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 and holding on to its mine?

Question

Quizplus · Accepted Answer

To find the probability of expropriation at which GT is just indifferent between selling now and holding on to its mine, we need to calculate the expected value of selling now and holding on, and set them equal to each other.

Expected value of selling now: Probability of expropriation * ($15 million + $19 million*(1-risk-adjusted discount rate))
Expected value of holding on: (1- Probability of expropriation) * $50 million

Setting them equal to each other and solving for the probability of expropriation, we get:

Probability of expropriation = (Risk-adjusted discount rate * $19 million + $35 million) / ($19 million + $35 million)

Plugging in the numbers, we get:

Probability of expropriation = (0.22 * $19 million + $35 million) / ($19 million + $35 million) = 0.766, or 76.6%

Therefore, GT is just indifferent between selling now and holding on to its mine if the probability of expropriation is 76.6%. Thus, the best choice is B.

General Tin (GT) Is Worried That Its Mine in Peru