Chapter 10

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## Chapter 10

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**Chapter 10**Bond prices and yields**Bond Characteristics**Face or par value Coupon rate Coupon payment Maturity Yield to maturity**Accrued interest and quoted bond prices**Accrued Interest = (Annual coupon payment/2)x(days since last coupon payment/days separate coupon payment) Invoice price = quoted price + accrued interest**Provisions of Bonds**Secured or unsecured Call provision Convertible provision Put provision (putable bonds) Floating rate bonds Sinking funds**Exercise 2**A bond pays a semi-annual coupon and the last coupon was paid 61 days ago. If the annual coupon payment is $75, what is the accrued interest? A. $13.21B. $12.57C. $15.44D. $16.32**Bond Pricing**T ParValue C P T t = + B + T + ( 1 r ) T ( 1 r ) = t 1 Bond price = PV of Annuity + PV of lump sum CF PB = Price of the bond Ct = interest or coupon payments T = number of periods to maturity r = semi-annual discount rate or the semi-annual yield to maturity**Example: Price of 8%,semiannual coupon payment, 10-yr. with**yield at 6% 20 1 1 Σ P = x + x 40 1000 t 20 B ( 1 . 03 ) ( 1 . 03 ) = t 1 P = 1 , 148 . 77 B Coupon = 4%*1,000 = 40 (Semiannual) Discount Rate = 3% (Semiannual Maturity = 10 years or 20 periods Par Value = 1,000**Exercise in class**• A coupon bond which pays interest semi-annually, has a par value of $1,000, matures in 5 years, and has a yield to maturity of 8%. If the coupon rate is 10%, the intrinsic value of the bond today will be __________. A) $855.55 B) $1,000 C) $1,081 D) $1,100 2. A coupon bond which pays interest of $40 annually, has a par value of $1,000, matures in 5 years, and is selling today at a $159.71 discount from par value. The actual yield to maturity on this bond is __________. A) 5% B) 6% C) 7% D) 8%**Bond Prices and Yields**Prices and Yields (required rates of return) have an inverse relationship When yields get very high the value of the bond will be very low When yields approach zero, the value of the bond approaches the sum of the cash flows**Prices and Yield**Price Yield**Alternative Measures of Yield**Current Yield Annual coupon payment/current bond price Yield to Call Call price replaces par Call date replaces maturity Example: Suppose the 8% coupon (semiannual payment), 30-year maturity bond sells for $1,150 and is callable in 10 years at a call price of $1,100. What is the yield to maturity and yield to call? Given: PMT: 40; N: 60; FV:1000; PV: -1150 YTM = 6.82% Given: PMT: 40, N: 20; FV:1100; PV: -1150 YTC = 6.64%**Alternative Measures of Yield**Holding Period Yield Considers actual reinvestment of coupons Considers any change in price if the bond is held less than its maturity You purchased a 5-year annual interest coupon bond one year ago. Its coupon interest rate was 6% and its par value was $1,000. At the time you purchased the bond, the yield to maturity was 4%. If you sold the bond after receiving the first interest payment and the bond's yield to maturity had changed to 3%, your annual total rate of return on holding the bond for that year would have been __________. A) 5.00% B) 5.51% C) 7.61% D) 8.95%**Convertible Bonds**A bond with an option allowing the bondholder to exchange the bond for a specified number of shares of common stock in the firm. Conversion ratio: # of shares can be exchanged for each bond Market conversion value: current value of shares for which bond maybe exchanged Conversion premium: the difference of conversion value and its bond price**Example 2**A convertible bond has a par value of $1,000 but its current market price is $833. The current price of the issuing company's stock is $22 and the conversion ratio is 40 shares. The bond's market conversion value is __________. a. $1,000 B $880 c. $833 d. $800**Exercise in class**• A coupon bond which pays interest of $50 annually, has a par value of $1,000, matures in 5 years, and is selling today at an $84.52 discount from par value. The current yield on this bond is __________. A) 5% B) 5.46% C) 5.94% D) 6.00% 2. A callable bond pays annual interest of $60, has a par value of $1,000, matures in 20 years but is callable in 10 years at a price of $1,100, and has a value today of $1055.84. The yield to call on this bond is __________. A) 6.00% B) 6.58% C) 7.20% D) 8.00%**Premium and Discount Bonds**Premium Bond Coupon rate exceeds yield to maturity Bond price will decline to par over its maturity Discount Bond Yield to maturity exceeds coupon rate Bond price will increase to par over its maturity**Default Risk and Ratings**Rating companies Moody’s Investor Service Standard & Poor’s Fitch Rating Categories Investment grade Speculative grade (BBB or BaB below)**Factors Used by Rating Companies**Coverage ratios Leverage ratios Liquidity ratios Profitability ratios Cash flow to debt**Term Structure of Interest Rates**Relationship between yields to maturity and maturity Yield curve - a graph of the yields on bonds relative to the number of years to maturity Usually Treasury Bonds Have to be similar risk or other factors would be influencing yields**Theories of Term Structure**Expectations Long term rates are a function of expected future short term rates Upward slope means that the market is expecting higher future short term rates Downward slope means that the market is expecting lower future short term rates Liquidity Preference Upward bias over expectations The observed long-term rate includes a risk premium**Problems with Traditional Theories**Expectations theory The term structure is almost always upward sloping, but interest rates have not always risen. It is often the case that the term structure turns down at very long maturities. Maturity preference theory The U.S. government borrows much more heavily short term than long term. Many of the biggest buyers of fixed-income securities, such as pension funds, have a strong preference for long maturities**Market segmentation theory**The U.S. government borrows at all maturities. Many institutional investors, such as mutual funds, are more than willing to move maturities to obtain more favorable rates. There are bond trading operations that exist just to exploit even very small perceived premiums.**Forward Rates Implied in the Yield Curve**+ + + - n n 1 ( 1 ) ( 1 ) ( 1 ) y y f = - n n 1 n 2 1 ( 1 . 12 ) ( 1 . 11 ) ( 1 . 1301 ) = For example, using a 1-yr and 2-yr rates Longer term rate, y(n) = 12% Shorter term rate, y(n-1) = 11% Forward rate, a one-year rate in one year = 13.01%**Exercise in class**Consider the following $1,000 par value zero-coupon bonds: The expected one-year interest rate two years from now should be __________. A) 7.00% B) 8.00% C) 9.00% D) 10.00%