United Petroleum is operating a deep water oil rig in the Gulf of Calexico. Management have been informed that the drilling riser may be susceptible to methane build up and hence at risk of an explosion. It is estimated that the repairs following such an explosion, together with the costs of cleaning up the resulting pollution and the associated fines, legal costs and loss of business will reach 32.2 billion dollars(i.e. $32.2 x 109 ). There is a 1% probability of such an explosion occurring.
To replace the drilling riser with new equipment which removes the risk will involve taking the rig off-line, at a cost of 162,000 barrels of oil per day. Oil is currently priced at 98 per barrel. In addition, a one off cost of 115 million( 0.115 billion or 115 x 10^6) will be incurred for the equipment.
a) If United Petroleum has initial assets of 220 billion and a utility function U(W) = ln(0.5W – 50) where W is measured in $billions, calculate the maximum number of days it will be prepared to take the rig off-line in order to carry out the replacement.
I find this question very difficult, I'm not sure how to start it, I tried to calculate the answer and ended up with 4701 days, which seems to be a ridiculous answer. Can anyone help me with this please?
The approach is this:
1) Calculate the expected utility $EU$ from not installing the new drill. (Compute W if catastrophy hits, compute utility for this case, and weight with probability of catastrophy; compute W if catastrophy does not hit, etc., and add the two.)
2) Now calculate the utility of replacing the drill, leaving the days it takes to install it as variable in the expression. You get something like $U(d)$, where $U$ is strictly decreasing in the days $d$.
3) Now you just have to find $d$ such that $EU=U(d)$. For this $d$, the firm is indifferent between replacing or not. More days it strictly prefers not replacing, fewer days it strictly prefers replacing.