New Energy is evaluating a new biofuel facility. The plant would cost $$4,000$ million to build and has the potential to produce up to $40$ million barrels of synthetic oil a year. The product is a close substitute for conventional oil and would sell for the same price. The market price of oil currently is fluctuating around $$100$ per barrel, but there is considerable uncertainty about future prices. Variable costs for the organic inputs to the production process are estimated at $$82$ per barrel and are expected to be stable. In addition, annual upkeep and maintenance expenses on the facility will be $$100$ million regardless of the production level. The plant has an expected life of $15$ years, and it will be depreciated straight$-$line over $10$ years. Salvage value net of clean$-$up costs is expected to be negligible. Demand for the product is difficult to forecast. Depending on consumer acceptance, sales might range from $25$ million to $35$ million barrels annually. The discount rate is $12\%$ and New Energy$$s tax bracket is $25\%.$

Oil price

Annual sales $($millions of barrels$)$ $$80/$Barrel $$100/$Barrel $$120/$Barrel

$25$

$30$

$35$

a$.$ Find the project NPV for the above combinations of oil price and sales volume. Which source of uncertainty seems most important to the success of the project?

b$.$ Estimate the number of years the project will pay back the investment for a combination of $30-$million$-$barrel sales and $$100/$barrel price.

c$.$ What will be the IRR for a combination of $25-$million$-$barrel sales and $$125/$barrel price?

d$.$ Assume that at one combination sales volume and price, NPV and IRR give contradictory results, i$.$ e$.$ one suggest to accept the project while the other reject the project. How do you resolve this problem?

e$.$ At an oil price of $$100,$ what level of annual sales, maintained over the life of the plant, is necessary for NPV break$-$even?