bond Valuation Process Current price of a bond (PV) Where: C=coupon payment paid in each period Par=par value k=required rate of return n=number of period to maturity 3

4. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Example of an annual coupon bond Par value of $1,000, pays $100 at the end of each year in coupon payments (coupon rate is 10%), and has three years remaining until maturity. The prevailing annualized yield (yield to maturity) is 12%. What is the price (present value)? 4

5. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Exhibit 8.1 Valuation of a Three-Year Bond 5

6. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. How to use the Financial Calculator? FV=1000 PMT=100 N=3 I/Y=12 CPT PV=… 6

7. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Another example of an annual coupon bond Par value of $1,000, annual coupon rate is 8% and pays at the end of each year, and has five years remaining until maturity. The current market price is $1250. How much is the yield to maturity? FV=1000, PMT=1000 x 8%=80, N=5, PV=-1250 I/Y=?= 2.60288 YTM=2.60288% 7

8. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Valuation of Bonds with semi-annual payments ■PMT: divide the annual coupon by two ■I/Y: divide the annual YTM by two ■N: double the number of years 8

9. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Example of a semi-annual coupon bond Par value of $1,000, coupon rate is 10% and the coupon is paid every 6 month, and has three years remaining until maturity. The prevailing annualized yield is 12%. What is the price (present value)? FV=1000, PMT=50, N=6, I/Y=6, PV=? 9

10. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Another example of semi-annual coupon bond Par value of $1,000, annual coupon rate is 8% and pays every 6 month, and has five years remaining until maturity. The current market price is $1250. How much is the yield to maturity? FV=1000, PMT=1000x8%/2=40, N=5x2=10, PV=-1250 I/Y=? = 1.31556 YTM = 1.31556 x 2 = 2.6311% 10

11. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Inflation-Indexed Treasury Bonds 10-year, par value of $10,000. annual coupon rate of 4%, coupon paid every 6 months. (page 168).  If inflation rate is 1% during the first six month since the bond was issued, then new par =10,000x(1+1%)=$10,100 coupon payment =10,100x2%=$202 2. If inflation increase to 3% in the following 6 months, then new par =10,100x(1+3%)=$10,403 coupon payment =10,403x2%=$208.06 11

12. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Interest rate risk Impact of the Discount Rate (YTM) on Bond Valuation (Exhibit 8.2) ■The appropriate discount rate for valuing any asset is the yield that could be earned on alternative investments with similar risk and maturities. ■High risk securities have higher discount rates. 12

13. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Exhibit 8.2 Relationship between Discount Rate and Present Value of $10,000 Payment to Be Received in 10 Years 13

14. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Explaining Bond Price Movements Factors That Affect the Credit (Default) Risk Premium  The general level of credit risk on bonds can change in response to a change in economic growth.  Strong economic growth can improve a firm’s cash flows and reduce the probability of default.  Weak economic conditions tend to reduce a firm’s cash flows and increase the probability of default. 14

15. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Explaining Bond Price Movements Factors That Affect the Credit (Default) Risk Premium (cont.)  Changes in Credit Risk Premium over Time (Exhibit 8.5)  Yields among securities are highly correlated.  Difference between the corporate and Treasury bond yields widened during periods when the economy was weak.  Impact of Debt Maturity on the Credit Risk Premium  Tends to be larger for bonds that have a longer term to maturity. 15

16. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Exhibit 8.5 Bond Risk Premium over Time 16 Source: Federal Reserve.

17. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Explaining Bond Price Movements  The effect of economic growth is uncertain: a high level of economic growth can adversely affect bond prices by raising the risk-free rate, but it can favorably affect bond prices by lowering the default risk premium.  Any new information about a firm that changes its perceived ability to repay its bonds could have an immediate effect on the price of the bonds. 17

18. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Exhibit 8.6 Framework for Explaining Changes in Bond Prices over Time 18

19. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Explaining Bond Price Movements Implications for Financial Institutions  Any factors that lead to higher interest rates tend to reduce the market values of bonds hold by financial institution.  Any factors that lead to lower interest rates tend to increase the market values of bonds hold by financial institution. 19

20. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Sensitivity of Bond Prices to Interest Rate Movements Bond Price Elasticity - The sensitivity of bond prices to changes in the required rate of return (k). 20

21. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Sensitivity of Bond Prices to Interest Rate Movements  Influence of Coupon Rate on Bond Price Sensitivity  A zero-coupon bond is most sensitive to changes in the required rate of return.  A bond that pays higher coupon payments is less sensitive to changes in the required rate of return.  Influence of Maturity on Bond Price Sensitivity - As interest rates decrease, long-term bond prices increase by a greater degree than short-term bond prices. Lower coupon rate, larger sensitivity Longer time to maturity, larger sensitivity 21

22. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Exhibit 8.7 Sensitivity of 10-Year Bonds with Different Coupon Rates to Interest Rate Changes 22

23. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Sensitivity of Bond Prices to Interest Rate Movements Duration - a measurement of the life of the bond on a present value basis. The longer a bond’s duration, the greater its sensitivity to interest rate changes. 23

24. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Duration examples: 3-year bond, 8% annual coupon payments, YTM = 10% 24

25. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Duration In-class exercise The duration of a bond with $1,000 par value and 6% annual coupon rate, 4 years remaining to maturity, and a 9% yield to maturity is 25 TimePaymentPVWeightWeight x Time 16055.050.0610 26050.500.05590.1119 36046.330.05130.1540 41060750.930.83183.3271 902.813.6539

26. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Modified Duration Not required  Modified Duration (DUR*): Can be used to estimate the percentage change in the bond’s price in response to a 1 percentage point change in bond yields 26

27. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Valuation and Risk of International Bonds International Bond Diversification - May diversify foreign bond holdings among countries to reduce their exposure to different types of risk  Reduction of Interest Rate Risk  Reduction of Credit Risk  Reduction of Exchange Rate Risk  International Integration of Credit Risk - When one country experiences weak economic conditions, its consumers in other countries are also affected. 27

28. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Valuation and Risk of International Bonds European Debt Crisis 2010 - 2012  Greece, Portugal, and Spain experienced debt crisis because of large budget deficits and inability to cover debt payments.  Because these countries commonly obtained debt financing from financial institutions in other European countries, these financial problems also spread to other countries. 28

29. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. SUMMARY  The value of a debt security (such as bonds) is the present value of future cash flows generated by that security, using a discount rate that reflects the investor’s required rate of return. As market interest rates rise, the investor’s required rate of return increases. The discounted value of bond payments declines when the higher discount rate is applied. Thus, the present value of a bond declines, which forces the bond price to decline.  Bond prices are affected by the factors that influence interest rate movements, including economic growth, the money supply, oil prices, and the dollar. Bond prices are also affected by a change in credit risk. 29

30. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. SUMMARY (Cont.)  Investors commonly measure the sensitivity of their bond holdings to potential changes in the required rate of return. Two methods used for this purpose are bond price elasticity and duration. Other things being equal, the longer a bond’s time to maturity, the more sensitive its price is to interest rate movements. Prices of bonds with relatively low coupon payments are also more sensitive to interest rate movements.  Foreign bonds may offer higher returns, but they are exposed to exchange rate risk. Investors can reduce their exposure to exchange rate risk by diversifying among various currency denominations. 30

31. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Homework Assignment 7 Chapter 8: Questions and Applications: 2,7,8,9,10,12,14. Problems: 1,2,3,11,12,13. 31