A Corporation has $34\%$ marginal tax bracket with a $30\%$ required rate of retum or cost of capital, is considering a new project. This project involves the introduction of a new product. The project is expected to last five years and then, because this is somewhat of a fad project, to be terminated.

Cost of new plant and equipment: $$9,900$

Shipping and installation cost: $$100$

Unit Sales:

$\backslash$table$[[$Year$,$Unit sold$],[1,500],[2,600],[3,700],[4,800],[5,900]]$

Sales price per unit: $$50/$ unit in years $1-4,$ $$35/$unit in year $5$

Variable cost per unit: $$30/$ unit

Annual fixed costs: $$3,000$

Working Capital Requirement: There will be an initial working capital requirement of $$50,000$ just to get production started. Then, for each year, the total investment requirement in NWC will be equal to $10\%$ of the dollar value of sales for that year. Finally, $90\%$ of working capital is liquidated at the termination of the project at the end of year $5.$

The Depreciation Method: Assume that Straight Line Method will be used over $5$ years. It is assumed that $20\%$ of the plant and equipment will be liquated at year $5.$

Given the following information,

a$)$ Determine the free cash flows associated with the project,

b$)$ Calculate and comment on the project's NPV$?$

c$)$ Calculate and comment on the project's IRR?

d$)$ Calculate and comment on the project's $P{I}_{?}?$