Kindly provide answers to the following assignment
A fixed interest stock is redeemable at 106% in 15 years' time and pays interest at 9% pa payable half-yearly in arrears. Calculate the price an investor should pay to obtain a gross redemption yield of 9% pa. [2] Instead of purchasing the stock, the investor decides to agree a forward contract to buy the security in six years' time, immediately after the coupon payment then due. Calculate the forward price based on a risk-free rate of return of 6% pa effective and no arbitrage. The current price of the stock is that calculated in part (i). [3] Three years later, the price of the security is such that the gross redemption yield is still 9%. Calculate the value of the forward contract if the risk-free yield has not changed. [6] Calculate the yield obtained if the investor sold the forward contract after three years. [2] [Total 13]On 15 May 2007 the government of a country issued an index-linked bond of term 15 years. Coupons are payable half-yearly in arrears, and the annual nominal coupon rate is 4%. Interest and capital repayments are indexed by reference to the value of a retail price index with a time lag of 8 months. The retail price index value in September 2006 was 200 and in March 2007 was 206. The issue price of the bond was such that, if the retail price index were to increase continuously at a rate of 7% pa from March 2007, a tax-exempt purchaser of the bond at the issue date would obtain a real yield of 3% pa convertible half-yearly. (i) (a) Derive the formula for the price of the bond at issue to a tax-exempt investor. (b) Show that the issue price of the bond is (1 1 1.53%. [12] (ii) An investor purchases a bond at the price calculated in (i) and holds it to redemption. The retail price index increases continuously at 5% pa from March 2007. A new tax is introduced such that the investor pays tax at 40% on any real capital gain, where the real capital gain is the difference between the redemption money and the purchase price revalued according to the retail price index to the redemption date. Tax is only due if the real capital gain is positive. Calculate the real annual yield convertible half-yearly actually obtained by the investor. [7] [Total 19]A loan of nominal amount of $100,000 is to be issued bearing interest payable quarterly in arrear at a rate of 8% pa. Capital is to be redeemed at $105% on a coupon date between 15 and 20 years after the date of issue, inclusive, the date of redemption being at the option of the borrower. (i) An investor who is liable to income tax at 40% and tax on capital gains at 30% wishes to purchase the entire loan at the date of issue. Calculate the price she should pay to ensure a net effective yield of at least 6% pa. [9] (ii) Exactly 10 months after issue the loan is sold to an investor who pays income tax at 20% and capital gains tax at 30%. Calculate the price this investor should pay to achieve a net yield of 6% pa on the loan: (a) assuming redemption at the earliest possible date (b) assuming redemption at the latest possible date [6] (iii) Explain which price the investor should pay to achieve a yield of at least 6% pa. [2] [Total 17]
