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a corporate bond has 2 years to maturity, a coupon rate of 8%, a face value of $1,000 and pays coupons semiannually. The market interest rate for similar bonds is 9.5%.a. What is the bond's duration in years?b. If yields fall by 0.8 percentage points, what is the new expected bond price based on its duration (in $)?c. What is the actual bond price after the change in yields (in $)?d. What is the difference between the two new bond prices (in absolute $)?

Respuesta :

The bondholder receives a semi-annual coupon payment twice per year. The annual dividend is cut in half and distributed twice. Due to the concept of time value of money, the current price of a semi-annual bond is higher than that of an annual bond.

Bond's par value is $5,000;

the annual coupon rate is 6.1%;

the semi-annual coupon rate is 3.05%;

the semi-annual coupon rate is 3.05% of $5,000; and the number of years until maturity (n) is 8;

the annual YTM is 6.2%;

the semi-annual YTM (r) is 3.1%.

Bond price = Semi-Annual Coupon P V A F (r, n) + P a r V a l u e P V F (r, n) = $ 152.5 P V A F (3.1 %, 8) + $ 1 000 P V F (3.1 %, 8) = $ 152.5 6.99017 + $ 1 000 0.78330 = $4,982.50 Now the YTM decreases by 0.8 percent.

Thus, the semi-annual YTM (r) is 2.7% and the new annual YTM is 6.2% minus 0.8%.

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