EXPECTED VALUES?

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    Gabriel
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    Envico Ltd, another subsidiary of the KCB Group, is well established and provides seminars on various aspects of current and recently announced changes in employment legislation. Envico Ltd has decided to enter into a one year renewable contract with Mieras Business Associates, which owns large premises that are suitable for holding educational seminars in each of eight cities. Envico Ltd has had similar dealings with Mieras Business Associates during recent years.

    Mieras Business Associates has offered a choice of four different contracts, each of which relates to seminar rooms of differing sizes. These are known as room types A,B, C and D, which are capable of accommodating 100,200,300 and 400 delegates respectively.

    Envico Ltd will charge an all inclusive fee of $80 per delegate at every seminar throughout the year. The cost incurred by Envico Ltd varies according to room type, as shown in the following table:

    Room type:
    A which has a 100 people attending the seminar and the cost of seminar is $6000
    B which has 200 people attending the seminar at a cost of $10,800
    C which has 300 people attending the seminar at a cost of $14,400
    D which has 400 people attending the seminar at a cost of $16,000

    Envico must decide in advance of the forthcoming year which size of conference room to contract for. It is not possible to contract for a different size conference room in different cities, i.e. only one size of room can be the subject of the contract with Mieras Business Associates.

    Due to the rapid growth in interest regarding environmental issues and corporate social responsibility, and the large amount of forthcoming legislative changes, Envico Ltd has decided to hold one seminar in every week of the year in each city. Sometimes a regional government representative will attend and speak at such seminars. On other occasions a national government representative will attend and speak at such seminars. The rest of the time the speakers at seminars are representatives from within Envico Ltd.

    Envico has estimated the following frequency regarding seminars to be held during the forthcoming year.

    Category of speaker

    Envico representative – 20%
    Regional government representative – 50%
    National government representative – 30%

    Market research has indicated that where a national government representative is in attendance, Envico Ltd can be reasonably assured of selling 400 seminar places and where a regional government representative is in attendance 200 seminar places can be sold. Envico Ltd expects to sell only 100 seminar places when there is no attendance by a government representative.

    Required:
    (i) Advise Envico Ltd on the size of seminar room that should be contracted from Mieras business associates, using the criterion of expected value. Your answer should show the expected annual contributions from each decision option (9 marks)
    (ii) Determine whether your decision in (i) would change if you were to use the Maximin and Minimax regret decision criteria. Your answer should be supported by relevant workings. (6 marks)
    (iii) A firm of consultants has offered to undertake a study on behalf of Envico Ltd which will provide perfect information regarding seminar attendance during the forthcoming year.
    Advise the management of Envico Ltd with regard to the maximum amount that they should pay to consultants for perfect information regarding seminar attendance and comment briefly on the use of perfect information in such decisions (5 marks)

    (total: 20 marks)

    What is the uncertain variable? The cost per seminar or what else? How do we to (i) and (ii). Please help. I’m don’t understand decision making in uncertain situations.


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    John Moffat
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    The uncertain variable is the category of speaker (because that will determine the size of the audience).
    The cost of the seminar is not uncertain because the cost will depend on which size room that you decide to contract for.

    So what you need to do is set up a table showing the final contribution that will result for each type of room chosen (there are 4 choices) and for which speaker (there are 3 possibilities). So your table will show 12 possible outcomes depending on the size of room (which is our choice) and on the speaker (which is uncertain).

    For part (1) all that remains is for each size room to calculate the expected value (by multiplying each possible contribution for that room by the probability). Then you can choose the room giving the highest expected value.

    Parts (ii) and (ii) are then applying the standard rules to the table you have prepared (the rules are explained in my lectures).


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    Gabriel
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    Thank you for your reply.

    So for part (i) are there 12 possible outcomes too, that we need to multiply the probabilities by or there are just 3 outcomes? In our lecture, we saw how to get the perfect information from a decision tree (and this is what most study texts explain by the way), but here we aren’t told to draw a decision tree, so how will we get the value of perfect information?

    For part (i). Could you just show me a small example on how to get the expected values, maybe with the room capacity being 400, please? Then I’ll pick up from there and do the rest

    Thanks,

    Gabriel.


