Your company is considering the purchase of a new machine to manufacture 100,000 widgets per year. The machine required to manufacture the widgets will cost $10M and it has a maximum expected life of 10 years. Funds to purchase the machine will need to be borrowed at an interest rate of 5%. Only the interest on the loan will be paid annually, with the principal to be paid back in full when production ceases to be profitable, or the machine is retired, whichever comes first. When production ceases the machine will be sold as scrap for recycling for an estimated amount of $2.5M. The costs of maintenance and material, and the income from sales, are all estimated to change linearly with time, as per the formulae in the table below (all values are in $million). Year Maintenance cost Material costs Sales $M $M $M N(>0) 0.5 + N*0.2 2 + N*0.1 10 - N*1 Additionally, factory overheads assigned to this line of production are fixed at $1M per year. If the rate of inflation is 3%, calculate; a) the number of years the machine should be utilised for production, and b) the net present value of the total profit generated after the machine is sold. Show all calculations. Your company is considering the purchase of a new machine to manufacture 100,000 widgets per year. The machine required to manufacture the widgets will cost $10M and it has a maximum expected life of 10 years. Funds to purchase the machine will need to be borrowed at an interest rate of 5%. Only the interest on the loan will be paid annually, with the principal to be paid back in full when production ceases to be profitable, or the machine is retired, whichever comes first. When production ceases the machine will be sold as scrap for recycling for an estimated amount of $2.5M. The costs of maintenance and material, and the income from sales, are all estimated to change linearly with time, as per the formulae in the table below (all values are in $million). Year Maintenance cost Material costs Sales $M $M $M N(>0) 0.5 + N*0.2 2 + N*0.1 10 - N*1 Additionally, factory overheads assigned to this line of production are fixed at $1M per year. If the rate of inflation is 3%, calculate; a) the number of years the machine should be utilised for production, and b) the net present value of the total profit generated after the machine is sold. Show all calculations