Nusantara Mining, a medium$-$sized coal mining entity, possesses $20$ mines spread across Sumatera Selatan, Kalimantan Timur, Kalimantan Selatan, and Kalimantan Utara. These mines encompass both deep and strip$-$mining operations. Primarily, the company sells its coal under contractual agreements, with surplus production being directed to the spot market. The coal mining sector, particularly high$-$sulfur coal ventures like Nusantara, has faced challenges due to environmental regulations. Nevertheless, recent developments, including heightened coal demand and advancements in pollution control technologies, have boosted the market for high$-$sulfur coal.Borneo Electric Company has approached Nusantara with a four$-$year coal supply request for its power generators. However, Nusantara lacks the excess capacity in its current mines to secure this contract. To address this, the company is contemplating opening a strip mine on a $5,000-$acre land parcel in Sumatera Selatan, acquired a decade ago for $$4$ million. Presently valued at $$6\mathrm{.}5$ million after taxes, this land presents an opportunity for expansion.Strip mining involves removing topsoil layers to access coal veins, and recent regulations mandate land reclamation post$-$mining. Nusantara intends to comply with these regulations, ensuring the land can be repurposed post$-$mining. Given its current operational capacity, Nusantara must procure additional equipment, costing $$95$ million and depreciated over seven years. Although the equipment is intended for the four$-$year contract, Nusantara plans to utilize it for a subsequent strip mine.The contract stipulates delivering $500,000$ tons of coal annually at $$86$ per ton. Nusantara anticipates producing $620,000,680,000,730,000,$ and $590,000$ tons over the next four years, with excess production sold on the spot market at $$77$ per ton. Variable costs per ton amount to $$31,$ with fixed costs totaling $$4,100,000$ annually. Additionally, a net working capital investment equivalent to $5$ percent of sales will be required, built up in the year preceding sales.Upon termination of mining operations in Year $5,$ Nusantara is obligated to reclaim the land, with an estimated cost of $$2\mathrm{.}7$ million. As part of permit agreements, the company will donate the reclaimed land for public park use in Year $6,$ resulting in a charitable expense deduction of $$6$ million. Subject to a $22$ percent tax rate, Nusantara demands a $12$ percent return on new strip mine ventures, with any losses generating tax credits.You have been approached by the president of the company with a request to analyze the project. Calculate:a$.$ The payback period, profitability index, net present value, and internal rate of return for the new strip mine. b$.$ Provide sensitivity chart for the coal prices, coal contract volume, fixed cost, variable cost, required return, and taxes.c$.$ Make scenario analysis based on three variables which have the most significant effect on the NPV$.$ Suppose that the worse and best conditions might happens with the followinginformation:VariablesWorseBestPrice$10\%$ decrease$15\%$ increaseCoal contract volume$15\%$ decrease$20\%$ increaseFixed cost$10\%$ increase$5\%$ decreaseVariable cost$5\%$ increase$5\%$ decreaseRequired return$10\%$ increase$10\%$ decreaseTaxes$3\%$ increase$2\%$ decrease$*$note: increase and decrease based on the current conditiond. Should Nusantara Mining take the contract and open the mine?