Consider a project to supply Detroit with $30,000$ tons of machine screws annually for

automobile production. You will need an initial $$4,600,000$ investment in threading

equipment to get the project started; the project will last for $3$ years. The accounting

department estimates that annual fixed costs will be $$750,000$ and that variable costs

should be $$410$ per ton; accounting will depreciate the initial fixed asset investment

straight$-$line to zero over the $3-$year project life. It also estimates a salvage value of

$$400,000$ after dismantling costs. The marketing department estimates that the

automakers will let the contract at a selling price of $$550$ per ton. The engineering

department estimates you will need an initial net working capital investment of

$$460,000.$ You require a return of $12$ percent and face a marginal tax rate of $24$ 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? $($Do not

round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,$

$32\mathrm{.}16.)$

b$.$ What about the sensitivity of NPV to changes in quantity supplied? $($Do not round

intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

c$.$ Given the sensitivity number you calculated, is there some minimum level of output

below which you wouldn't want to operate? $($Do not round intermediate calculations

and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$