An oil company is drilling a series of new wells on the perimeter of a producing oil field.

About $20\%$ of the new wells will be dry holes. Even if a new well strikes oil, there is still uncertainty about the amount of oil produced: $40\%$ of new wells that strike oil produce only $1,000$ barrels a day; $60\%$ produce $5,000$ barrels per day.

a$.$ Forecast the annual cash revenues from a new perimeter well. Use a future oil price of

$$50$ per barrel.

b$.$ A geologist proposes to discount the cash flows of the new wells at $30\%$ to offset the risk of dry holes. The oil company$$s normal cost of capital is $10\%.$ Does this proposal make sense? Briefly explain why or why not.