Corporate finance chapter 08 contents

Chapter Contents • Using Present Value Formulas to Value Known Flows • The Basic Building Blocks: Pure Discount Bonds • Coupon Bonds, Current Yield, and Yield-toMaturity • Reading Bond Listings • Why Yields for the same Maturity Differ • The Behavior of Bond Prices Over Time Bond Prices Rise as the Interest Rates Fall • Write the PV of the fixed income security as the sum terms j      PV = ∑ pmt j *     1+ i   j =1  n       = pmt1 *  + pmt * + + pmt *     n −1  + i + i + i       n −1   + pmt n *   + i   n US Treasury Yiled Curve, Jan 97 7.50 Annualized Yield (%) 7.00 6.50 6.00 5.50 5.00 4.50 10 15 Years to Maturity 20 25 30 Pure Discount Bonds • The pure discount bond is an example of the present value of a lump sum equation we analyzed in Chapter • Solving this, the yield-to-maturity on a pure discount bond is given by the relationship: F = P (1 + i ) n  F n ⇒ i =   −1 P Pure Discount Bonds F = P (1 + i ) n  F n ⇒ i =   −1 P • In this equation, – P is the present value or price of the bond – F is the face or future value – n is the investment period – i is the yield-to-maturity Pure Discount Bonds n F  10000  i =   −1 =   − = 5.41% P  9000  N I PV PMT FV ? 5.41% 9,000 -10,000 Bonds Trading at Par • Bond Pricing Principle #1: (Par Bonds) – If a bond’s price equals its face value, then its yield-to-maturity = current yield = coupon rate Proof: n n   pmt       P= 1−  + F      i  1+ i   1+ i  & P=F ⇒    n  pmt    n  pmt    P 1 −  = − ⇒ P = =F      + i    i  1+ i   i   First Solution Method 960 890 810 (1000 + 100) P= 100 + 100 + 1000 1000 1000 P = $1076.00 Second Solution Method 1  1,000  i0,1 =   − = 4.17%  960  i0, 2  1,000  =  − = 6.00%  890   1,000  i0,3 =   − = 7.28%  810  100 100 1000 + 100 P= + + 1.0417 1.0600 1.07283 P = $1,075.91 The YTM of the Coupon Bond N I PV ? -1076 100 7.10% 10 PMT FV 1000 n n  x         + f   &i > 0&n > 0& x > ⇒  p = 1 −  i  1+ i    + i     x    n  x (1 + i ) −  p i = =  n ( ) p + i − f − ( f − p)  p (1 + i ) n −  ( ) (  ( f − p)  & 1 − > 0 n p (1 + i ) −   ( ) 11 )       n n    x        + f   &i > 0&n > 0& x > ⇒  p = 1 −  i  1+ i    + i     1    −  = (1 + i ) − n  −  ⇒  x i  x i  p   f  () ()  1  1  −n    = (1 + ytm)   − −  current yield ytm   coupon yield ytm  12 Yield Relationships 0.2 0.18 0.16 coupon_y current_y y_t_m 0.14 Yield 0.12 0.1 0.08 0.06 0.04 0.02 600.00 800.00 1000.00 1200.00 Price 13 1400.00 1600.00 1800.00 Yield Relationships Yield 0.13 coupon_y current_y y_t_m 0.11 0.09 0.07 800.00 1000.00 Price 14 1200.00 Two Yield Curves (Pure Discount) 9.00% 8.00% Yield to Maturiry 7.00% 6.00% 5.00% 4.00% 3.00% 2.00% 1.00% 0.00% 10 15 Years to Maturity 15 20 Dymanic Yield Curve 8.00% 7.00% Yield to matutiry 6.00% 5.00% Current 5-year 10-year 15-Year 20-Year 4.00% 3.00% 2.00% 1.00% 0.00% 10 16 to maturity years 15 20 Interest Rates 9.00% 8.00% Rate 7.00% 6.00% spot 5.00% long_forward 4.00% 3.00% 2.00% 1.00% 0.00% 10 17 Years 15 20 20-Year Bond Value Over Time 1060 1040 1000 980 960 940 920 20 15 10 Time to Maturity 18 Value 1020 [...]... i  x i  p   f  () ()  1 1  1 1  −n    = (1 + ytm)   − −  current yield ytm   coupon yield ytm  12 Yield Relationships 0.2 0.18 0.16 coupon_y current_y y_t_m 0.14 Yield 0.12 0.1 0 .08 0.06 0.04 0.02 0 600.00 800.00 1000.00 1200.00 Price 13 1400.00 1600.00 1800.00 Yield Relationships Yield 0.13 coupon_y current_y y_t_m 0.11 0.09 0.07 800.00 1000.00 Price 14 1200.00 Two Yield Curves