Sunday, January 30, 2011

Assignment-2: Quantitative Techniques (Decision Trees)

Assignment-2 (Group Activity)

Context: What follows is a set of hypothetical scenarios compiled from specific source/s. All the necessary numbers (data) are provided in the scenario specific to each group. Each group of students is expected to collectively discuss the relevant scenarios and prepare decision trees relevant for the group scenario. Kindly place yourself in the role of a member of the managing board and perform your role honestly in the interest of the group. Ponder over all possible alternatives and take decisions on the basis of majority opinion. Record the minority view as ideas for risk management.

Activity Rules:

(1) Before starting discussions nominate one of you as a chairperson or moderator of the discussion. The role of the moderator is to ensure participation of all members in the group and avoid digression from the agenda.
(2) Nominate one of you as a secretary who shall document the key issues, points emerging out of the discussion. The role of secretary is to ensure that all views expressed by all the members (no matter how irrational these views may seem at the moment) are documented comprehensively.
(3) Each group shall make two presentations before the class.
1. First presentation will elaborate the decision making process and the decision tree (5-6 minutes)
2. Second presentation will focus on the pros and cons of the decision taken.
Decision Tree Activity-1 Date 31 January 2010

Group-1
Your company is considering whether it should tender for two contracts (MS1 and MS2) on offer from a government department for the supply of certain components. The company has three options:
tender for MS1 only; or
tender for MS2 only; or
tender for both MS1 and MS2.
If tenders are to be submitted the company will incur additional costs. These costs will have to be entirely recouped from the contract price. The risk, of course, is that if a tender is unsuccessful the company will have made a loss.
The cost of tendering for contract MS1 only is £50,000. The component supply cost if the tender is successful would be £18,000.
The cost of tendering for contract MS2 only is £14,000. The component supply cost if the tender is successful would be £12,000.
The cost of tendering for both contract MS1 and contract MS2 is £55,000. The component supply cost if the tender is successful would be £24,000.
For each contract, possible tender prices have been determined. In addition, subjective assessments have been made of the probability of getting the contract with a particular tender price as shown below. Note here that the company can only submit one tender and cannot, for example, submit two tenders (at different prices) for the same contract.
Option Possible Probability
tender of getting
prices (£) contract
MS1 only 130,000 0.20
115,000 0.85
MS2 only 70,000 0.15
65,000 0.80
60,000 0.95
MS1 and MS2 190,000 0.05
140,000 0.65
In the event that the company tenders for both MS1 and MS2 it will either win both contracts (at the price shown above) or no contract at all.
What do you suggest the company should do and why?
What are the downside and the upside of your suggested course of action?
A consultant has approached your company with an offer that in return for £20,000 in cash she will ensure that if you tender £60,000 for contract MS2 only your tender is guaranteed to be successful. Should you accept her offer or not and why?

Decision Tree Activity-1 Date 31 January 2010

Group-2
The Metal Discovery Group (MDG) is a company set up to conduct geological explorations of parcels of land in order to ascertain whether significant metal deposits (worthy of further commercial exploitation) are present or not. Current MDG has an option to purchase outright a parcel of land for £3m.
If MDG purchases this parcel of land then it will conduct a geological exploration of the land. Past experience indicates that for the type of parcel of land under consideration geological explorations cost approximately £1m and yield significant metal deposits as follows:
manganese 1% chance
gold 0.05% chance
silver 0.2% chance
Only one of these three metals is ever found (if at all), i.e. there is no chance of finding two or more of these metals and no chance of finding any other metal.
If manganese is found then the parcel of land can be sold for £30m, if gold is found then the parcel of land can be sold for £250m and if silver is found the parcel of land can be sold for £150m.
MDG can, if they wish, pay £750,000 for the right to conduct a three-day test exploration before deciding whether to purchase the parcel of land or not. Such three-day test explorations can only give a preliminary indication of whether significant metal deposits are present or not and past experience indicates that three-day test explorations cost £250,000 and indicate that significant metal deposits are present 50% of the time.
If the three-day test exploration indicates significant metal deposits then the chances of finding manganese, gold and silver increase to 3%, 2% and 1% respectively. If the three-day test exploration fails to indicate significant metal deposits then the chances of finding manganese, gold and silver decrease to 0.75%, 0.04% and 0.175% respectively.
What would you recommend MDG should do and why?
A company working in a related field to MDG is prepared to pay half of all costs associated with this parcel of land in return for half of all revenues. Under these circumstances what would you recommend MDG should do and why?

