1. In December 2023, your company faces a decision to bid for a eight-year lease
on a coal mine offered by the government. The lease gives the winner of the
auction the right to actually develop the mine for four years. Once development
takes place (if ever at all), the leaseholder can extract 25 million tons of coal
per year for exactly four years with the fixed extraction cost of $4 per ton.
Development of the mine costs $50 million. There are no reclamation costs at
the end of the life of the mine. If development did not take place by December
2027 (four years down the road), then the lease would end at that time.
At the time of the auction, the spot price of coal was $4.58. The risk-free rate
of interest is 6% per year and the net convenience yield on coal is 3.5% per
year, both of which are constant and compounded continuously. The standard
deviation of log changes in coal prices is 15% per year. Development costs are
depreciated on a straight-line basis over four years. There are no net working
capital requirements. The marginal tax rate of your company is 40%. There is
no inflation.
(a) Suppose that your company commits to an immediate development of the
mine. What is the maximum amount that your company should bid in the
auction for the lease?
(b) Build a four-step binomial tree with a time step set equal to one year.
Calculate the value of the lease by the real options approach.
(c) Now, your company knows that the government might terminate the lease
(if development has not occurred) at the beginning of the fourth year with
a 10% chance. However, if development has started at or before the end
of the third year, there is no risk of a government termination of the lease.
Redo part (b). Why is the value of the lease different from that in part
(b)