Chapter 4: Time Value of Money - Pearson Education

Chapter 4: Time Value of Money - Pearson Education

Chapter 8 Contents 1 Using Present Value Formulas to Value Known Flows 2 The Basic Building Blocks: Pure Discount Bonds 3 Coupon Bonds, Current Yield, and Yield-toMaturity 4 Reading Bond Listings 5 Why Yields for the same Maturity Differ 6 The Behavior of Bond Prices Over Time 1 Bond Prices Rise as the Interest Rates Fall Write the PV of the fixed income security as the sum terms j 1 PV pmt j * 1 i j 1 n 1 2 1

1 1 pmt1 * pmt * ... pmt * 2 n 1 1 i 1 i 1 i 2

n 1 1 pmtn * 1 i n US Treasury Yiled Curve, Jan 97 7.50 Annualized Yield (%) 7.00 6.50 6.00 5.50 5.00 4.50 0 5 10

15 20 Years to Maturity 3 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 4 Solving this, the yield-to-maturity on a pure discount bond is given by1the F n n relationship: F P 1 i i 1 4 P Pure Discount Bonds 1 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 5 Pure Discount Bonds 1 n 1 2 F 10000 i 1 1 5.41% P 9000 N I PV

PMT FV 2 ? 5.41% 9,000 0 -10,000 6 Bonds Trading at Par Bond Pricing Principle #1: (Par Bonds) If a bonds price equals its face value, then its yield-to-maturity = current yield = coupon rate. Proof: n n pmt 1 1 P 1 F

& P F i 1 i 1 i 1 n pmt 1 n pmt P 1 1 P F 1 i i 1 i i 7 First Solution Method 960 890 810

1000 100 P 100 100 1000 1000 1000 P $1076.00 8 Second Solution Method 1 1 1,000 i0,1 1 4.17% 960 i0, 2 1 2 1,000 1 6.00% 890 1 3 1,000 i0,3 1 7.28%

810 100 100 1000 100 P 2 1.0417 1.0600 1.07283 P $1,075.91 9 The YTM of the Coupon Bond N I PV PMT 3 ? -1076 100 7.10% 10 FV 1000

n n x 1 1 f &i 0&n 0& x 0 p 1 i 1 i 1 i x n p x 1 i 1 i n

f p 1 p1 i f 1 n p 1 i 1 f p 1 & 1 0 n p 1 i 1

11 n n x 1 1 f &i 0&n 0& x 0 p 1 i 1 i 1 i 1 1 1 i n 1 1 x 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 1400.00 Price 13 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 1200.00

Price 14 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% 0 5 10 15 15 Years to Maturity 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% 0 5 10 16 years to maturity 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% 0 5 10 Years 15 17 20 20-Year Bond Value Over Time 1060 1040 1000

980 960 940 920 20 15 10 Time to Maturity 5 18 0 Value 1020

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