a) A seven-year $1000 bond has a nominal rate of 8% per annum, with semiannual coupons, redeemable at par. The current market rate is 6% compounded semiannually. Find the price of the bond.
b) A ten-year callable bond with par value 1000 and annual coupons of 6%, has redemption value 1050 after 10 years and is callable for 1050 after coupons are paid at end of years 6,7,8,9. The purchase price is 1025. At the end of which year (6,7,8,9,10) is the lowest annual yield going to occur? Give reasons.
Question - (a)
Answer -
Calculation of the price of the bond
Particulars | Explanation | Amount ($) | |
I. | Present value of bonds interest payments |
Bonds interest * PVAF of $1 _{(i%, n)} = [($1000 * 8%) * 6/12] * PVAF of $1 _{(3%, 14)} = $40 * PVAF of $1 _{(3%, 14)} = $40 * 11.29607 = $452 |
$452 |
II. | Present value of face value of bond |
Face Value of bond * PVIF of $1 _{(i%, n)} = $1000 * PVIF of $1 _{(3%, 14)} = $1000 * 0.66112 = $661 |
$661 |
Price of the bond | I + II | $1113 |
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