Lecture+7

# Lecture+7 - I nterest Rates and Bond Valuation by Diep...

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Interest Rates and Bond Valuation by Diep Duong

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Outline Bonds and Bond Valuation More about Bond Features Term Structure of Interest Rate Inflation and Interest Rates Bond Ratings Some Different Types of Bonds Bond Markets
Bond Definitions Bond is a debt security, a class of financial asset Bond issuer is borrower and has to pay to the bond holder + Coupon payments: Periodic interests (periodic equal payments) + The Principal or Par Value or Face Value Coupon rate: similar to interest rate which is the percentage of the principal (usually semi-annually) Maturity date: The date that the bond finishes and paid off Yield or Yield to maturity: The rate required in the market on a bond (Market Discount Rate)

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Bond Valuation and PV Model Bond is a financial asset which is bought and sold Why buys bond ? Why do you want to own bond ? A reminder: Financial Asset generates future income. Bond is a typical example Owner of bond owns the future cash flows. What are they ? Asset Pricing: How much is this asset valued? Market Value ? If bond market value = PV of future cash flows Bond Value = PV of coupons + PV of par Bond Value = PV of annuity + PV of lump sum
The Bond Pricing Equation t t r) (1 FV r r) (1 1 - 1 C Value Bond + + + = ANNUITY, PAYMENT PER PERIOD =C, t periods PV OF SINGLE FUTURE CASH FLOW If we know discount rate r then we have the formula If this is market value, r is the key in pricing. We call it Yield to Maturity (YTM) or Yield

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Valuing a Discount Bond with Annual Coupons Consider a bond with a coupon rate of 10% and annual coupons. The par value is \$1,000, and the bond has 5 years to maturity. The yield to maturity is 11%. What is the value of the bond? Using the formula: B = PV of annuity + PV of lump sum B = 100[1 – 1/(1.11) 5 ] / .11 + 1,000 / (1.11) 5 B = 369.59 + 593.45 = 963.04 Price of the bond is lower than it’s face value, so called discount bond
Valuing a Premium Bond with Annual Coupons Suppose you are reviewing a bond that has a 10% annual coupon and a face value of \$1000. There are 20 years to maturity, and the yield to maturity is 8%. What is the price of this bond? Using the formula: B = PV of annuity + PV of lump sum B = 100[1 – 1/(1.08)20] / .08 + 1000 / (1.08)20 B = 981.81 + 214.55 = 1196.36 Price of the bond is higher than it’s face value, so called premium bond

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Graphical Relationship Between Price and Yield-to-maturity (YTM ) 600 700 800 900 1000 1100 1200 1300 1400 1500 0% 2% 4% 6% 8% 10% 12% 14% Bond Price Yield-to-maturity (YTM) Coupon rate = 8% with annual coupons; Par value = \$1,000; Maturity = 10 years
Bond Prices: Relationship Between Coupon and Yield If YTM = coupon rate, then par value = bond price If YTM > coupon rate, then par value > bond price Why? The discount provides yield above coupon rate

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## This note was uploaded on 07/01/2010 for the course ECON 393 taught by Professor D during the Spring '10 term at Rutgers.

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Lecture+7 - I nterest Rates and Bond Valuation by Diep...

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