Dmd Case Analysis of Making a Decision of Buying a House

Assignment Form |Course: | Data, Model and Decision | |Instructor: | Dr. Feng Haolin | |Homework: |Decision Analysis | |Name: | Group 1. Li Yuechuan/ Pankaj Malhotra/ Liang Yuan/ Wu Zhuhua/ Tan Jing/ Gu Junling | |Student ID No. | | |Class: |11FB | STUDENT DECLARATION I declare that this assignment is my own work, which all sources of reference are acknowledged in full and it has not been submitted for any other course. Signature:…………………… Date:………… Content: Part 1. Case Description—————————————————————————– 3 Part 2.

Decision Making Analysis——————————————————————-4 Part 3. Decision Tree———————————————————————————-5 Part 4. Sensitivity Analysis—————————————————————————6 Part 5. Conclusion————————————————————————————-8 Part 1. Case Description The case is about a house that has been on sale in Shaker Heights, Ohio, for one day. Debbie and George Calvert are seriously thinking of making an offer towards the house, which has been valued at $400,000.

Their broker has advised them to make an offer of as close to the asking price as possible, as there are around 20 other interested potential buyers. Debbie has assigned an additional $10,000 as the ‘emotional value’. That is, whereas the fair market value of the house is $400,000, the house would be worth $410,000 to them. The couple has decided to make one of the three offers listed in the table below. In case of there being multiple bids, they will have to rethink on whether to withdraw the offer, submit the same offer or increase the offer by $5000.

In order to be able to construct a decision tree to help her make the optimal decision, Debbie has assigned a few probabilities as follows: |Event |Probability | |Bidding price |One bidder (0. 30) |Multiple bids (0. 70) | |$390,000 |0. 40 |0. 20 | |$400,000 |0. 0 |0. 50 | |$405,000 |0. 90 |0. 70 | |$395,000 | |0. 30 | |$410,000 | |0. 80 | | | | |

Part 2. Decision-making analysis The basic knowledge in decision tree: Decision analysis is a logical systematic way to address a wide variety of problems involving decision-making in an uncertain environment. A Decision Node represents a decision in the decision tree; we use a square box to mark it. An uncertain event is represented with a small circle called an Event Node. The analysis of decision making: There are two steps in decision-making analysis. The first one is structuring the problem, and the second one is analyzing it. In the case, structuring the problem is as below: 1) How to make our offer when there is only one bidder and multiple bidder? (2) What is Decision Node, what is the Event Node? (3) What is the probability of each event node? Analyzing the problem is as below: (1) Evaluate options and find out the best way of offers; (2) Select the best choice. Part. 3 Decision Tree [pic] Chart 1 Decision Tree First of all, Debbie and George (D&G) have three choices to make offer with $390,000, 400,000 and 405,000 respectively. Take offer $390,000 for example, the probability of acceptance for this offer is 0. , whereas probability of rejection is 0. 7. If it is accepted, the deal is made for $390,000. On the other hand, if it is rejected, D&G will have three alternatives at second stages, which are withdraw offer, remain same offer and increase offer by 5,000 respectively. The probabilities of The EMV of these three choices are 0, 4,000 and 4,500, as calculated in the decision tree. Hence the decision F will take the highest EMV value of 4,500. Afterwards, we summarize decision E and F according to their weight, and get the EMV for event B as 5,550.

Likewise, we can get EMV of event B and C as 5,300 and 3,800 respectively. Part. 4 Sensitivity Analysis, From the decision tree above, the main data include two parts, the price and the percentage of acceptance, so the basic calculation is as followed: |Data | | | | | | |Probability of accepting the price and the correspondent EMV | | |No. f bidders |Price |Probability |EMV | | |1 |390000 |0. 40 |20000 | | |1 |400000 |0. 60 |10000 | | |1 |405000 |0. 90 |5000 | | |>1 |390000 |0. 0 |20000 | | |>1 |395000 |0. 30 |15000 | | |>1 |400000 |0. 50 |10000 | | |>1 |405000 |0. 70 |5000 | | |>1 |410000 |0. 0 |0 | | | | | | | | |EMV of Nodes | | | | | |Node |EMV |Decision |Probability | | |B |5550 |option 390,000 |Chosen | | |C |5300 |option 400,000 |? | | |D |3800 |option 405,000 |? | | |E |8000 |accept 390,000 immediately |0. 3 | | |F |4500 |increase 5000 |0. 7 | | |G |0 |withdraw |0. 7 | | |I |4500 |increase 5000 |0. | | |H |4000 |keep same |0. 7 | | |J |6000 |accept 400,000 immediately |0. 3 | | |K |5000 |keep same with 400,000 |0. 7 | | |L |0 |withdraw |0. 7 | | |M |5000 |keep same |0. | | |N |3500 |increase 5000 |0. 7 | | |L |4500 |accept 405,000 immediately |0. 3 | | |O |3500 |keep same with 405,000 |0. 7 | | |P |0 |withdraw |0. 7 | | |Q |3500 |keep same |0. | | |R |0 |increase 5000 |0. 7 | 1) In the circumstance of only one bidder, if the probability of $390,000 decreases to 0. 3 from 0. 4, and other elements remain the same, the optimal price strategy will turn to submit $400,000 as the first time bidding price, and following decision tree will goes to if the seller accept $400,000, the deal is done, and if seller need second time to submit the price, Debbie and George will still offer $400,000 as the final price. 2) In the circumstance of only one bidder, if the probability of $400,000 increases to 0. 7 from 0. , and other elements remain the same, the optimal price strategy will turn to submit $400,000 as the first time bidding price, and the following decision will goes the same as situation (1) 3) In the circumstance of only one bidder, if the suggested price is $390,000, $395,000 and $405,000, and the correspondent probability is 0. 4, 0. 5 and 0. 9, and the other elements remain the same, then the optimal price strategy will turn to submit $395,000 and if the seller accept $395,000, the deal is done, and if the seller need second time to submit the price, Debbie and George will increase $5,000 to $400,000 as the final price. 4) In the circumstance of multiple bidder, if the probability of suggested price of $395,000 increase to 0. 4 from 0. , and other elements remain same, the optimal price strategy will remain the same as the original one, the strategy of which firstly choose $390,000. In summary, due to the EMV of $390,000 and $400,000 are quite close, thus any changes in the price or probability may result differently, so the assumption for the price and correspondent probability is extremely crucial in this case. Part. 5 Conclusion From the decision tree, we can see that event B and decision E bear the highest EMV, which are 5,550 and 8,000 respectively. Under such circumstance, Debbie and George should offer 390,000 at the first stage. If it is accepted, then they can finish the deal. If it need submit second time, they should further increase their offer to 395,000.