Hickock Mining is evaluating when to open a gold mine. The mine has 60,000 ounce

Question

Hickock Mining is evaluating when to open a gold mine. The mine has 60,000 ounces of gold left that can be mined, and mining operations will produce 7,500 ounces per year. The required return on the gold mine is 12 percent, and it will cost $14 million to open the mine. When the mine is opened, the company will sign a contract that will guarantee an after-tax cash flow of $500 per ounce and a 40 percent probability that the after-tax cash flow will be $410 per ounce. What is the value of the option to wait?

The answer is 169,382.21 but I need to know how to get to it. Thanks!

Explanation / Answer

The trick here is to realize that the option to wait is one year later, and we must discount the NPV 1 year for both states of waiting i.e. 60% and 40%. So Let us do it this way: First we must determine the life of the project 60,000 ounces left/7,500 per year production = 8 years Our revenues for each year is simply the price if we invest now ($450/ounce) x 7,500 qty = 3.375 million per year cash flow. Therefore we get the NPV of investing now by using these cash flows either through excel or financial calculator. CF0 = -14,000,000 this is our initial outlay CF1 = 3,375,000 cash flow for the first year F01 = 8 years frequency Discount rate (I) = 12% we get NPV to be $2,765,784.21 Now, assume that in one year the price will be 500, so we do the same thing and get the cash flows to be $500 x 7,500 = 3.750 million for each year. Using the same approach as before, we get the NPV to be 4,682,649.13. However, note that this is the NPV 1 year in the future, so we must discount this back 1 year using the discount rate of 12% to get the PV of the NPV = 4,132,722.43. Finally, we note that there is a 60% probability that we are getting this value so we just multiply it by 60% to get = 2,479,633.46. Again, we do the same exact thing for the price of $410 and probability of 40%. we get a final value of 455,532.96 Now we add the NPV of both states i.e. 60% and 40% or 2479633.46 + 455532.96 = 2,935,166.42 The value of our option will be the the Expected NPV of the two states - NPV investing now : 2935166.42 - 2765784.21 = 169,382.21 and this is what you were looking for. Enjoy and all the Best. Nayef

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