1、Bonds and Their Valuation,Key Features of Bonds Bond Valuation Measuring Yield Assessing Risk,7-1,Chapter 7,What is a bond?,A long-term debt instrument in which a borrower agrees to make payments of principal and interest, on specific dates, to the holders of the bond.,7-2,Bond Markets,Primarily tra

2、ded in the over-the-counter (OTC) market. Most bonds are owned by and traded among large financial institutions. The Wall Street Journal reports key developments in the Treasury, corporate, and municipal markets. Online edition lists trading each day for the most actively-traded investment-grade, hi

3、gh-yield, and convertible bonds.,7-3,Key Features of a Bond,Par value: face amount of the bond, which is paid at maturity (assume $1,000). Coupon interest rate: stated interest rate (generally fixed) paid by the issuer. Multiply by par value to get dollar payment of interest. Maturity date: years un

4、til the bond must be repaid. Issue date: when the bond was issued. Yield to maturity: rate of return earned on a bond held until maturity (also called the “promised yield”).,7-4,Effect of a Call Provision,Allows issuer to refund the bond issue if rates decline (helps the issuer, but hurts the invest

5、or). Borrowers are willing to pay more, and lenders require more, for callable bonds. Most bonds have a deferred call and a declining call premium.,7-5,What is a sinking fund?,Provision to pay off a loan over its life rather than all at maturity. Similar to amortization on a term loan. Reduces risk

6、to investor, shortens average maturity. But not good for investors if rates decline after issuance.,7-6,How are sinking funds executed?,Call x% of the issue at par, for sinking fund purposes. Likely to be used if rd is below the coupon rate and the bond sells at a premium. Buy bonds in the open mark

7、et. Likely to be used if rd is above the coupon rate and the bond sells at a discount.,7-7,The Value of Financial Assets,7-8,Other Types (Features) of Bonds,Convertible bond: may be exchanged for common stock of the firm, at the holders option. Warrant: long-term option to buy a stated number of sha

8、res of common stock at a specified price. Putable bond: allows holder to sell the bond back to the company prior to maturity. Income bond: pays interest only when interest is earned by the firm. Indexed bond: interest rate paid is based upon the rate of inflation.,7-9,What is the opportunity cost of

9、 debt capital?,The discount rate (ri) is the opportunity cost of capital, and is the rate that could be earned on alternative investments of equal risk. ri = r* + IP + MRP + DRP + LP,7-10,What is the value of a 10-year, 10% annual coupon bond, if rd = 10%?,7-11,Calculating the Value of a Bond,This b

10、ond has a $1,000 lump sum (the par value) due at maturity (t = 10), and annual $100 coupon payments beginning at t = 1 and continuing through t = 10, the price of the bond can be found by solving for the PV of these cash flows. Excel: =PV(.10,10,100,1000),7-12,Whats the value of its 10-year bonds ou

11、tstanding with the same risk but a 13% annual coupon rate?,The annual coupon payment is $130. Since the risk is the same it has the same yield to maturity as the previous bond (10%). This bond sells at a premium because the coupon rate the yield to maturity. Excel: =PV(.10,10,130,1000),7-13,Whats th

12、e value of its 10-year bonds outstanding with the same risk but a 7% annual coupon rate?,The annual coupon payment is $70. Since the risk is the same it has the same yield to maturity as the previous bonds (10%). This bond sells at a discount because the coupon rate the yield to maturity. Excel: =PV

13、(.10,10,70,1000),7-14,Changes in Bond Value over Time,What would happen to the value of these three bonds if the required rate of return remained at 10%?,7-15,Bond Values over Time,At maturity, the value of any bond must equal its par value. If rd remains constant: The value of a premium bond would

14、decrease over time, until it reached $1,000. The value of a discount bond would increase over time, until it reached $1,000. The value of a par bond stays at $1,000.,7-16,What is the YTM on a 10-year, 9% annual coupon, $1,000 par value bond, selling for $887?,7-17,Must find the rd that solves this m

15、odel.,Solving for the YTM,Solving for I/YR, the YTM of this bond is 10.91%. This bond sells at a discount, because YTM coupon rate. Excel: =RATE(10,90,-887,1000),7-18,Find YTM If the Bond Price is $1,134.20,Solving for I/YR, the YTM of this bond is 7.08%. This bond sells at a premium, because YTM co

16、upon rate. Excel: =RATE(10,90,-1134.20,1000),7-19,Definitions,7-20,An Example: Current and Capital Gains Yields,Find the current yield and the capital gains yield for a 10-year, 9% annual coupon bond that sells for $887, and has a face value of $1,000.,7-21,Calculating Capital Gains Yield,YTM = Curr

17、ent yield + Capital gains yield Could also find the expected price one year from now and divide the change in price by the beginning price, which gives the same answer.,7-22,What is price risk? Does a 1-year or 10-year bond have more price risk?,Price risk is the concern that rising rd will cause th

