Question

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	103.5423	103.5301	+.3261	5.939
6.102	May 31	104.4913	104.6370	+.4257	??
6.148	May 41	??	??	+.5366	3.971

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 .0644, what is the bid price in dollars? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:-

1. Calculation of Ask price of bond:-

Face value = $1,000

Coupon rate = 6.148%

Semi-annual coupon amount = $1,000 * 6.148% * ½ = $30.74

Years to maturity = May 2019 to May 2041 = 22 years

Semi-annual periods to maturity (n) = 22 years * 2 = 44

Yield on the bonds = 3.971%

Semi-annual yield (r) = 3.971%/2 = 1.9855% = 0.019855

Price of bond = Present value of remaining coupon payments + Present value of face value

Present value of annuity = Annuity*{1-(1+r)^-n}/r

Present value of annuity of remaining 44 coupon payments = $30.74*(1-1.019855)^-44)/0.019855 = $30.74*29.1601 = $896.38

Present value of face value = $1,000/1.019855^44 = $1,000/2.3751 = $421.03

Price of bond = $896.38+$421.03 = $1,317.41

Ask price of bond = $1,317.41

2. Calculation of Bid price :-

Bid ask spread = 0.0644

Bid price = $1,317.41 - $0.0644 = $1,317.35

Bid price = $1,317.35

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