Usually find decision trees quite easy, however I can't reconcile the answer on the Pearson P1 mock test (hoping you could help)...
A company is considering whether to develop and market a new product. Cost of developing is estimated to be $200,000. There is 60% probability that development will succeed and 40% that development will be unsuccessful, and the development costs will be lost.
If development is successful, the product will be marketed. There is 50% chance marketing will be successful, and product will make profit of $250,000. There is 30% chance marketing will be reasonably successful and product will make profit of $150,000, and 20% chance marketing will be unsuccessful, making a loss of $80,000. The profit and loss figures are after taking account of the development costs of $200,000.
The expected value to develop and market the product is:
Answer is $12,400 according to the mock.
My workings so far are (60% x $200,000) - (40% x $200,000) = $40,000
and (0.5 x $250,000) + (0.3 x $150,000) - (0.2 x 80,000) = $154,000
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Decision Tree Question
Hi,
Yes right - its a tricky one.
The problem to usual method has been caused because the profit and loss figures relating to developing and marketing already have the costs of developing ( $200,000 deducted from them.).
This cost of $200,000 is not a probability - its a certainty - if we go ahead ( even if we fail) so its wrong to include this cost in the figures when you are doing the below analysis.
(0.5 x $250,000) + (0.3 x $150,000) – (0.2 x 80,000) = $154,000
Instead we can add the 200k back to those profit figures so that you have
(0.5 x 450,000) + (0.3 x $350,000) + (0.2 x 120,000) = $354,000
$354,000 is the expected value of the marketing results before the cost of development is deducted.
We have a 60% chance of getting to that point ( i.e. only if the development succeeds)
0.6 x 354000 = $212400
Then we take off the cost of development which is a certainty of $200,000 - leaving us with expected value of $12,400.
We ignore the 40% chance of failure because the question only asks what is the expected value of developing AND marketing the product - so just the value of one branch.
Hope this helps
Kind Regards
Cath
Thanks very much, this really helps.
You're welcome
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