be$.$ "Tahiti is one of Chevron's five big projects," said Peter Robertson, vice

chairman of the company's board, to the Wall Street Joumal. ${?}^8$ Nevertheless

it was unclear whether the project would result in the blockbuster success

Chevron was hoping for. As of June $2007$$$4$ billion had been invested in

the high$-$tech deep sea platform, which sufficed to perform early well tests.

Aside from offering information on the type of reservoir, the tests would

produce enough oil to just cover the incremental costs of the testing $($beyond

the $$4$ billion investment$).$

Following the test wells, Chevron predicted one of three possible scenar$-$

ios. The optimistic one was that Tahiti sits on one giant, easily accessible oil

reservoir, in which case the company expected to extract $200,000$ barrels a

day after expending another $$5$ billion in platform setup costs, with a cost

of extraction of about $$10$ a barrel. This would continue for $10$ years, after

which the field would have no more economically recoverable oil. Chevron

believed this scenario had a $1-$in$-6$ chance of occurring. A less rosy scenario,

twice as likely as the optimistic one, was that Chevron would have to drill

two more wells at an additional cost of $$0\mathrm{.}5$ billion each $($above and beyond

the $$5$ billion setup costs$),$ in which case production would be around $100,000$

barrels a day with a cost of extraction of about $$30$ a barrel, and the field would

still be depleted after $10$ years. The worst$-$case scenario involves the oil being

tucked away in numerous pockets, requiring expensive water injection tech$-$

niques, which would involve upfront costs of another $$4$ billion $($above and

beyond the $$5$ billion setup costs$)$ and extraction costs of $$50$ a barrel; produc$-$

tion would be estimated to be at about $60,000$ barrels a day for $10$ years. Bill

Varnado, Tahiti's project manager, was quoted as giving this least desirable

outcome odds of $50-50.$

The current price of oil is $$70$ a barrel. For simplicity assume that the

price of oil and all costs will remain constant $($adjusted for inflation$)$ and that

Chevron faces a $0\%$ cost of capital $($also adjusted for inflation$).$

a$.$ If the test wells would not produce information about which one of

three possible scenarios would result, should Chevron invest the setup

costs of $$5$ billion to be prepared to produce under whichever scenario

is realized?

b$.$ If the test wells do produce accurate information about which of three

possible scenarios is true, what is the added value of performing these

tests?