The Rustic Welt Company is proposing to replace its old welt$-$making machinery with more modern equipment. The new equipment costs $$9$ million $($the existing equipment has zero salvage value$).$ The attraction of the new machinery is that it is expected to cut manufacturing costs from their current level of $$8$ a welt to $$4.$ However, as the following table shows, there is some uncertainty about both the future sales and the performance of the new machinery:

Pessimistic Expected Optimistic

Sales $($million welts$)0\mathrm{.}40\mathrm{.}50\mathrm{.}7$

Manufacturing cost $($$ per welt$)643$

Life of new machinery $($years$)71013$

Conduct a sensitivity analysis of the replacement decision assuming a discount rate of $12\%.$ Rustic does not pay taxes. Calculate the NPV of each