# 05_Oheads - Lecture Notes 5 Valuing Bonds and Stocks...

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1 Lecture Notes 5 Valuing Bonds and Stocks Valuing bonds • A bond is a contract showing that a borrower owes: i. a specified sum ii. that will be repaid on a number of specified dates iii. along with a schedule of interest payments. 1. Zero coupon bonds • A pure discount or zero coupon bond makes one payment (the bond’s face value ) at a specified future date (the maturity date ). • A pure discount bond paying F in T years, when the annual mar- ket interest rate is r in each year 1,… T , will have a value (1) • A discount bond of value PV paying F in T years has spot return (2) PV F 1 r + () T ------------------- = r F -------   1 T / 1 =

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2 Example 1. Suppose a pure discount bond with a par value of \$100 and maturing in one year sells for \$93.46 while a similar two-year discount bond sells for \$84.17. What are the current one- and two-year spot rates of interest? and 2. Level coupon bonds • Most bonds pay coupons (typically constant and uniform) in ad- dition to a face value (or principal or denomination ) at maturity. • If the interest rate is r , the value of a level-coupon bond with face value F , coupon C and a maturity of T years will be (3) Example 2. What is the PV of a two-year \$100 par value bond paying 10% semi-annually if the current stated rate is 8% com- pounded semi-annually (the effective semi-annual return is 4%)? r 1 100 93.46 -------------   1 –7 % == r 2 100 84.17 12 / 1 –9 % PV C 1 r + ----------- C 1 r + () 2 ------------------ C 1 r + T ------------------- F 1 r + T ++ CA r T F 1 r + T + 5 1.04 t ---------------- t 1 = 4 100 1.04 4 ----------------- + 103.6299
3 3. US government bonds • A US Treasury bond called a “13 of November 2004” will have: i. a face value of \$1000 ii. an annual coupon of \$130 (13% of the \$1,000 face value) iii. coupon paid as \$65 in May and \$65 in November until iv. November 2004 when the bond is redeemed for \$1,000. • Suppose the coupon due November 2000 has just been paid, and the stated annual market rate is 10%, so the effective semi-annu- al rate is 5%. The cash flow from the bond would be: yielding a PV ( quoted as 109.6 30 / 32 ), which can be calculated by or . Table 1: Payments on a 13 of November 2004 from November 2000 date 5/01 11/01 5/02 11/02 5/03 11/03 5/04 11/04 payment \$65 \$65 \$65 \$65 \$65 \$65 \$65 \$1,065 PV 65 1.05 i ----------- i 1 = 8 1000 1.05 8 ------------ + 1096.9482 == 65 A 0.05 8 1000 1.05 8 + 65 6.4632 () 1000 0.6768 +

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4 • Treasury bonds mature in more than 7 years, Treasury notes in one to seven years. • One feature of Treasury bonds we shall ignore is that they are callable at par 5 years before maturity. • Treasury notes, like bonds, pay interest semi-annually. • Treasury bills are even shorter term US obligations, issued on a discount basis and redeemed at face value, without interest, on the date of maturity. 4. Consols Consols are bonds that do not have a maturity date. If the coupon is C and the interest rate is r the value of the consol will be (4) 5. Bond values and interest rates • From (1), (3) and (4), the value of a bond depends inversely on r . Coupons reflect interest rates at issue time. If market rates rise, a bond sells at a discount . If rates fall, a bond sells at a premium .
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## This note was uploaded on 12/20/2011 for the course ECON 448 taught by Professor Bejan during the Spring '06 term at Rice.

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05_Oheads - Lecture Notes 5 Valuing Bonds and Stocks...

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