Question

You own a copper mine. The price of copper is currently €1.50 per pound. The mine produces 1 million pounds of copper per year and costs €2 million per year to operate. It has enough copper to operate for 100 years. Shutting the mine down would entail bringing the land up to environmental standards and is expected to cost €5 million. Reopening the mine once it is shut down would be an impossibility given current environmental standards. The price of copper has an equal (and independent) probability of going up or down by 25% each year for the next two years and then will stay at that level forever. Calculate the NPV of continuing to operate the mine if the cost of capital is fixed at 15%. Is it optimal to abandon the mine or keep it operating? Explain how you reach your conclusion and provide an estimate of the net present value of the company as a function of the year 2 copper price.

Answer 1

It is optimal to close down the mine since the cost of closing down is lesser than the probability of incurring more loss if the mine is operated.
Cost to be incurred for closing down the mine					5000000
The below workings project the prospective Loss/profit is the mine is operated for the next 2 years
Since the price increase of Copper mine is based on probability we need to take the probability of 0.5 while calculating Revenue
Since Cost of Capital is given as 15%, to arrive at the Present value, we need to consider the following
For year 1	0.869565217
For year 2	0.756143667
Calculation of Revenue :
Year	Adjustment factor		Rate	Probability	Revenue	PV of cost
Y1	0.869565217	1000000	1.875	0.5	937500	8,15,217.39
Y2	0.756143667	1000000	2.34375	0.5	1171875	8,86,105.86
						17,01,323.25
Calculation of Cost :
Year	Adjustment factor	Quantity	Rate	Probability	Cost	PV of cost
Y1	0.869565217	1000000	2	1	2000000	1739130.435
Y2	0.756143667	1000000	2	1	2000000	1512287.335
						3251417.769
					Prospective Loss	-15,50,094.52
It is optimal to close down the mine since the cost of closing down is lesser than the probability of incurring more loss if the mine is operated.
Cost to be incurred for closing down the mine					5000000
The below workings project the prospective Loss/profit is the mine is operated for the next 2 years
Since the price increase of Copper mine is based on probability we need to take the probability of 0.5 while calculating Revenue
Since Cost of Capital is given as 15%, to arrive at the Present value, we need to consider the following
For year 1	0.869565217
For year 2	0.756143667
Calculation of Revenue :
Year	Adjustment factor		Rate	Probability	Revenue	PV of cost
Y1	0.869565217	1000000	1.875	0.5	937500	8,15,217.39
Y2	0.756143667	1000000	2.34375	0.5	1171875	8,86,105.86
						17,01,323.25
Calculation of Cost :
Year	Adjustment factor	Quantity	Rate	Probability	Cost	PV of cost
Y1	0.869565217	1000000	2	1	2000000	1739130.435
Y2	0.756143667	1000000	2	1	2000000	1512287.335
						3251417.769
					Prospective Loss	-15,50,094.52