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

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