武汉大学公司金融课件(三).doc

Premium BondsIf the market rate of interest for a similar bond were only 3.75%, what would you be prepared to pay for the bond in question?SEMIANNUAL COUPONS Most bonds have semiannual interest payments. In our example, there would have been a $30 coupon every six months. Bond yields are quoted as APRs (annual percentage rates). With a quoted yield of 6% and semiannual payments, the true yield is 3% per 6 months.Example: What is the value of a $1,000 bond with a 6% coupon rate and semiannual payments, if the current market rate of interest were 6%? PVbond = 30 * PVIFA3%,20 + 1,000 * PVIF 3%,20 = 30 * 1 1/(1.03)20 + 1,000 * 1/(1.03)20 .03 = ( 30 * 14.87747) + (1,000 * .55368)PVbond = 446.32 + 553.68 = 1,000FINDING YIELD TO MATURITY Example, a broker will offer to sell you a 15-year bond, with a 7.2% coupon, for $1,126. To decide whether or not you wish to buy the bond, you must calculate the yield to maturity. Whether or not you would buy, depends upon the rates available elsewhere.ANNUAL vs SEMIANNUAL COUPONSANNUALPVbond = 60*( 1 1/(1.06)10) +1,000 * 1/(1.06)10 .06 = ( 60 * 7.3601) + (1,000 * .55839)PVbond = 441.61 + 558.39 = $1,000SEMIANNUALPVbond = 30 * PVIFA3%,20 + 1,000 * PVIF 3%,20 = 30 * 1 1/(1.03)20 + 1,000 * 1/(1.03)20 .03 = ( 30 * 14.87747) + (1,000 * .55368)PVbond = 446.32 + 553.68 = 1,000WHY?BOND RISK There is a general misconception that bonds are secure and riskless investments. Types of risks: Interest-rate risk If interest rates rise, the value of a bond can fall greatly. Default risk If a company or developing country cannot pay either the interest or the principal at the maturity date, the value of the bond can even fall to zero. Liquidity Risk Some bond issues, particularly for corporations or provincial governments, are relatively small-perhaps only $50 or $100 million. As a result, there may be relatively few of the bonds traded over any period. Consequently, if you owned such bonds and wished to sell, a very “thin” market may require the bonds to be sold at a discount relative to other similar bond issues that trade more. The potential that they would sell at a discount is an added risk. Currency risk While we wont discuss currency issues to any extent, a bond denominated in another currency may have its value fall dramatically with a devaluation of that currency.INTEREST RATE RISK Example: Long-term BondYou own a 30-year bond with a 10% coupon paid annually.If the current market interest rate for such a bond is 10%, its value is: PV = 100 * PVIFA10%,30 + 1,000 * PVIF10%,30 PV = 942.69 + 57.31 = 1,000If the current market interest rate rose dramatically to 15%. Whats the value of the bond now?The PV of the bond has fallen by 32.8%. Example: Short-term BondYou own a 1-year bond with a 10% coupon paid annually.If the current market interest rate for such a bond is 10%, its value is: PV = 100/1.1 + 1,000/1.1 PV = 90.91 + 909.09 = 1,000Suppose the current market interest rate for a similar bond rose dramatically to 15%. Whats the value of the bond now?The PV of the short-term bond has fallen by 4.5%. Thats a much lower level of interest rate risk than with the longer-term bond. Example: Low Coupon BondYou own a 20-year bond with a 6% coupon paid annually.If the current market interest rate for such a bond is 10%, its value is: PV = 60 * PVIFA10%,20 + 1,000 * PVIF10%,20 PV = 510.81 + 148.64 = 659.45Suppose the current market interest rate for a similar bond rose dramatically to 15%. The value of the bond has fallen by over 33.8%. Example: High Coupon BondYou own a 20-year bond with a 12% coupon paid annually.If the current market interest rate for such a bond is 10%, its value is:PV = 120 * PVIFA10%,20 + 1,000 * PVIF10%,20PV = 1,021.63 + 148.64 = 1,170.27Suppose the current market interest rate for a similar bond rose dramatically to 15%. The value of the bond has fallen by 30.6%.A lower level of interest rate risk than with the low coupon bond. What influences the level of interest rate risk?If you believe that interest rates will rise over the next year and you want to reduce your interest rate risk, what types of bonds would you prefer to hold?DEFAULT RISK Bond rating agencies throughout the world analyze and rate all bonds, both government and corporate. The ratings assess how likely the issuer is to default and the protection that creditors have in the event of default. In the North American context, the relevant agencies are Moodys, Standard and Poors, BOND RATINGS ONLY EVALUATE THE POSSIBILITY OF DEFAULT. RETURN ON A BOND Terms considered to this point.Coupon rate: The annual interest as a percentage of face value.Yield to Maturity: The discount rate that equates a bonds present value of interest payments and principal repayment with its price. (Note: if the yield to maturity isnt equal to the yield for a comparable bond, an arbitrage opportunity exists).RETURN ON A BONDSuppose you buy a bond, hold it for a year, and then sell. What is the return on your investment?Total = Interest + ChangeReturn Earned in ValueExample BUY: a 10-year, 7% coupon bond for $1,000. ( Since the bond sells at par, we know the yield to maturity is 7%).SELL: 1-year later, when the yield to maturity is 6%.What is the price that you could get in the bond market and what was your nominal ( as opposed to real) return on the bond?REAL VS NOMINAL RATES OF INTEREST If prices rise over time, the purchasing power of a dollar falls. With a 7% interest rate. A $1,000 bond will have a value of $1,070 after 1 year (if interest rates do not change). 7% in this case is the:NOMINAL INTEREST RATE: Rate at which money invested grows, without adjusting for the rate of inflation. If there were 5% inflation over the same year, the $1,070 nominal cash flow would not buy 7% more goods and services, since the price of those goods and services would be 5% higher. After we adjust for inflation, we could buy only 1.905% more.REAL INTEREST RATE Rate at which the purchasing power of an investment increases.FISHER EFFECT Real Interest = Nominal Interest Rate Rate Inflation RateORNominal = Real Interest * InflationInterest Rate Rate Rate ( 1 + R ) = ( 1 + r ) ( 1 + h )In our example:1.07 = (1.019