QUESTION $3(22$ MARKS$)$ Using the information provided below, answer the following questions. INFORMATION Patara Squibb Ltd $($PSL$),$ a company specialising in the production of various types of jewelry$-$including necklaces, bracelets, earrings, rings, brooches, pins, anklets, hair jewelry, cufflinks, and pendants$-$ is considering an investment in new equipment with a capital cost of R$8$ million. The equipment is expected to have a useful life of five years, at the end of which it would be sold for $\backslash (\backslash$mathrm$\{$R$\}900,000\backslash ).$ If the new equipment were to be purchased, the existing machine could be either sold immediately for $\backslash (\backslash$mathrm$\{$R$\}500,000\backslash )$ or leased to another company at a rental amount of R$200,000$ per annum, payable in advance, for three years. If the equipment is hired out rather than sold, it will have no residual value at the end of the three$-$year period. The existing equipment generates annual revenues of R$16$ million, and its running costs are R$1,680,000$ per annum. If the new equipment is purchased, revenues are expected to increase by $\backslash (20\backslash \%\backslash ).$ In addition to this, however, the running costs of the new equipment are also expected to increase. Estimates have shown that, in the first year with the new equipment, running costs will increase by $\backslash (18\backslash \%\backslash ).$ In every subsequent year thereafter, running costs will continue to be $\backslash (18\backslash \%\backslash )$ higher than each previous year's costs. PSL$\text{'}$s cost of capital is $10\backslash \%.$ All workings should be in R$\text{'}000.$ REQUIRED: $3\mathrm{.}1.$ Calculate the net present value of the proposed investment, over five years, and state with reasons whether the machine should be purchased. $3\mathrm{.}2.$ Calculate the Internal Rate of Return $($IRR$)$ of the investment $($round off answer to two decimal places$).3\mathrm{.}3.$ Calculate the Modified Internal Rate of Return $($IRR$)$ of the investment $($round off answer to two decimal places$).3\mathrm{.}4.$ State two $(2)$ factors that explain the importance of controlling capital expenditure at Patara Squibb Ltd$.$