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FinancialManagement Chapter 9 Theory and Practice Tenth Edition Bonds and their Valuation Eugene F. BrighamMichael C. Ehrhardt Instructor: Sanam Taimoor Institute of Business Management
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Topics• Bonds and bond’s characteristics• Types of bonds• Bond Valuation• Yield to Maturity• Calculating YTM• Bond Price and Yield relationship
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BOND• A long term contract under which a borrower agrees to make payments of interest and principal on specific date, to the holders of the bond• Bond Indenture – Is a legal document that specifies both the rights of the bondholders and duties of the issuing corporation
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Types of Bonds• Treasury Bonds – Issued by the government• Corporate Bonds – Issued by companies• Municipal Bonds – Issued by local governments• Foreign Bonds – Issued by foreign governments or companies
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Characteristics of a Bond• Par Value – the stated face value of a bond• Coupon Interest Rate – the fixed “rate of interest” which remains the same throughout the life of the bond• Maturity Date – Specified maturity date on which par value must be paid• Call Option – It gives the issuer the opportunity to repurchase the bonds prior to maturity
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Other Types of Bonds• Floating Rate Bonds• Zero Coupon Bonds• Perpetual Bonds• Convertible Bonds
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Bond Valuation VB INT PVIFA kd , N M PVIF kd , NINT = Coupon InterestM = Par valueKd = Market rate of interestN = Number of years before the bond matures
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Example• Bond C has a $1,000 face value and provides an 8% annual coupon for 30 years. The appropriate discount rate is 10%. What is the value of the coupon bond? – VB = $80 (PVIFA10%, 30) + $1,000 (PVIF10%, 30) = $80 (9.427) + $1,000 (.057) = $754.16 + $57.00 = $811.16.
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Perpetual Bond Example• Bond P has a $1,000 face value and provides an 8% coupon. The appropriate discount rate is 10%. What is the value of the perpetual bond? I VB kd VB = $80 / 10% = $800
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Zero Coupon Bond Example• Bond Z has a $1,000 face value and a 30-year life. The appropriate discount rate is 10%. What is the value of the zero-coupon bond? M VB n M PVIF kd , N 1 kdV = $1,000 (PVIF10%, 30) = $1,000 (.057) = $57.00
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Semi Annual Compounding• Some Bonds pay interest twice a year• Adjustments needed – Divide kd by 2 – Multiply N by 2 – Divide INT by 2
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Semi Annual Compounding Example• Bond C has a $1,000 face value and provides an 8% semiannual coupon for 15 years. The appropriate discount rate is 10% (annual rate). What is the value of the coupon bond? – VB = $40 (PVIFA5%, 30) + $1,000 (PVIF5%, 30) = $40 (15.373) + $1,000 (.231) = $614.92 + $231.00 = $845.92
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Yield to Maturity• The rate of return (Kd) that investors earn if they buy a bond at a specified price and hold it until maturity• In other words it is the rate of interest that sets the present value of the bond’s expected future cash-flow stream equal to the bond’s current market price
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Calculating YTM Consider a $1,000 par value bond with thefollowing characteristics : a current market price of $ 761; 12 years until maturity and an 8% coupon rate . What is the YTM?
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Calculating YTM• YTM Solution (Interpolate) b a A YTM a A B a = Lower interest rate b = Higher interest rate A = Value at lower rate B = Value at higher rate• Answer: 12.90%
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Calculating YTM• Julie Miller want to determine the YTM for an issue of outstanding bonds at Basket Wonders (BW). BW has an issue of 10% annual coupon bonds with 15 years left to maturity. The bonds have a current market value of $1,250.• 7.40%
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Bond Price- Interest Rate Relationship• A bond’s price and interest rates are inversely related; – When interest rates rise, bond’s price falls – When interest rates fall, bond’s prices rises
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Bond Price- Interest Rate Relationship 1600BOND PRICE ($) 1400 1200 1000 5 Year 600 15 Year 0 0 2 4 6 8 10 12 14 16 18 Coupon Rate MARKET REQUIRED RATE OF RETURN (%)
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Bond Price- Interest Rate Relationship• Assume that the required rate of return on a 15-year, 10% coupon-paying bond rises from 10% to 12%. What happens to the bond price?• When interest rates rise, then the market required rates of return rise and bond prices will fall
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Bond Price- Interest Rate Relationship 1600 1400BOND PRICE ($) 1200 1000 5 Year 600 15 Year 0 0 2 4 6 8 10 12 14 16 18 Coupon Rate MARKET REQUIRED RATE OF RETURN (%)
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Bond Price- Interest Rate Relationship• Assume that the required rate of return on a 15-year, 10% coupon-paying bond falls from 10% to 8%. What happens to the bond price?• When interest rates fall, then the market required rates of return fall and bond prices will rise.
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Bond Price- Interest Rate Relationship 1600 1400BOND PRICE ($) 1200 1000 Par 5 Year 600 15 Year 0 0 2 4 6 8 10 12 14 16 18 Coupon Rate MARKET REQUIRED RATE OF RETURN (%)
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Bond Price- Interest Rate Relationship• Discount Bond -- The market required rate of return exceeds the coupon rate (Par > P0 ).• Premium Bond -- The coupon rate exceeds the market required rate of return (P0 > Par).• Par Bond -- The coupon rate equals the market required rate of return (P0 = Par).
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