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Decision tree

Forums › Ask ACCA Tutor Forums › Ask the Tutor ACCA PM Exams › Decision tree

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  • February 23, 2026 at 12:43 am #724830
    Prajnya
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    • Topics: 2
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    Hello Sir,
    Please help me understand the following question, I have come across a doubt in
    Kaplan Study text
    Decision tree- Value of imperfect Information example:

    (a) You have the mineral rights to a piece of land that you believe may have oil underground. There is only a 10% chance that you will strike oil if you drill, but the profit is $200,000.
    It costs $10,000 to drill. The alternative is not to drill at all, in which case your profit is zero.
    Should you drill? Draw a decision tree to represent your problem.
    (b) Before you drill, you may consult a geologist who can assess the promise of the piece of land. She can tell you whether the prospects are good or poor, but she is not a perfect predictor. If
    there is oil, the probability that she will say there are good prospects is 95%. If there is no oil, the probability that she will say prospects are poor is 85%.
    Draw a decision tree and calculate the value of imperfect information for this geologist. If the geologist charges $7,000, would you use her services?

    a)
    EV (‘Drill’) = ($190K × 0.1) + (–$10K × 0.9) so EV (‘Drill’) = $10K.
    We should drill, because the expected value from drilling is $10K, versus nothing for not drilling.

    b)We will calculate the Expected Value of profits if we employ the geologist.
    If this exceeds $10,000, the geologist would be worth employing as long as the benefit of employing her exceeds her charge of $7,000.
    assessments can be tabulated as follows (assume 1,000 drills in total):

    Oil present No oil Total

    Geologist says
    ‘Prospects are good’ 95% × 100 = 95 drills 15% × 900 =135 drills 230 drills

    Geologist says
    ‘Prospects are poor’ 5% × 100 = 5 drills 85% × 900 = 765 drills 770 drills

    100 drills 900 drills 1,000 drills

    A decision tree can be drawn to calculate the expected value of profits if a geologist is employed:

    Working from right to left:
    EV(A) = (41.30% × $200,000) – $10,000 drilling costs = $72,600.
    The decision at ‘C’ should be to drill, as this generates higher benefits than not drilling.
    EV(B) = (0.65% × $200,000) – $10,000 drilling costs = –$8,700. The decision at ‘D’ should be not to drill.
    EV(E) = 0.23 × $72,600 = $16,698. This is the expected value of profits if a geologist is employed and exceeds the EV of profits if she is not employed.
    Expected Value of Imperfect Information = $16,698 – $10,000 = $6,698.
    Since this is less than the cost of buying the information ($7,000), we should not employ the geologist at point ‘F’.

    Sorry, I couldn’t attach the decision tree diagram here. However, EV at Decision point E, only the probability and profit outcome of (A) is considered and (B) is not considered. I don’t understand why the EV multiplies only 0.23 * $72,600 but not 0.77* (–$8,700) “poor prospects” part? Please help me understand.

    Thanks!

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