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Q. As a fresh graduate from MSBA program and with a good job, you are now planning to purchase a house in Boston. Currently, there are 6000 houses listed on the market which are within your budget. There are two types of house in the market – good (G) and bad (B) with a breakdown of 3600 (G) and 2400 (B) houses of each type.
The seller knows EXACTLY the type of house s/he is selling in the market but you cannot distinguish between a good and bad house. However, you can hire a professional home inspector to get the house inspected before making an offer to the seller. The home inspector can provide you a report indicating if the house is G or B. The report, however, is not always perfect or error free. The report correctly detects a good house 100% of the time but identifies a bad house 70% of the time. In other words, if the house is G, the report will show it is G 100% of the time but if the house is B, then report will show is it B only 70% of the time.
Each house, whether G or B, is listed for $500k in the market. Your valuation* for a good house is $510k, and for a bad house is $410k. The seller’s valuation for a good house is $495k and for a bad house is $405k.
(* For a seller, valuation $v1 means the seller will accept any offer of $v1 or above. For a buyer, valuation $v2 means the maximum amount the buyer is willing to pay for the house)
A. What are the possible decisions you can take based on home inspector reporting? Please write all possible decisions in using notations/simple wordings.
B. Please intuitively explain the decisions in QA. For example, if your friend (who is not analytically savvy and does not understand technical wordings and explanations) asks you about your possible decisions, what/how you are going to explain to him/her?
C. Suppose you fully trust the home inspection report, i.e., if the report says it is G, then you also believe it is G and if the report says it is B, then you also believe it is B. What would be your expected valuation of the house under this decision? Please show your steps in calculations.
D. Suppose you make an offer to a seller with price equal to your expected valuation in QC. What would be possible set of actions by the seller? And which set of action(s) the seller is going to choose?
E. Suppose the seller accepts your offer of purchasing the house in QD. Are you going to proceed with the next step of purchasing the house or will back out of the deal? (assuming you can legally back out of the deal at this stage with no penalty). Please provide a brief explanation for your choice.
F. If you back out of the deal in QE, how you are going to plan for purchasing a house in the future? Any creative ways to add conditions/clauses in your offer to potential sellers, i.e., something which can help protect both you and the seller and may be help you in identifying the type of the house**?

 

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