Nathan Caldwell Welding Company has decided to sell an improved design of gate posts. The posts will sell for $$790$ per set and have a variable cost of $$390$ per set. The company has spent $$149,000$ for a marketing study that determined the company will sell $53,000$ sets per year for seven years. The marketing study also determined that the company will lose sales of $9,400$ sets of its high$-$priced posts. The high$-$priced posts sell at $$1,090$ and have variable costs of $$690.$ The company will also increase sales of its cheap posts by $10,900$ sets. The cheap posts sell for $$430$ and have variable costs of $$225$ per set. The fixed costs each year will be $$9,090,000.$ The company has also spent $$1,100,000$ on research and development for the new posts. The plant and equipment required will cost $$28,630,000$ and will be depreciated on a straight$-$line basis. The new posts will also require an increase in net working capital of $$1,290,000$ that will be returned at the end of the project. The tax rate is $34$ percent, and the cost of capital is $10$ percent.

Suppose you feel that the values are accurate to within only $\backslash$pm $10$ percent. What are the best$-$case and worst$-$case NPVs$?($Hint: The price and variable costs for the two existing sets of posts are known with certainty; only the sales gained or lost are uncertain.$)($A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$ A$.$ Calculate the payback period B$.$ Calculate the NPV C$.$ Calculate the IRR D$.$ Calculate the Best Case NPV E$.$ Calculate the Worst case NPV What is the sensitivity of the NPV to the price and quantity of the new posts? f$.\backslash$Delta NPV$/\backslash$Delta P g$.\backslash$Delta NPV$/\backslash$Delta Q