Respond to the following questions appropriately.

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 f1 11.53% [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]10 An investment project has been evaluated using Monte Carlo simulation. After running the simulation 2.5 million times, the results have stabilised and the expected net present value is positive and averages $1 million, with a range of outcomes varying from minus $200,000 to plus $1.8 million. Which of the following statements best interprets these results? A The project satisfies the net present value criterion. B The project should definitely proceed. C This is a low risk project. D The model should be run another 2.5 million times in order to be certain. [2] 11 Joan is an actuarial consultant who has operated as a sole trader for several years. She has decided to bring Frank, a colleague, into the business. Describe the advantages to Joan of a traditional partnership over a limited company for the business arrangement with Frank. [5] Describe the usefulness of bank overdrafts in managing a company's working capital requirements. [5] 13 Describe why quoted companies are required to disclose their diluted earnings per share (EPS). [5]