Problem:

A light manufacturing firm has set up a project for developing a new machine for one of its production lines. The most likely estimated cost of the project itself is $1,000,000, but the most optimistic estimate is $900,000 while the pessimists predict a project cost of $1,200,000. The real problem is that even if the project costs are within those limits, if the project itself plus its implementation costs exceed $1,425,000, the project will not meet the firm's NPV hurdle. There are four cost categories involved in adding the prospective new machine to the production line: (1) engineering labor cost, (2) nonengineering labor cost, (3) assorted material cost, and (4) production line down-time cost.

The engineering labor requirement has been estimated to be 600 hours, plus or minus 15 percent at a cost of $80 per hour. The nonengineering labor requirement is estimated to be 1500 hours, but could be as low as 1200 hours or as high as 2200 hours at a cost of $35 per hour. Assorted material may run as high as $155,000 or as low as $100,000, but is most likely to be about $135,000. The best guess of time lost on the production line is 110 hours, possibly as low as 105 hours and as high as 120 hours. The line contributes about $500 per hour to the firm's profit and overhead.

Required:

Question 1) What is the probability that the new machine project will meet the firm's NPV hurdle? Solve the given numerical problem and illustrate step by step calculation.