# Chapter 5 - Chapter 5 Valuing Stocks and Bonds Valuing...

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Chapter 5 Valuing Stocks and Bonds

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Valuing Bonds 1. Pure Discount Bonds Promise to pay a single cash payoff at some maturity date Key parameters: Time to maturity ( T ) = maturity date - today’s date Face value ( F ), Discount rate ( r ) T r F PV ) 1 ( + = Present value of a pure discount bond at time 0 0 0 \$ 1 0 \$ 2 0 \$ 1 - T F \$ T
Example of a pure discount bond Find the value of a 30-year zero-coupon bond with a \$1,000 par (face) value. The appropriate discount rate is 6%. 11 . 174 \$ 30 ) 06 . 1 ( 000 , 1 \$ ) 1 ( = = + = T r F PV 0 0 \$ 1 0 \$ 2 0 \$ 29 000 , 1 \$ 30

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2. Level-Coupon Bonds Promise of a regular coupon payment each period plus face value (i.e., principal) repayment at maturity Key parameters: Coupon payment dates and amounts (C) Time to maturity (T), Face value (F) Discount rate (r) T r F T r r C PV ) 1 ( ) 1 ( 1 1 + + + - = Value of a Level-coupon bond = (PV of coupon payment annuity) + ( PV of F) 0 C \$ 1 C \$ 2 C \$ 1 - T F C \$ \$ + T
Example of a Level-Coupon Bond Find the present value (as of 1/1/2002), of a 6-3/8% coupon T-bond with semi- annual payments, maturity date of 12/31/2009, assume effective annual r = 5.0625%,  semiannual r of 2.5% 6-3/8 coupon means (.06375/2) x \$1000 = \$31.875 semiannual interest 02 / 1 / 1 875 . 31 \$ 02 / 30 / 6 875 . 31 \$ 02 / 31 / 12 875 . 31 \$ 09 / 30 / 6 875 . 031 , 1 \$ 09 / 31 / 12 75 . 089 , 1 \$ 16 ) 025 . 1 ( 000 , 1 \$ 16 ) 025 . 1 ( 1 1 025 . 875 . 31 \$ = + - = PV

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Bond Concepts Interest Rates and Bond Prices Since value of a bond is a present value, if r then denominator in PV formula, thus bond value (esp. for bonds with distant maturity date) Example : Consider a bond that pays \$95 interest at date 1 and date 2 and also repays \$1,000 principal (face value) at date 2 Value if r=.10 is: (95/1.10) + (1,095)/(1.10)2 = \$991.3 (sells at a discount ) Value if r=.08 is: (950/1.08) + (1,095)/(1.08)2 = \$1,026.7 (sells at a premium )
Yield to Maturity Definition : The yield to maturity (YTM) of a bond is the discount rate that makes the present value equal to the current bond price Example : Consider a bond that pays \$300 at date 1 and date 2 and also repays \$1,000 principal (face value) at date 2. The bond currently sells for \$1,200. What is it’s YTM? 1,200 = 300/(1+r) + 1,300/(1+r)2 .1733 = r So YTM is 17.33%

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Default risk is likelihood that a borrower will not make the promised payments Because of default risk, corporate bonds offer higher yields than government bonds; the difference is known as the default risk premium Private firms evaluate default risk and assign a credit rating, charging borrowers a one-time fee prior to the release of the rating. (1) Moody’s
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## This note was uploaded on 10/17/2011 for the course ECON 101 taught by Professor Thompson during the Spring '11 term at Michigan State University.

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Chapter 5 - Chapter 5 Valuing Stocks and Bonds Valuing...

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