1. A loan of nominal amount $100,000 is to be issued bearing coupons payable quarterly in arrear at a rate of 5% per annum. Capital is to be redeemed at 103 on a single coupon date between 15 and 20 years after the date of issue, inclusive. The date of redemption is at the option of the borrower. An investor who is liable to income tax at 20% and capital gains tax of 25% wishes to purchase the entire loan at the date of issue.
Calculate the price which the investor should pay to ensure a net e ective yield of at least 4% per annum.
2. An investor purchased a bond with exactly 15 years to redemption. The bond, redeemable at par, has a gross redemption yield of 5% per annum eff ective. It pays coupons of 4% per annum, half yearly in arrear. Assume that the investor pays 25% income tax on coupons only.
(a) Calculate the price paid for the bond.
(b) After exactly eight years, immediately after the payment of the coupon then due, this investor sells the bond to another investor who pays income tax at a rate of 25% and capital gains tax at a rate of 40%. The bond is purchased by the second investor to provide a net return of 6% per annum e ffective.
i. Calculate the price paid by the second investor.
ii. Calculate, to one decimal place, the annual e ffective net rate of return earned by the first investor during the period for which the bond was held.