Bethesda Mining is a midsized coal mining company with $20$ mines located in Ohio, Pennsylvania, West Virginia, and Kentucky. The company operates deep mines as well as strip mines. Most of the coal mined is sold under contract, with excess production sold on the spot market.

The coal mining industry, especially high$-$sulfur coal operations such as Bethesda, has been hard$-$hit by environmental regulations. Recently, however, a combination of increased demand for coal and new pollution reduction technologies has led to an improved market demand for high$-$sulfur coal. Bethesda has just been approached by Mid$-$Ohio Electric Company with a request to supply coal for its electric generators for the next four years. Bethesda Mining does not have enough excess capacity at its existing mines to guarantee the contract. The company is considering opening a strip mine in Ohio on $5,000$ acres of land purchased $10$ years ago for $$5\mathrm{.}4$ million. Based on a recent appraisal, the company feels it could receive $$7\mathrm{.}3$ million on an aftertax basis if it sold the land today.

Strip mining is a process where the layers of topsoil above a coal vein are removed and the exposed coal is removed. Some time ago, the company would simply remove the coal and leave the land in an unusable condition. Changes in mining regulations now force a company to reclaim the land; that is$,$ when the mining is completed, the land must be restored to near its original condition. The land can then be used for other purposes. As they are currently operating at full capacity, Bethesda will need to purchase additional equipment, which will cost $$43$ million. The equipment will be depreciated on a seven$-$year MACRS schedule. The contract only runs for four years. At that time the coal from the site will be entirely mined. The company feels that the equipment can be sold for $60$ percent of its initial purchase price. However, Bethesda plans to open another strip 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 $$60$ per ton. Bethesda Mining feels that coal production will be $750,000$ tons, $810,000$ tons, $830,000$ tons, and $720,000$ tons, respectively, over the next four years. The excess production will be sold in the spot market at an average of $$48$ per ton, Variable costs amount to $$21$ per ton and fixed costs are $$3\mathrm{.}7$ million 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.

Bethesda will be responsible for reclaiming the land at termination of the mining. This will occur in Year $5.$ The company uses an outside company for reclamation of all the company$$s strip mines. It is estimated the cost of reclamation will be $$3\mathrm{.}9$ million. After the land is reclaimed, the company plans to donate the land to the state for use as a public park and recreation area as a condition to receive the necessary mining permits. This will occur in Year $5$ and result in a charitable expense deduction of $$7\mathrm{.}3$ million. Bethesda faces a $38$ percent tax rate and has a $12$ percent required return on new strip mine projects. Assume 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. Answer the following:

$1.$ Calculate the payback period, and show your work in excel, showing the formula and answer. Explain how you got the answer and formula.

$2.$ Calculate the profitablitity index and show your work in excel, showing the formula and answer. Explain how you got the answer and formula.

$3.$ Calculate the net present value, and show your work in excel, showing the formula and answer. Explain how you got the answer and formula.

$4.$ Calculate internal rate of return for the new strip mine and show your work in excel, showing the formula and answer.

$5.$ Then answer the following: Should Bethesda Mining take the contract and open the mine? why or why not?