LECTURE5

# LECTURE5 - Lecture 5 Lecture How to Value Bonds and Stocks...

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Lecture 5 Lecture 5 How to Value Bonds and Stocks

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Valuing Bonds How to value Bonds A bond bond is a certificate (contract) showing that a borrower owes a specified sum that will be repaid on a number of specified dates , along with a schedule of interest payments Pure discount bonds (zero coupon bonds) Level coupon bonds US government bonds Consoles
Pure discount bonds (zero coupon bonds) ( 29 T r F PV + = 1 A pure discount bond pure discount bond paying F in T years, when the annual interest rate r in each 1,…,T year will have a value A discount bond discount bond of value PV paying F in T years has spot return ( T -year spot rate) 1 1 - = T PV F r A pure discount bond pure discount bond makes one payment (the face value ) at a specified date (the maturity date ). The face value is also called principal or denomination

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Level coupon bonds ( 29 ( 29 ( 29 ( 29 ( 29 T T r T T r F A C r F r C r C r C PV + + × = + + + + + + + + = 1 1 1 1 1 2 The value of a level coupon bond level coupon bond with face value F , coupon C and a maturity of T years will be, where r is the annual interest rate Most bonds issued by governments or corporations pay coupons C in addition to a face value F at maturity T
US government bonds A US government bond US government bond called “ 13 of November 1999 ” will have - a face value of \$1000 - an annual coupon of 13% of the face value \$ 130 - coupons paid in May and in November \$ 65 until November 1999 when the bond is redeemed for \$1000 Suppose - it is November 1995 , - the stated annual market rate is 10% , and hence the semi annual rate is 5% .

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US government bonds (continued) Date 96.5 96.11 97.5 97.11 98.5 98.11 99.5 99.11 Payment 65 65 65 65 65 65 65 65+1000 ( 29 ( 29 ( 29 ( 29 ( 29 95 . 1096 05 . 1 1000 65 05 . 1 1000 05 . 1 65 05 . 1 65 05 . 1 65 8 8 05 . 0 8 8 2 = + × = + + + + = A PV The cash flows from the bond would be The value of this bond is
Consoles r C PV = Consoles Consoles are bonds with no maturity date . The value of a console console with the coupon C at the interest rate r will be

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Interest rates Determining Yields from Bond Prices : The yield to maturity is the interest rate that equates the PV of the payments on the bond to the current bond price . Value of a bond depends inversely inversely on interest rate r . Coupons reflect interest rates at issue time. Coupon rate is the market interest rate at the issue time. If
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LECTURE5 - Lecture 5 Lecture How to Value Bonds and Stocks...

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