Question

You find the following Treasury bond quotes. To calculate the number of years until maturity, assume that it is currently May 2016. The bonds have a par value of $1,000. Rate Maturity Mo/Yr Bid Asked Chg Ask Yld ?? May 25 103.5449 103.5327 +.3287 5.979 6.202 May 30 104.4939 104.6396 +.4281 ?? 6.158 May 40 ?? ?? +.5392 4.011 In the above table, find the Treasury bond that matures in May 2040.

What is the asked price of this bond in dollars?

Asked price $ If the bid-ask spread for this bond is .0651, what is the bid price in dollars?

Answer 1

(a)-Asked Price of this Bond

Face Value of the bond = $1,000

Semi-annual Coupon Amount = $30.79 [$1,000 x 6.158% x ½]

Semi-annual Yield to Maturity = 2.0055% [4.011% x ½]

Maturity Period = 48 Years [(May 2016 to May 2040) x 2]

The Asked Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $30.79[PVIFA 2.0055%, 48 Years] + $1,000[PVIF 2.0055%, 48 Years]

= [$30.79 x 30.63882] + [$1,000 x 0.38554]

= $943.37 + $385.54

= $1,328.91

“Hence, the Asked Price for the Bond = $1,328.91”

(b)- Bid price in dollars

Bid price in dollars = Asked Price for the Bond – Change in bid-ask spread in Dollars

= $1,328.91 – [$1,000 x (0.0651 / 100)]

= $1,328.91 – 0.6510

= $1,328.26

“Therefore, the Bid price in dollars = $1,328.26”

NOTE

-The formula for calculating the Present Value Annuity Inflow Factor (PVIFA) is [{1 - (1 / (1 + r)ⁿ} / r], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.  

--The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)ⁿ], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.