4. A company is considering an investment in a mine that starts in 1-year. The mine is located in northern Norway thus transportation and production costs are high, esti- mated at $30/gram of gold. This includes getting the gold out of the ground, refining it, and selling the refined product. It will cost the company $1,000,000 today to begin the mine which will produce 800 000 grams of gold in 1-year. The current spot price of gold is 29.8441$/gram. The one-year forward price of the gold is $31.5. The one-year risk-free rate is 5.4% and your best analysis says that the price of gold in one-year will be either $29/gram and $35/bbl. Assume for simplicity all the gold that will be mined can be sold at the start of production, there are no storage costs, and the mine can be shutdown without cost. (a) What is the risk risk-neutral probability of an up-movement in the gold price? Explain how this is related to the forward price. (b) What is the value of this mine using the risk-neutral approach? (c) Explain why this is a real option approach? Why is delay valuable even though investing today? (d) Calculate the value using the standard NPV approach if you invested in the project today and could not shut the mine down