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A BBB-rated, $1000 face value, corporate bond has a yield to maturity of 8.2%. A U.S. Treasury security has a yield to maturity of 6.5%. These yields are quoted as APRs with semiannual compounding. Both bonds pay semiannual coupons at a rate of 7% and have five years to maturity. What is the price (expressed as a percentage of the face value) of the treasury bond?

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Answer:

Price of treasury bond in terms of percentage of face value is 102.106%

Explanation:

Given:

Face value (FV) = $1000

Coupon rate = 7% or 3.5% semi-annually

Coupon payment  (PMT) = 1000×0.035 = $35

YTM (rate) = 6.5% or 3.25% semi-annually

Maturity period (nper) = 5×2 = 10 periods

Using PV function to calculate price of treasury bond:

=PV(rate,nper,pmt,FV)

Price of bond is $1021.06 (it is negative as it is a cash outflow)

Price of bond in terms of percentage of face value = [tex]\frac{1021.06}{1000} \times100[/tex]

=102.106%

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