You are working for an Unnamed Coal Mining company in Colorado $($UCM$).$ The company has recently been approached by the Electric Company with a request to supply coal for its electric generators for the next four years. Since UCM does not have any excess capacity, they are considering opening a new mine on $5,000$ acres of land purchased $10$ years ago for $$4$ million. Based on a recent appraisal, the company feels it could receive $$6\mathrm{.}5$ million on an after$-$tax basis if it sold the land today.

UCM is following all current sustainability standards and therefore needs to buy equipment to restore the land to its original condition after mining it $($this is commonly referred to as reclaiming the land$).$ This equipment will cost $$95$ million and will be depreciated on a seven$-$year MACRS schedule. The contract runs for four years $$ after that the company feels that the equipment can be sold for $60\%$ of its initial purchase price. However, UCM plans to open another mine at that time and will use the equipment at the new mine.

The contract calls for the delivery of $500,000$ tons of coal per year at a price of $$86$ per ton. UCM feels that coal production will be $620,000$ tons, $680,000$ tons, $730,000$ tons, and $590,000$ tons, respectively, over the next four years. The excess production will be sold at an average of $$77$ per ton in the spot market. Variable costs amount to $$31$ per ton, and fixed costs are $$4,100,000$ per year. The mine will require a net working capital investment of $5$ percent of sales. The NWC will be built up in the year prior to the sales.

UCM will be responsible for reclaiming the land at termination of the mining. This will occur in Year $5.$ It is estimated the cost of reclamation will be $$2\mathrm{.}7$ million. UCM faces a $25$ percent tax rate and has a $10$ percent required return on new mine projects. Assume that a loss in any year will result in a tax credit.

You have been approached by the president of the company with a request to analyze the project. Calculate the payback period, profitability index, net present value, and internal rate of return for the new mine. Should UCM take the contract and open the mine?