Question

7. A $1000 callable bond will be redeemed in either 8, 9, or 10 years; the actual redemption date is unknown to the purchaser. The bond pays semiannual coupons with a coupon rate of 6%. An investor buys this bond at a price to yield at least 7%. Find the purchase price of the bond.

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Answer 1

Actually in this case there is not a fix time of maturity or redemption here we can try at each maturity period is given.

Face value = $ 1000 ( assumed)

Redemption value = $ 1000

coupon rate = 6% annually or 3 % Semi- annually

yield rate = 7 % annually or 3.5 % semi - annually

semi-annually interest = $ 1000 * 3 % = $ 30

If maturity period is 8 year

Value of bond = interest * PVAF (3.5% ,8 years) + Redemption Value * PVF (3.5% , 8 year)

= $ 30 * 6.8739 + $ 1000 * 0.7594

= $ 206.22 + $ 759.41

= $ 965.627  

If maturity value is 9 year

Value of bond = interest * PVAF (3.5% ,9 years) + Redemption Value * PVF (3.5% , 9 year)

= $ 30 * 7.6077 + $ 1000 * 0.7337

= $ 961.93

If maturity value is 10 year

Value of bond = interest * PVAF (3.5% , 10 years) + Redemption Value * PVF (3.5% , 10 year)

= $ 30 * 8.3166 + $ 1000 * 0.7089

= $ 758.398

At different maturity , there are different value of bond , therefore investor take decision accordingly.