Chapter 5 - 1 Chapter 5 Introduction to the Valuation of...

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Unformatted text preview: 1 Chapter 5 Introduction to the Valuation of Debt Securities 2 General principles of valuation Price of a security (or asset) = PV of the securitys expected cash flows discounted at an interest rate appropriate for its risk level Tradeoff between expected rate of return and risk Time value of money This is what we have learned in ADMS3530 3 General principles of valuation Valuation is the process of determining the fair value of a financial asset. It involves the following three steps : Step 1 : Estimate the expected cash flows Could be difficult for bonds with embedded options (e.g., call, prepayment, put, and conversion options etc.) and for floating rate securities This chapter : Valuation of option free bonds Chapter 9 : Valuation of bonds with embedded options Chapter 12 : Valuation of mortgage backed and asset backed securities 4 General principles of valuation Valuation ( continued from previous slide ): Step 2 : Determine the appropriate interest rate (or interest rates) used to discount the cash flows We use the on the run Treasury yield for a security issued by the U.S. government; for non- U.S. government securities, we add a yield premium over the on the run Treasury yield Step 3 : Calculate the present value (or the discounted value ) of the expected cash flows in Step 1 using the interest rate (or discount rate ) in Step 2 5 Bond valuation A zero coupon bond pays no interest (coupon), only repays its face value at maturity 54 . 385 $ = + = 10 10%) (1 $1,000 bond the of price 10%, of rate interest annual an bond, coupon- zero year - 10 a example, For $1,000) e.g., bond, the of value face the (i.e., flow cash single a of PV the is price its So 6 Bond valuation Fixed rate bonds : pay coupons until its maturity date and the coupon rate is fixed First, suppose the bond pays coupon once per year (i.e., annually ) Consider a 3 year bond pays an annual coupon of $75 (i.e., coupon rate is 7.5% = $75 / $1,000), a face value of $1,000, and the annual interest rate is 6% ( see the next slide for the timeline of the bond cash flows ) 7 Bond valuation Fixed rate bonds The timeline of the bond cash flows (time in years ) 1 2 3 $75 $75 $75 1 2 3 $1,000 Coupons Face value 8 Bond valuation Fixed rate bonds This bond is equivalent to a 3-year annuity of $75 and a single payment of $1,000 in 3 years. So the price of this bond is: 10 . 040 , 1 $ 62 . 839 $ 48 . 200 $ 62 . 839 $ 673 . 2 75 $ ) 06 . 1 ( 000 , 1 $ ] 1 r 1 ] ) r 1 ( r 1 r 1 3 t = + = + = + + + - = + + +- = 3 t 0.06) (1 0.06 0.06 1 [ $75 Price ) ( value Face [ Coupon Price 9 Bond valuation Fixed rate bonds So far, we have assumed annual coupons ....
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Chapter 5 - 1 Chapter 5 Introduction to the Valuation of...

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