A CONDOMINIUM CONUNDRUM
After another stressful year of leading, managing, and teaching leading and managing at the Piedmont Business School, Allie Fraggle has decided to take a year-long sabbatical to pursue her life-long dream of bringing leading and managing skills to disadvantaged people in developing countries. She is trying to rent out her trendy loft condominium for the year that she will be gone.
A prospective renter has arrived to have a look at Fraggle's condo. The gentleman offers to pay her $600 per month to rent the condo for the year. This is a higher rent than she thought she could get, but she wonders if she should trust the gentleman and his credit.
Her colleague Marcus Lanky has taken many sabbaticals and has rented out his condominium many times, and he has advised Fraggle to purchase a credit report from Reports-R-Us before offering anyone a lease. The credit report costs $100 and will indicate whether the prospective renter has good, medium, or bad credit. In Lanky's experience, renters with good credit always pay the full year of rent, renters with medium credit pay 75% of the full year of rent, and renters with bad credit pay just 25% of the full year of rent. Furthermore, half of the renters with bad credit end up causing $1000 of damage to the condo! Fraggle contacts Reports-R-Us and learns that, in the population of renters, 50% of people have good credit, 30% have medium credit, while the remaining 20% have bad credit.
If she ends up not offering a lease to the gentleman, her fallback option is to lease the condo to a group of her MBA students, who have offered to rent the condo for the year for a total of $6500 so that they will have a quiet place to study near Franklin Street. They will pay the $6500 upfront so she doesn't have to worry about their credit, but she is fairly confident that they will cause $500 of damage.
As you answer the following questions, please assume that Allie will be out of the country and out of touch for the next 12 months. Therefore, if the renter fails to pay his rent, she will be powerless to evict the renter or to find a new tenant within the 12 month period. Also, don't worry about the time value of money for the purposes of this question.
You are allowed to access the TreePlan Excel add-in, if so, include your Excel Spreadsheet. In all cases, please show the calculations behind your answers.
a) Suppose that Fraggle has decided not to purchase a credit report on the gentleman. Assume that Fraggle's goal is to maximize her expected profit. How much profit should Fraggle expect to get if she does not order a credit report? Draw a decision tree to support your answer.
b) Now suppose that Fraggle has decided to purchase a credit report on the gentleman. Assume that Fraggle's goal is to maximize her expected profit. How much profit should Fraggle expect to get if she orders a credit report? Include the $100 cost of the credit report in your calculations. Draw a decision tree to support your answer.
For parts (c), (d), and (e), assume that Allie can choose to order or not to order a credit report.
c) Assuming that Allie can choose either to order or not to order a credit report, how many different alternatives or strategies are available to her? State the complete strategy that maximizes Allie's expected profit.
d) Suppose that in reality the cost of a credit report is somewhat negotiable. Sketch a graph of Fraggle's optimal expected profit as a function of the cost of the credit report which varies between $0 and $1000. Your plot should have the cost of a credit report on the horizontal axis and E[profit] on the vertical axis.
e) Assume that the credit report costs $100. Allie suddenly realizes that the gentleman looks kind of familiar. He might be her second cousin's ex-boyfriend's former roommate, Fast Eddie. She thinks that there is a 50% chance that he is Fast Eddie, in which case she is sure her second cousin can reveal his credit status for free. However, there is also a 50% chance that the gentleman is not Fast Eddie, in which case her second cousin will provide no useful information. What is Allie's expected profit now?
I have attached a sample. Will need to show all work including decision trees
Attachment:- sample.rar