# 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

## Recently Viewed Presentations

• FRN301/Composition & Conversation 1/Reprise Chapitre 1 Il y a trois types de verbes réguliers: verbes en -er verbes en -ir verbes en -re je tu elle/il/on vous nous elles/ils Parler Finir Vendre Je parle Je finis Je vends Tu parles...
• National Certificate National Diploma Technical Certificate 6 units 12 units 18 units = 1 'A' level = 2 'A' levels = 3 'A' levels Entry to Vocational Qualifications Level 3 Entry Criteria Direct Entry - 16 year olds 5 GCSEs...
• The figure shown below is a hub which has multiple ports for connecting interfaces to a network. ... Two ways to enable multiple computers to share a public IP address are with a router that supports the Network Address Translation...
• Mathsmadeeasy.com - past papers (old spec) Past papers. Be aware of your target grade. Read the questions carefully. Show all working out. Please remember there are only 6 sets of AQA past papers and we have used some of them...
• Homeostasis and Transport Concentration The amount of solute in a solution. Often measured as a percentage. Deciding factor as to where particles move. Passive Transport Movement of particles that does not require energy.
• Idiom Dictionary Isabelle Evans Gwin Oaks Elementary Media Festival 2007 What is an idiom? An idiom is an expression whose meaning cannot be understood based on the definition of its constitutional elements He spilled the beans Get off my back!...
• First Age of Empires, Classical Greece, Ancient Rome and Early Christianity Pre-AP Unit #3 - Chapters 4-6 Constantine (272-337 A.D.) / Pope Constantine - Emperor of the Roman Empire during the 4th century A.D. , most famous for proclaiming official...
• Organizational Communication The most challenging task for managers ... word usage Channel used Content Characteristics of the sender and receiver Context Organizational Communication Do you hear what I'm saying? Use of multiple techniques, leads to interference and misinterpretations ...