Nathan Caldwell Welding has decided to sell an improved design of gate posts. the post will be set for $$790$ per set and have a variable cost of $$390$ per set. The company has spent $$149,000$ for a marketing study that determined the company will sell $53,000$ sets per year for seven years. the marketing study also determined that the company will lose sales of $9400$ sets of its high priced posts. The high$-$priced posts sell at $$1,090$ and have a variable cost of $$690.$ The company will also increase sales of its cheap posts by $10,900$ sets. The cheap post sells for $$430$ and have a variable cost of $$225$ per set. The fixed costs each year will be $$9,090,000.$ The company has $$1,100,000$ on research and development for the new posts. The plant and equipment required will cost $$28,630,000$ and will be depreciated on a straight$-$line basis. The new post will also require an increase in net working capital of $$1,290,000$ which will be returned at the end of the project. The tax rate is $34$ percent and the cost of capital is $10$ percent.

a$.$ calculate the payback period.

b$.$ calculate the npv

c$.$ calculate the IRR

Suppose you feel that the values are accurate to within $+/-10$ percent. What are the best case and worse case NPVs$?$

d$.$ calculate the best npv

e$.$ calculate the worse npv

what is the sensitivity of the npv to the price and quantity of the new posts?