Question

Problem 6-29 Bond Prices [LO 2] You find the following Treasury bond quotes. To calculate the number of years until maturity, assume that it is currently May 2019 and the bond has a par value of $1,000. Rate Maturity Mo/Yr Bid Asked Chg Ask Yld ?? May 26 103.5527 103.5405 +.3080 6.099 5.474 May 31 104.5017 104.6474 +.4353 ?? 6.188 May 41 ?? ?? +.5470 4.131 a. In the above table, find the Treasury bond that matures in May 2041. What is the asked price of this bond in dollars? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. If the bid-ask spread for this bond is .0559, what is the bid price in dollars? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

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Answer:

Given from the data Asked price= $1295.41 Bid price= $1294.86 Calculations:- Coupon rate of the bond =6.188% Time to mature =22 years. Semiannual interest amount = $1000*6.188%/2 = $30.94 Number of payments periods (N) = 22*2= 44 Half yearly ask yield (Yield)= 4.131%/2=2.0655% The bond coupon payments are semiannual, so the asked price is P= Semi-annual interest *PVIFA( Yield, N)+maturity value *PVIF(Yield, N) P= $30.94*PVIFA(2.0655%,44) + $1,000*PVIF(2.0655%,44) P= $30.94*28.72196+$1000*0.406748 P= $1295.41 Hence the asked price= $1295.41 The bid-ask spread is .0559. We also know the bid price must be less than the asked price, so the bid price will be Bid price =$1295.41 - 6.0559/100) ($1,000) Bid price = $1294.86