Maxine Peru, the CEO of Peru Resources, hardly noticed the plate of savory quenelles de brochet and the glass of Corton Charlemagne $\text{'}94$

on the table before her. She was absorbed by the engineering report handed to her just as she entered the executive dining room.

The report described a proposed new mine on the North Ridge of Mt$.$ Zircon. A vein of transcendental zirconium ore had been discovered

there on land owned by Ms$.$ Peru's company. Test borings indicated sufficient reserves to produce $340$ tons per year of transcendental

zirconium over a seven$-$year period.

The vein probably also contained hydrated zircon gemstones. The amount and quality of these zircons were hard to predict because they

tended to occur in "pockets." The new mine might come across one, two, or dozens of pockets. The mining engineer guessed that $150$

pounds per year might be found. The current price for high$-$quality hydrated zircon gemstones was $$3,300$ per pound.

Peru Resources was a family$-$owned business with total assets of $$45$ million, including cash reserves of $$4$ million. The outlay required for

the new mine would be a major commitment. Fortunately, Peru Resources was conservatively financed, and Ms$.$ Peru believed that the

company could borrow up to $$9$ million at an interest rate of about $8\%.$

The mine's operating costs were projected at $$900,000$ per year, including $$400,000$ of fixed costs and $$500,000$ of variable costs. Ms$.$ Peru

thought these forecasts were accurate. The big question marks seemed to be the initial cost of the mine and the selling price of

transcendental zirconium.

Opening the mine, and providing the necessary machinery and ore$-$crunching facilities, was supposed to cost $$10$ million, but cost overruns

of $10\%$ or $15\%$ were common in the mining business. In addition, new environmental regulations, if enacted, could increase the cost of the

mine by $$1\mathrm{.}5$ million.

There was a cheaper design for the mine, which would reduce its cost by $$1\mathrm{.}7$ million and eliminate much of the uncertainty about cost

overruns. Unfortunately, this design would require much higher fixed operating costs. Fixed costs would increase to $$850,000$ per year at

planned production levels.

The current price of transcendental zirconium was $$10,000$ per ton, but there was no consensus about future prices. I Some experts were

projecting rapid price increases to as much as $$14,000$ per ton. On the other hand, there were pessimists saying that prices could be as low

as $$7,500$ per ton. Ms$.$ Peru did not have strong views either way: Her best guess was that price would just increase with inflation at about

$3\mathrm{.}5\%$ per year. $($Mine operating costs would also increase with inflation.$)$

Ms$.$ Peru had wide experience in the mining business, and she knew that investors in similar projects usually wanted a forecast nominal rate

of return of at least $14\%.$

You have been asked to assist Ms$.$ Peru in evaluating this project. Lay out the base$-$case NPV analysis, and undertake sensitivity$,$ scenario,

or break$-$even analyses as appropriate. Assume that Peru Resources pays tax at a $30\%$ rate. For simplicity, also assume that the investment

in the mine could be depreciated for tax purposes straight$-$line over seven years.

What forecasts or scenarios should worry Ms$.$ Peru the most? Where would additional information be most helpful? Is there a case for

delaying construction of the new mine?The most likely outcomes for a particular project are estimated as follows:

However, you recognize that some of these estimates are subject to error. Suppose each variable turns out to be either $10\%$ higher or

$10\%$ lower than the initial estimate. The project will last for $10$ years and requires an initial investment of $$1\mathrm{.}9$ million, which will be

depreciated straight$-$line over the project life to a final value of zero. The firm's tax rate is $21\%,$ and the required rate of return is $10\%.$

a$.$ What is project's NPV in the best$-$case scenario, that is$,$ assuming all variables take on the best possible value?

b$.$ What is project's NPV in the worst$-$case scenario?

Note: For all the requirements, a negative amount should be indicated by a minus sign. Enter your answers in dollars, not in

millions. Do not round intermediate calculations. Round your answers to the nearest dollar amount.

Answer is complete but not entirely correct.