Chapter 6 Valuing Bonds

Copyright ©2014 Pearson Education, Inc. All rights reserved Bond Cash Flows, Prices, and Yields Bond Terminology –Bond Certificate States the terms of the bond –Maturity Date Final repayment date –Term The time remaining until the repayment date –Coupon Promised interest payments

Copyright ©2014 Pearson Education, Inc. All rights reserved.6-3 Zero-Coupon Bonds Zero-Coupon Bond –Does not make coupon payments –Always sells at a discount (a price lower than face value), so they are also called pure discount bonds –Treasury Bills are U.S. government zero- coupon bonds with a maturity of up to one year. –Brokerage houses can “create” zero coupon treasury securities.

Copyright ©2014 Pearson Education, Inc. All rights reserved.6-4 Zero-Coupon Bonds (cont'd) Suppose that a one-year, risk-free, zero- coupon bond with a $100,000 face value has an initial price of $96, The cash flows would be: –Although the bond pays no “interest,” your compensation is the difference between the initial price and the face value.

Copyright ©2014 Pearson Education, Inc. All rights reserved.6-5 Alternative Example 6.1 Problem –Suppose that the following zero-coupon bonds are selling at the prices shown below per $100 face value. Determine the corresponding yield to maturity for each bond. Maturity1 year2 years3 years4 years Price$98.04$95.18$91.51$87.14

Copyright ©2014 Pearson Education, Inc. All rights reserved.6-6 Alternative Example 6.1 (cont'd) Solution:

Copyright ©2014 Pearson Education, Inc. All rights reserved.6-7 Zero-Coupon Bonds Risk-Free Interest Rates –Spot Interest Rate Another term for a default-free, zero-coupon yield –Zero-Coupon Yield Curve A plot of the yield of risk-free zero-coupon bonds as a function of the bond’s maturity date

Copyright ©2014 Pearson Education, Inc. All rights reserved.6-8 Coupon Bonds –Pay face value at maturity –Pay regular coupon interest payments Treasury Notes –U.S. Treasury coupon security with original maturities of 1–10 years Treasury Bonds –U.S. Treasury coupon security with original maturities over 10 years

Copyright ©2014 Pearson Education, Inc. All rights reserved.6-9 Alternative Example 6.2 The U.S. Treasury has just issued a ten-year, $1000 bond with a 4% coupon and semi-annual coupon payments. What cash flows will you receive if you hold the bond until maturity?

Copyright ©2014 Pearson Education, Inc. All rights reserved.6-10 Bond Valuation Primary Principle: –Value of financial securities = PV of expected future cash flows Bond value is, therefore, determined by the present value of the coupon payments and par value. Interest rates are inversely related to present (i.e., bond) values.

Copyright ©2014 Pearson Education, Inc. All rights reserved.6-11 Coupon Bonds (cont'd) Yield to Maturity –The YTM is the single discount rate that equates the present value of the bond’s remaining cash flows to its current price. Rate of return investors earn if they buy the bond at P 0 and hold it until maturity. The YTM on a bond selling at par will always equal the coupon interest rate.

Copyright ©2014 Pearson Education, Inc. All rights reserved.6-12 Basic Investment Rules If the value of an asset (it’s worth) is >= current market price, then you would buy it. –If the benefit >= cost, you would buy If the expected return of an investment is >= required return, you would buy it. –Remember: required return contains inflation and RISK

Copyright ©2014 Pearson Education, Inc. All rights reserved.6-13 Valuation Example If the bond sells for $825, would you buy it? What is the yield to maturity? Bond Valuation

Copyright ©2014 Pearson Education, Inc. All rights reserved.6-14 Valuation Example If the bond sells for $450, would you buy it? What is the yield to maturity? Bond Valuation

Copyright ©2014 Pearson Education, Inc. All rights reserved.6-15 Alternative Example 6.3 Problem –Consider the following semi-annual bond: $1000 par value 7 years until maturity 9% coupon rate Price is $1, –What is the bond’s yield to maturity?

Copyright ©2014 Pearson Education, Inc. All rights reserved Dynamic Behavior of Bond Prices Discount –A bond is selling at a discount if the price is less than the face value. Par –A bond is selling at par if the price is equal to the face value. Premium –A bond is selling at a premium if the price is greater than the face value.