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    Gabriel
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    Also, please evaluate this. I do the table and for the option of Envico Co having it’s own representatives (then they will only be 100 people attending the seminar), so to find the annual contribution of Envico Co’s own representative with room type A, I did the following:

    100*52(as there is one meeting in each of the weeks of a year) and then we get 5200 attendees*80 (the fee) = $416000 less the cost for room A of $6000*52 = 312,000 to get (416,000-312,000) 104,000 as the annual contribution. So is this the correct working for the combination of room A with Envico’s own speaker? I have used a very similar approach for the rest of 11 outcomes, so if this is right, then I’ve got the whole of part (a) right basically.

    Please advise.

    Thanks.


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    Gabriel
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    Also, in my table I’ve got negative profits (losses) so do I use those negative profits when using minimax or minimax regret or do I just take the smallest possible profit and ignore the losses, in the minimax decison?

    Please advise


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    Gabriel
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    Also, I need help for the last part of the question (iii).

    How do we calculate the value of perfect information. I know the formula is expected value without perfect information – expected value with perfect information.

    Well, in part (i) to the question I got the highest expected value as room A and I got $686,400. So this is the value of expected value without perfect information, but then how do we get the value of the expected value with perfect information? (drawing a decision tree in this example would be so hard). Also, what other factors (the written factors) do we need to take into account when using the value of perfect information?

    Thanks. Please advise.


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    John Moffat
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    If you choose room D (400 people) then there are 3 possible outcomes for that can occur depending on the speaker.

    If it is Envico representative:
    400 places are sold (and the room will fit 400). So the revenue per seminar is 400 x $80 = $32,000. The cost is $16,000 and so the profit is $16,000.
    If it is reg govt rep:
    200 places are sold, to revenue per seminar is 200 x $80 = $16,000. Cost is $16,000 and so profit is $0
    If it is nat govt rep:
    100 places are sold, so revenue per seminar is 100 x $80 = $8,000. Cost is $16,000 and so profit is $(8,000)

    So the expected value if you choose room D is: (0.20 x 16,000) + (0.50 x 0) + (0.30 x (8,000)) = $800
    This is per week, and so the annual contribution is 52 x 800 = $41,600.
    (or you could have done it per year from the start – you would get the same answer)

    You can do the same for each choice of room and then choose the one with the highest expected value. (But remember that for room A, the max number of people will be 100 whatever the speaker, for room B it will be a maximum of 200 whatever the speaker and so on).

    Your workings for room A are correct.


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    John Moffat
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    You do not ignore negative values. So for example (and these are invented figures) if you were to get contributions for one of the rooms of (20,000), (5,000), 10,000, 20,000, then doing maximin the minimum would be (20,000).


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    John Moffat
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    Decision trees are not needed for perfect information (you only ever need to draw a decision tree for any part of the question if the examiner specifically asks for it).

    To calculate for perfect information, what you do is say first of all which would be the best room if it was the Enrico representative. You can look at your table and decide which of the 4 rooms would give the highest contribution, and note how much that contribution would be.
    The do the same thing if it was the reg govt rep. – which would be then the best of the 4 rooms and what would be the contribution.
    Finally to the same for the nat gov rep – which would then be the best room to choose and what would be the contribution.

    You then have 3 ‘best’ contributions depending on which of the speakers it was.

    Then work out the expected value using the three values and the probabilities of each of the speakers.

    The two big problems with this way of valuing perfect information are firstly that although you could have market research etc done to tell you which speaker it would be, in real life perfect information does not exist – the research might be 90% likely to give the correct answer but not 100% (which is what we assume). Secondly, the normal problem with expected values – how on earth would you know the probabilities in real life. If the probabilities were a bit different then the solution could end up being completely different.


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    Gabriel
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    Thank you but I got the expected value of the perfect information the same as the expected value without perfect information and thus I got 0 as the value of perfect information. Would this be correct?


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    John Moffat
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    No – it cannot be correct.

    Check the figures in your table and read my last reply again and make sure you have applied it properly.

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