A real estate speculator is considering buying property at a resort island for $400 thousand. The local government is considering a proposal to rezone the property for commercial use, which has the potential to increase its value drastically. Once the government makes its decision, the speculator would lose the chance to purchase the property. As it stands, there’s a 30% chance the property will be rezoned. If it were rezoned, there’d be a 20% chance the speculator can incite a bidding war over the property and sell it for $3 million; there’d be a 40% chance he could interest a developer in the property and sell it for $1.8 million, and even if neither possibility played out, he could still sell it for $700 thousand. If the property isn’t rezoned, there’s a 25% chance he could resell it and recoup $300 thousand, but failing that, he would be stuck with a useless property, which would increase his liability by an additional $100 thousand.

The real estate developer discusses his options with a trusted consultant, who offers to look into the political situation on the island for a flat fee of $50 thousand. The consultant has a good reputation; she has a 90% probability of correctly identifying that a property is going to be rezoned, and a 70% probability of correctly identifying that the motion to rezone a property will fail.

While he’s considering her offer, she mentions another possibility: if he’s willing to pay her an additional $75 thousand (for a total of $125 thousand), she’ll use that money to make some generous campaign contributions to some of the island’s key government officials in exchange for future considerations. She estimates, with this strategy, the chance the property would be rezoned after the speculator’s purchase would increase to 60%, but there would be a 5% chance one of the island’s less enterprising functionaries would catch wind of her efforts. In this instance, the speculator would end up losing the amount he paid her, eating the cost of the property, and paying an additional $1.5 million in fines.

Use a decision tree to answer the following questions (Excel recommended):

a)   What  is the  investor’s  optimal  decision  under the  EMV  rule? What  is the  EMV  of the

investment opportunity?

There exists 3 major decisions:

1.   Do Nothing

a)    EMV=0

2.   Not hiring the consultant

a)    Property rezoned (30% chance)

i.       Sell for $3 million (20% chance)

ii.       Sell for $1.8 million (40% chance)

iii.       Sell for $700 thousand (40% chance)

b)    Property doesn’t rezoned (70% chance)

i.       Sell for $300 thousand (25% chance)

ii.       Lose $100 thousand (75% chance)

3.   Hiring the consultant without bribery – cost $50 thousand

a)    Consultant has true prediction

i.       True with rezoned (90% chance in 30% chance)

ii.       True with not rezoned (70% chance in 70% chance)

b)    Consultant has false prediction

i.       False with rezoned (10% chance in 30% chance)

ii.       False with not rezoned (30% chance in 70% chance)

4.   Hiring the consultant with bribery – cost $525 thousand

a)    Rezoned (60% chance)

b)    Not rezoned (35% chance)

c)    Catch bribery (5% chance)

The investor's optimal decision under the EMV rule is to hiring the consultant with bribery, as the EMV is the highest at approximately $760 thousand.

b)  Assume the investor has a risk tolerance of $2 million. Using the utility curve we discussed in class, what is his optimal decision? What is the certainty equivalent of that decision?

The exponential utility function mentioned in class has the following form:

U(x) = 1 − e−x/R

In this representation, e is the natural logarithm, x is a monetary value and R is $2 million in this question.

With different decision, we have:

1.   Not hiring the consultant

2.   Hiring the consultant without bribery

3.   Hiring the consultant with bribery

The  investor's  optimal  decision  using  the  Exponential  Utility  Function  is  hiring  the consultant without bribery, as this decision is the highest at approximately 0.22.

To calculate the certain equivalent of the decision, we can use the inverse exponential utility function:

X = −R ∗ ln (1 − U(X)

So  the  certainty  equivalent  of  chosen  decision  is  -2000000*ln(1 -0.21864),  which approximates $493,438.58

c)   As it turns out, the consultant was just joking about bribing the government; this is not a

decision alternative after all. What is the expected value of the information the consultant can provide?

The Expected Value of the investment opportunity without any information is calculated in question a which is $480000, and the expected value of the investment opportunity with consultant is $718000.

So  the  expected  value  of  the  information  the  consultant  can  provide  is  718000- 480000=238000.

Develop a Monte Carlo simulation to answer the following question: