Mr. Warren operated a real estate agency that specialized in finding buyers for commercial properties. Warren was approached one day by a prospective client, who had three properties that he wished to have sold. The client wished to receive the following prices:
Warren would receive a commission of 4% on any of the properties he was able to sell.
The client laid down the following conditions for an exclusive listing:
(i) Allston had to be sold first.
(ii) If Warren failed to sell Allston within a month, then the deal was off. Warren would not receive any commission or the chance to sell other properties.
(iii) If Warren could ...view middle of the document...
Warren would not receive any further commission or the chance to sell the third property.
(v) If successful, Warren had the option to terminate the contract or sell the third
property. If Warren decided to sell the third property, the terms were same as in the previous cases.
After the client left, Warren proceeded to analyze the proposal to determine whether or not to accept it. He figured his selling costs and his chances of selling each property at the price set by the client to be:
Selling Cost Probability of Sale
Allston $800 0.7
Belmont $200 0.6
Cambridge $400 0.5
He believed that the sale of a particular property would not make it more or less likely that the two remaining properties could be sold. Selling costs would have to be incurred whether or not a particular property was sold but could be avoided by deciding not to attempt to sell the property.
a. Draw a decision tree for the problem. Identify the decision nodes and chance nodes.
Demonstrate how you got the terminal values.
b. Suppose Warren successfully sold Allston first and Belmont second. Should he decide to terminate the contract? Why or why not?
c. Suppose Warren successfully sold Allston first and Cambridge second. Should he decide to terminate the contract? Why or why not?
d. Suppose Warren sold Allston successfully. Should he terminate the contract? If not, which property should he sell second?
e. Should Warren accept the contract?
f. Based on the decision tree, what is the option value of the contract (that is, if Warren accepts the contract instead of rejecting it, how much more or less can he expect to make)?