Copyright ©2014 Pearson Education, Inc. All rights reserved.6-17 Discounts and Premiums (cont'd) Table 6.1 Bond Prices Immediately After a Coupon Payment

Copyright ©2014 Pearson Education, Inc. All rights reserved.6-18 Time and Bond Prices Holding all other things constant, a bond’s yield to maturity will not change over time. Holding all other things constant, the price of discount or premium bond will move towards par value over time. If a bond’s yield to maturity has not changed, then the IRR of an investment in the bond equals its yield to maturity even if you sell the bond early.

Copyright ©2014 Pearson Education, Inc. All rights reserved.6-19 Figure 6.1 The Effect of Time on Bond Prices

Copyright ©2014 Pearson Education, Inc. All rights reserved.6-20 Bond valuation 1)c = 12% k = 10% n = (6.1446) (.3855) = )c = 10% k = 10% n = )c = 8% k = 10% n = 10 80(6.1446) (.3855) = premium discount

Copyright ©2014 Pearson Education, Inc. All rights reserved.6-21 Price Converges on Par at Maturity $1,000 $877 $1,122 time 10 yrs A) Go back to bond 3 on the previous slide. Put the value in for the price. What is the YTM? When you buy a bond what types of returns do you receive? B) Go back to bond 1 on the previous slide. Put the value in for the price. What is the YTM?

Copyright ©2014 Pearson Education, Inc. All rights reserved.6-22 Interest Rate Changes and Bond Prices There is an inverse relationship between interest rates and bond prices. –As interest rates and bond yields rise, bond prices fall. –As interest rates and bond yields fall, bond prices rise.

Copyright ©2014 Pearson Education, Inc. All rights reserved.6-23 Bond returns Yield to call –Refunding –Yield premium Realized YTM –Set a certain investment horizon –Predict price at end of the horizon

Copyright ©2014 Pearson Education, Inc. All rights reserved.6-24 Bond Valuation

Copyright ©2014 Pearson Education, Inc. All rights reserved.6-25 Interest Rate Risk Price Risk – Change in price due to changes in interest rates – Long-term bonds have more price risk than short- term bonds – Low coupon rate bonds have more price risk than high coupon rate bonds. Reinvestment Rate Risk – Uncertainty concerning rates at which cash flows can be reinvested – Short-term bonds have more reinvestment rate risk than long-term bonds. – High coupon rate bonds have more reinvestment rate risk than low coupon rate bonds.

Copyright ©2014 Pearson Education, Inc. All rights reserved.6-26 Interest Rate Changes and Bond Prices (cont'd) The sensitivity of a bond’s price to changes in interest rates is measured by the bond’s duration. –Bonds with high durations are highly sensitive to interest rate changes. –Bonds with low durations are less sensitive to interest rate changes.

Copyright ©2014 Pearson Education, Inc. All rights reserved.6-27

Copyright ©2014 Pearson Education, Inc. All rights reserved Corporate Bonds The primary difference is the riskiness of the debt. Credit publishing companies primarily analyze the risk of default.

Copyright ©2014 Pearson Education, Inc. All rights reserved.6-29 Corporate Bond Yields Investors pay less for bonds with credit risk than they would for an otherwise identical default-free bond. The yield of bonds with credit risk will be higher than that of otherwise identical default-free bonds.

Copyright ©2014 Pearson Education, Inc. All rights reserved.6-30 Bond Ratings Investment Grade Bonds Speculative Bonds –Also known as Junk Bonds or High-Yield Bonds

Copyright ©2014 Pearson Education, Inc. All rights reserved.6-31 Table 6.4 Bond Ratings

Copyright ©2014 Pearson Education, Inc. All rights reserved.6-32 Table 6.4 Bond Ratings (cont’d)

Copyright ©2014 Pearson Education, Inc. All rights reserved.6-33 Corporate Yield Curves Default Spread –Also known as Credit Spread –The difference between the yield on corporate bonds and Treasury yields

Copyright ©2014 Pearson Education, Inc. All rights reserved.6-34 Figure 6.3 Corporate Yield Curves for Various Ratings, June 2012 Source: Bloomberg

Copyright ©2014 Pearson Education, Inc. All rights reserved Sovereign Bonds Bonds issued by national governments –U.S. Treasury securities are generally considered to be default free –All sovereign bonds are not default free e.g. Greece defaulted on its outstanding debt in 2012 –Importance of inflation expectations Potential to “inflate away” the debt –European sovereign debt, the EMU, and the ECB

Copyright ©2014 Pearson Education, Inc. All rights reserved.6-36 Discussion of Data Case Key Topic Look at the Financial Industry Regulatory Authority’s website. What bond issues does Sirius Satellite Radio (ticker: SIRI) currently have outstanding? What are their yields? What are their ratings? Source: