(Total 100 marks) 6. (a) Assume that you have a coal mine, and the most recent valuation of the mine was 7.8 million. Due to the increasing demand for coal, the price of similar mines has grown by 10% with an annual standard deviation of 20%. A buyer has recently approached you and wants an option to buy the mine in the next 12 months for 8 million. The risk-free rate of interest is 5% per year, compounded continuously. Required: i. What are the di and d2 of this option? (Rounding to four decimal places) (20 marks) ii. What are the cumulative probabilities of N(di) and N(dz)? (Rounding to four decimal places) (10 marks) How much should you charge for the call option? (Rounding to two decimal places) (20 arks) iii. (b) Discuss the possible reasons used to justify mergers and acquisitions. (500 words limit) (50 marks) (Total 100 marks)