A company is set up to refurbish old mills and turn them into retail outlets. The company purchases 5 mills each costing half a million pounds. One mill is purchased at the start of each of the next 5 years. The cost of refurbishment is $20,000 per mill and is payable continuously for one year after the purchase. Once the refurbishment for a particular mill is complete, retail stores pay rent to the company for the mill at a rate of f48,000 per year payable monthly in arrears. Each mill is sold 10 years after completion of its refurbishment for $600,000. The company employs a manager to run this project. She is paid $50,000 pa payable at the end of each month whilst the company has ownership of any of the mills. Calculate: (1) the net present value of the project assuming an interest rate of 4% pa effective [8] (ii) the discounted payback period [3] (Hii the accumulated profit on the day that the last mill is sold. [1] [Total 12](i) Explain what is meant by the "no arbitrage" assumption in financial mathematics. [2] (ii) A three-year forward contract is to be issued on a particular company share. The current market value of the share is $4.50 and a dividend of EO.20 per share has just been paid. The parties to the contract assume that the future quarterly dividends will increase by 1% per quarter-year compound for the first two years and by 1/2% per quarter-year compound for the final year. Assuming a risk-free force of interest of 5% per annum, and no arbitrage, calculate the forward price. [7]On 1 January 2006 an investor agrees to pay the fair price of $3,000 in four years* time for a security. The security pays no interest and the price of the security at the time of the agreement was (2,680. On 1 July 2007 the price of the security is $2,800. Calculate the value of the forward contract on 1 July 2007, assuming no arbitrage and a onstant risk-free force of interest over the four years