Question

A real estate investor owns a small office building she has leased to a major insurance company for a rental fee based on a share of the profits. If the insurance company is successful, the present value of future rentals is estimated at $15 million. If the insurance company is not successful, the present value of the rentals will be $2 million. The insurance company has offered the investor $6 million to buy the property outright. On an expected monetary value basis, what probability would need to be assigned to “success” for the investor to be indifferent between selling and not selling?

Answer 1

Let the probability of success =P(x); So, the probability of failure =1 - P(x); Expected monetary value =EMV

EMV =P(x)*15 million + (1 - P(x))*2 million =6 million

P(x)*15 million + 2 million - P(x)*2 million =6 million

P(x)[15 million - 2 million] =4 million

P(x) =4 million/13 million =4/13 =0.3077

Verification:

EMV =P(x)*15 million + (1 - P(x))*2 million =0.3077*15 million + (1 - 0.3077)*2 million =4.6155 million + 1.3846 million =6 million ​​​​​​

Thus, the probability that would need to be assigned to “success” for the investor to be indifferent between selling and not selling =0.3077