You are given the opportunity to play a game of high stakes gambling. The game begins by you paying an entry fee of $35,000,000 followed by a fair coin toss. If the coin toss is "heads" then you have an 80% probability of receiving a perpetuity of $10,000,000 per year and a 20% probability of receiving a perpetuity of $1,000,000 per year. Assume that the proper discount rate for the perpetual cash flow is 10%. If the coin toss is "tails"you can continue to play but you will lose $50,000,000 with certainty. Alternatively, you can make a make an opt-out payment of $10,000,000 after a "tail" to prevent you from going down such a costly path. What is the present value of playing such a game?

Question

Quizplus · Accepted Answer

Value of Heads node: .8(10,000,000/.1) + .2(1,000,000/.1) = 82,000,000
Value of Tails node: -10,000,000 (since you will always opt for that instead of the 50,000,000 payment)
Present Value: -35,000,000 + .5(82,000,000) + .5(-10,000,000) = 1,000,000

You Are Given the Opportunity to Play a Game of High