Question $3($Sensitivity Analysis$)$

Consider a project to supply Detroit with $30,000$ tons of machine screws annually for automobile production. You will need an initial $$3,800,000$ investment in threading equipment to get the project started; the project will last for $4$ years. The accounting department estimates that annual fixed costs will be $$600,000$ and that variable costs should be $$340$ per ton; accounting will depreciate the initial fixed asset investment straight$-$line to zero over the $4-$year project life. It also estimates a salvage value of $$340,000$ after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of $$450$ per ton. The engineering department estimates you will need an initial net working capital investment of $$380,000.$ You require a return of $12$ percent and face a marginal tax rate of $25$ percent on this project. Suppose you're confident about your own projections, but you're a little unsure about Detroit's actual machine screw requirements.

a$.$ What is the sensitivity of the project OCF to changes in the quantity supplied?

$1$

Neil@UPMKB$2$O$24$

b$.$ What about the sensitivity of NPV to changes in quantity supplied?

c$.$ Given the sensitivity number you calculated, is there some minimum level of output below which you wouldn't want to operate?