18、e value of a bond to fall. rd 1-yearChange10-yearChange 5%$1,048$1,386 10% 1,000 1,000 15% 956 749 The 10-year bond is more sensitive to interest rate changes, and hence has more price risk.,7-23,Illustrating Price Risk,7-24,10-Year Bond,1-Year Bond,Value ($),YTM(%),What is reinvestment risk?,Reinve

19、stment risk is the concern that rd will fall, and future CFs will have to be reinvested at lower rates, hence reducing income. EXAMPLE: Suppose you just won $500,000 playing the lottery. You intend to invest the money and live off the interest.,7-25,Reinvestment Risk Example,You may invest in either

20、 a 10-year bond or a series of ten 1-year bonds. Both 10-year and 1-year bonds currently yield 10%. If you choose the 1-year bond strategy: After Year 1, you receive $50,000 in income and have $500,000 to reinvest. But, if 1-year rates fall to 3%, your annual income would fall to $15,000. If you cho

21、ose the 10-year bond strategy: You can lock in a 10% interest rate, and $50,000 annual income for 10 years, assuming the bond is not callable.,7-26,Conclusions about Price Risk and Reinvestment Risk,CONCLUSION: Nothing is riskless!,7-27,Semiannual Bonds,Multiply years by 2: Number of periods = 2N Di

22、vide nominal rate by 2: Periodic rate (I/YR) = rd/2 Divide annual coupon by 2: PMT = Annual coupon/2,7-28,What is the value of a 10-year, 10% semiannual coupon bond, if rd = 13%?,Multiply years by 2: N = 2 x 10 = 20 Divide nominal rate by 2: I/YR = 13/2 = 6.5 Divide annual coupon by 2: PMT = 100/2 =

23、 50 Excel: =PV(.065,20,50,1000),7-29,The semiannual bonds effective rate is: Excel:=EFFECT(.10,2) = 10.25% 10.25% 10% (the annual bonds effective rate), so you would prefer the semiannual bond.,Would you prefer to buy a 10-year, 10% annual coupon bond or a 10-year, 10% semiannual coupon bond, all el

24、se equal?,7-30,If the proper price for this semiannual bond is $1,000, what would be the proper price for the annual coupon bond?,The semiannual bond has a 10.25% effective rate, so the annual bond should earn the same EAR. At these prices, the annual and semiannual bonds are in equilibrium. Excel:

25、=PV(.1025,10,100,1000),7-31,A 10-year, 10% semiannual coupon bond selling for $1,135.90 can be called in 4 years for $1,050, what is its yield to call (YTC)?,The bonds yield to maturity is 8%. Solving for the YTC is identical to solving for YTM, except the time to call is used for N and the call pre

26、mium is FV. Excel: =RATE(8,50,-1135.90,1050),7-32,Yield to Call,3.568% represents the periodic semiannual yield to call. YTCNOM = rNOM = 3.568% x 2 = 7.137% is the rate that a broker would quote. The effective yield to call can be calculated. YTCEFF = (1.03568)2 1 = 7.26% Excel:=EFFECT(.07137,2) = 7

27、.26%,7-33,If you bought these callable bonds, would you be more likely to earn the YTM or YTC?,The coupon rate = 10% compared to YTC = 7.137%. The firm could raise money by selling new bonds which pay 7.137%. Could replace bonds paying $100 per year with bonds paying only $71.37 per year. Investors

28、should expect a call, and to earn the YTC of 7.137%, rather than the YTM of 8%.,7-34,When is a call more likely to occur?,In general, if a bond sells at a premium, then (1) coupon rd, so (2) a call is more likely. So, expect to earn: YTC on premium bonds. YTM on par and discount bonds.,7-35,Default

29、Risk,If an issuer defaults, investors receive less than the promised return. Therefore, the expected return on corporate and municipal bonds is less than the promised return. Influenced by the issuers financial strength and the terms of the bond contract.,7-36,Types of Bonds,Mortgage bonds Debenture

30、s Subordinated debentures Investment-grade bonds Junk bonds,7-37,Evaluating Default Risk:Bond Ratings,7-38,Bond ratings are designed to reflect the probability of a bond issue going into default.,Factors Affecting Default Risk and Bond Ratings,Financial performance Debt ratio TIE ratio Current ratio

31、 Qualitative factors: Bond contract terms Secured vs. unsecured debt Senior vs. subordinated debt Guarantee and sinking fund provisions Debt maturity,7-39,Other Factors Affecting Default Risk,Miscellaneous qualitative factors Earnings stability Regulatory environment Potential antitrust or product l

32、iabilities Pension liabilities Potential labor problems,7-40,Bankruptcy,Two main chapters of the Federal Bankruptcy Act: Chapter 11, Reorganization Chapter 7, Liquidation For large organizations, reorganization occurs more frequently than liquidation, particularly in those instances where the business is worth more “alive than dead.”,7-41,Chapter 11 Bankruptcy