Decision Tree Activity-1 Date 31 January 2010 -1st February 2010

Group-3
A company is trying to decide whether to bid for a certain contract or not. They estimate that merely preparing the bid will cost £10,000. If their company bid then they estimate that there is a 50% chance that their bid will be put on the "short-list", otherwise their bid will be rejected.
Once "short-listed" the company will have to supply further detailed information (entailing costs estimated at £5,000). After this stage their bid will either be accepted or rejected.
The company estimate that the labour and material costs associated with the contract are £127,000. They are considering three possible bid prices, namely £155,000, £170,000 and £190,000. They estimate that the probability of these bids being accepted (once they have been short-listed) is 0.90, 0.75 and 0.35 respectively.
What should the company do and what is the expected monetary value of your suggested course of action?

Decision Tree Activity-1 Date 31 January 2010 -1st February 2010

Group-4
A householder is currently considering insuring the contents of his house against theft for one year. He estimates that the contents of his house would cost him £20,000 to replace.
Local crime statistics indicate that there is a probability of 0.03 that his house will be broken into in the coming year. In that event his losses would be 10%, 20%, or 40% of the contents with probabilities 0.5, 0.35 and 0.15 respectively.
An insurance policy from company A costs £150 a year but guarantees to replace any losses due to theft.
An insurance policy from company B is cheaper at £100 a year but the householder has to pay the first £x of any loss himself. An insurance policy from company C is even cheaper at £75 a year but only replaces a fraction (y%) of any loss suffered.
Assume that there can be at most one theft a year.
Draw the decision tree.
What would be your advice to the householder if x = 50 and y = 40% and his objective is to maximise expected monetary value (EMV)?
Decision Tree Activity-1 Date 31 January 2010 -1st February 2010

Group-5
A government committee is considering the economic benefits of a program of preventative flu vaccinations. If vaccinations are not introduced then the estimated cost to the government if flu strikes in the next year is £7m with probability 0.1, £10m with probability 0.3 and £15m with probability 0.6. It is estimated that such a program will cost £7m and that the probability of flu striking in the next year is 0.75.
One alternative open to the committee is to institute an "early-warning" monitoring scheme (costing £3m) which will enable it to detect an outbreak of flu early and hence institute a rush vaccination program (costing £10m because of the need to vaccinate quickly before the outbreak spreads).
What recommendations should the committee make to the government if their objective is to maximise expected monetary value (EMV)?
The committee has also been informed that there are alternatives to using EMV. What are these alternatives and would they be appropriate in this case?

Decision Tree Activity-1 Date 31 January 2010 -1st February 2010
Group-6

Your company is considering whether it should tender for two contracts (C1 and C2) on offer from a government department for the supply of certain components. If tenders are submitted, the company will have to provide extra facilities, the cost of which will have to be entirely recouped from the contract revenue. The risk, of course, is that if the tenders are unsuccessful then the company will have to write off the cost of these facilities.
The extra facilities necessary to meet the requirements of contract C1 would cost £50,000. These facilities would, however, provide sufficient capacity for the requirements of contract C2 to be met also. In addition the production costs would be £18,000. The corresponding production costs for contract C2 would be £10,000.
If a tender is made for contract C2 only, then the necessary extra facilities can be provided at a cost of only £24,000. The production costs in this case would be £12,000.
It is estimated that the tender preparation costs would be £2,000 if tenders are made for contracts C1 or C2 only and £3,000 if a tender is made for both contracts C1 and C2.
For each contract, possible tender prices have been determined. In addition, subjective assessments have been made of the probability of getting the contract with a particular tender price as shown below. Note here that the company can only submit one tender and cannot, for example, submit two tenders (at different prices) for the same contract.
Possible Probability
tender of getting
prices (£) contract
Tendering for C1 only 120,000 0.30
110,000 0.85
Tendering for C2 only 70,000 0.10
65,000 0.60
60,000 0.90
Tendering for both C1 and C2 190,000 0.05
140,000 0.65
100,000 0.95
In the event that the company tenders for both C1 and C2 it will either win both contracts (at the price shown above) or no contract at all.
What do you suggest the company should do and why?
What is the "downside" of your suggested course of action?

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