Question

QUESTION 8 (16 marks) (a) [5 marks] John purchases a $1000 face value 10-year bond with coupons of 8% per annum paid half-yearly. The bond will be redeemed at C. The purchase price is $800 and the exact present value of the redemption amount C is $301.5116. Calculate the redemption amount C, and state if the bond is redeemed at par, discount or premium. (Hint: a at 3% is 14.87747 ag at 4% is 13.59033, a at 5 % is 12.46221 and a at 6% is 11.46992) (b) [6 marks] Tony is considering to purchase a $1000 face value callable bond (the bond can be redeemed at any time during the agreed callable period). The bond pays coupons of 10% per annum half-yearly and matures at the end of 10 years, if not called. The bond is callable at the following periods for the following redemption amounts: C 1050; ends of years 4-6 C-900; ends of years 8-10. Find the minimum price that Tony annum convertible half-yearly. (Hint: you may find it helpful by trying to find the impact of redemption time on bond price first, given different values of C) can offer and still be certain of a yield rate of 10% per (c) [5 marks] Simon purchases a $1000 face value 10-year bond with 8% per annum half-yearly paid coupons. He can reinvest those coupons at a nominal rate of 6% per annum convertible half-yearly. The bond is redeemed at par. Coupon payments are taxed at 20%. Capital gains are taxed at 30%. There is no additional tax on reinvestment proceeds. Find the price Simon should pay for the bond to ear a yield of 8% per annum convertible half-yearly.

Answer 1

a. Redemption Amount = Present Value / (PVAF(4%,20) - PVAF(4%,19))

Redemption Amount = 301.5116 / (13.59033 - 13.13394)

Redemption Amount = 301.5116 / 0.45639

Redemption Amount = $660.6446

The Bond is redeemed at Discount as the redemption value is less than face value

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