Arnold Inc. is considering a proposal to manufacture high$-$end protein bars used as food supplements

by body builders. The project requires use of an existing warehouse, which the firm acquired three

years ago for $$1$ million and which it currently rents out for $$120,000.$ Rental rates are not expected to

change going forward. In addition to using the warehouse, the project requires an up$-$front investment

into machines and other equipment of $$8$m$.$ This investment can be fully depreciated straight$-$line over

ten years for tax purposes. However, Arnold Inc. expects to terminate the project at the end of four

years and to sell the machines and equipment for $$1$m$.$

The project requires an initial investment in net working capital equal to $10\%$ of predicted first$-$year

sales. Subsequently, the net working capital at the beginning of each year is $10\%$ of the predicted sales

over the following year. For example, the net working capital at the beginning of the second year $($ie at

t $=1)$ is $10\%$ of the sales at t $=2$; the net working capital at the beginning of the third year $($ie at t $=2)$

is $10\%$ of the sales at t $=3,$ and so on$.$ Assume that the net working capital is fully recovered at the end

of the project.

Sales of protein bars are expected to be $$10$ million in the first year and to increase at $10\%$ per year

over the life of the project. Total manufacturing costs and operating expenses $($excluding depreciation$)$

are $70\%$ of sales, and profits are taxed at $20\%.$

a$.$ What are the free cash flows of the project? Calculate the free cash flows using both methods to

account for depreciation.

b$.$ If the cost of capital is $15\%,$ what is the NPV of the project?

c$.$ Redo your calculations assuming that the investment can be fully depreciated straight$-$line over the

next four years $($instead of ten years$)$ for tax purposes. Why does the NPV change?