448_05StocksBonds

# 448_05StocksBonds - Lecture Notes 5 Valuing Bonds and...

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34 Lecture Notes 5 Valuing Bonds and Stocks Valuing bonds • A bond is a certificate showing that a borrower owes a specified sum that will be repaid on a num- ber of specified dates along with a schedule of interest payments. • A pure discount or zero coupon bond makes a single payment at a specified future date. The pay- ment date is also called the maturity date of the bond, and the bond is said to mature or expire on that date. The payment at maturity is termed the bond’s face value . • If a pure discount bond pays a face value of F in T years time and the market interest rate is r in each of the years up to the maturity date, the value of the bond will be (1) Example . Suppose a pure discount bond with a par or face 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? To answer this question, we need to solve (1) for the interest rate r . For the one-year bond, we have (2) so the one-year rate is approximately 7%. For the two-year bond, we have (3) so the two-year rate is approximately 9%. • Most bonds offer cash payments, or coupons , in addition to a fixed payment at maturity. Typical- ly, these coupon payments are constant. The fixed payment at maturity in this case is sometimes PV F 1 r + () T ---------------- = 1 r + F ------- 100 93.46 ------------- 1.0699765 == = 1 r + 2 F 1 r + 100 84.17 1.089987 =

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35 also called the principal or denomination of the bond. Bonds issued in the US typically have face values of \$1,000. • If the market interest rate is r , the value of a level-coupon bond with a face value of F , a coupon payment of C and a maturity of T years will be . (4) • When examining bond values it is important to note the distinction between the stated annual in- terest rate and the effective annual interest rate. In particular, interest on US government bonds is paid twice a year. Thus, consider the following example. If it is November 1995, a US Bond that is called a “13 of November 1999” will have an annual coupon payment of \$130 (13% of the \$1,000 face value) paid out as \$65 in May and \$65 in November until November 1999, at which date the bond is redeemed for its face value of \$1,000. The cash flow from the bond would be: Now suppose the stated annual interest rate is 10 percent. The effective semi-annual rate will be 5 percent. The value of the bond will therefore be (5) which would be quoted as 109.6 15 / 16 . The effective annual interest rate corresponding to this stat- ed rate of 10% will be (1.05) 2 -1 = 0.1025 or 10.25%. • Equation (5) also can be evaluated using the tables in the appendix to the text. For this purpose, we write (5) as (6) Table 1: Payments on a 13 of November 1999 from November 1995 date 5/96 11/96 5/97 11/97 5/98 11/98 5/99 11/99 payment \$65 \$65 \$65 \$65 \$65 \$65 \$65 \$1,065 PV C 1 r + --------- C 1 r + () 2 ---------------- & C 1 r + T F 1 r + T ++ CA r T F 1 r + T + == 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 + 1096.908 =
36 where the first term in (6) is obtained with the help of appendix table A.2 and the second term with the help of appendix table A.1.

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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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448_05StocksBonds - Lecture Notes 5 Valuing Bonds and...

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