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Shell has recently signed a sale and purchase agreement (SPA) with XTRA Pty Ltd. to acquire 100 percent interest in TANVA Oilfield in Production License offshore Western Australia for $20 million. At the moment, oil from the field is produced from horizontal wells and processed through a fixed central production facility platform with 50,000 barrels per day capacity. Oil is then transported by pipeline to the floating storage offloading (FSO) facility and loaded to shuttle tankers for North Asian customers. It is crunch time over the next few days as Shell rallies its investors for the green light on the purchase. Assume that the voting power is only limited to a few trusted and institutional shareholders. The decision requires a simple majority of the seven decision-making shareholders. If each is believed to have a 0.35 probability of voting yes on the purchase, what is the probability that the oilfield will be purchased by Shell? Currently each share of Shell is traded for 2.13 USD. After the successful purchase of the oilfield, the stock price of Shell has 0.75 probability of going up next year. However, if the company does not puchase the oildfield, its stock has only 0.15 probability of increasing in value. What is the probability of Shell’s share price going up next year?.
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Thank you for this detailed explanation/input.
After reading this text, I can formulate/re-formulate the problem in this way.
What is the probability to have the majority (4 or 5 or 6 or 7 votes "Yes"),
if each participant votes "Yes" with the probability 0.35.
The probability to have 4 votes "Yes" is ;
The probability to have 5 votes "Yes" is ;
The probability to have 6 votes "Yes" is ;
The probability to have 7 votes "Yes" is ;
Here the coefficients are the binomial coefficients, also known as the number of combinations of 7 things taken k at a time.
Now calculate the sum of these four particular probabilities. It is
+ + + = = 0.649.
Thus the probability to have the majority of votes "Yes" (4 or 5 or 6 or 7 votes) is equal to 0.649.
Having this, we can answer the major/final question:
What is the probability of Shell’s share price going up next year?
It is 0.649*0.75 + (1-0.649)*0.15 = 0.539.
Answer. The probability of Shell’s share price going up next year is 0.539, under formulated conditions.