The following 6.00% p.a. semi-annual coupon U.S. treasury bond has 2 years until maturity. Calculate the fair value of the bond (rounded to 2 decimal places), assuming the current market yield for this bond is 5.45%. The bond has a face value of $100.00.
Question
The following 6.00% p.a. semi-annual coupon U.S. treasury bond has 2 years until maturity. Calculate the fair value of the bond (rounded to 2 decimal places), assuming the current market yield for this bond is 5.45%. The bond has a face value of $100.00.
Solution
To calculate the fair value of the bond, we need to calculate the present value of the bond's future cash flows, which include the semi-annual coupon payments and the face value at maturity.
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First, we need to calculate the semi-annual coupon payment. The bond pays a 6.00% annual coupon rate, semi-annually, so each payment is 3.00% of the face value.
Coupon Payment = 100 * 3.00% = $3.00
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Next, we need to calculate the present value of these coupon payments. Since the bond has 2 years until maturity and pays semi-annually, there are 4 periods. The market yield is 5.45% per annum, so the semi-annual yield is 2.725%.
Present Value of Coupon Payments = 3.00 / (1 + 2.725%)^2 + 3.00 / (1 + 2.725%)^4 = $11.41
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We also need to calculate the present value of the face value, which will be received at the end of the 4th period.
Present Value of Face Value = 89.56
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Finally, we add these two present values together to get the fair value of the bond.
Fair Value of Bond = Present Value of Coupon Payments + Present Value of Face Value = 89.56 = $100.97
So, the fair value of the bond is approximately $100.97.
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