Answer ALL the questions. $[100$ MARKS$]$ QUESTION ONE $(20$ Marks$)$ INFORMATION Mantengu Limited is planning to acquire new machinery to increase its production capacity. It is considering the following $2$ options: Option A The machine can be purchased in South Africa for a purchase price of R$2000000.$ A further R$200000$ will have to be spent on transport and installation of the machine in its factory. This machine is expected to have a useful life of five years after which it can be sold for R$60000.$ The machine is expected to generate the following net cash inflows over the next five years: Year Net cash inflow R $15250002550000358000046250005660000$ Option B The machine can be imported from Nigeria and is expected to cost R$1800000.$ The machine will have a useful life of five years and will have no scrap value. The machine will result in a net cash inflow of R$500000$ per year. Other information: The company has a cost of capital of $10\%.$ The company pays tax at $27\%.$ All machinery is depreciated on a straight$-$line basis over its useful life. REQUIRED: $1\mathrm{.}1$ Calculate the payback period for option A and option B$.(4$ marks$)($answer to be reflected in years and months$)1\mathrm{.}2$ calculate the net present value for option A and option B$.(7$ marks$)($use discount factors to $4$ decimal places as found in your module guides$)1\mathrm{.}3$ Calculate the profitability index of option A and option B $($round off to $2$ decimal places$)(2$ marks$)1\mathrm{.}4$ Calculate the accounting rate of return on average investment for option A $($answer to be rounded to $2$ decimal places$)(3$ marks$)1\mathrm{.}5$ Calculate the internal rate of return for option B$.(3$ marks$)($use the interpolation method with $2$ consecutive percentages$)($answer to be rounded to $2$ decimal places$)1\mathrm{.}6$ Based on the net present value calculated which option$/$s should be chosen if these are mutually exclusive options. $(1$ m