General Tin GT is worried that its mine in Peru will be expropriated during the next 12 months.The Peruvian government has promised,however,to pay compensation of $15 million at the year's end if it expropriates the mine.GT believes that this promise would be kept.If expropriation does not occur this year,it will not occur anytime in the foreseeable future.The mine is expected to be worth $50 million at the end of the year.A wealthy Peruvian has just offered GT $19 million for the mine today.If GT's risk-adjusted discount rate is 22%,what is the probability of expropriation at which GT is just indifferent between selling now or holding on to its mine?

Question

Quizplus · Accepted Answer

The first step is to calculate the expected value of the mine at the end of the year, taking into account the probability of expropriation:

EV(end of year) = (Probability of expropriation x Compensation) + (Probability of no expropriation x Expected value of the mine)

EV(end of year) = (P x $15 million) + [(1-P) x $50 million]

where P is the probability of expropriation.

To find the probability of expropriation at which GT is just indifferent between selling now or holding on to its mine, we need to find the expected value of the mine today, discounted at GT's risk-adjusted discount rate of 22%:

EV(today) = EV(end of year) / (1 + Discount rate)^t

where t is the time in years to the end of the year (which in this case is 1).

EV(today) = [P x $15 million + (1-P) x $50 million] / (1.22)^1

We can now set up the equation to find the value of P:

$19 million = [P x $15 million + (1-P) x $50 million] / (1.22)^1

Solving for P, we get:

P = 0.766 or 76.6%

Therefore, if the probability of expropriation is greater than 76.6%, it would be better for GT to sell the mine now, and if the probability is less than 76.6%, it would be better to hold on to the mine. The correct answer is B, which is the closest to 76.6%.

General Tin GT Is Worried That Its Mine in Peru