You run a mail$-$order firm, selling upscale clothing. You are considering replacing your

manual ordering system with a computerized system to make your operations more efficient

and to increase sales. $($All the cash flows given below are in real terms.$)$ The real discount

rate is $8\%.$

$$ The computerized system will cost $$10$ million to install, and $$500,000$ to operate

each year. It will replace a manual order system that costs $$1\mathrm{.}5$ million to operate

each year.

$$ The system is expected to last $10$ years, and have no salvage value at the end of the

period.

$$ The computerized system is expected to increase annual revenues from $$5$ million to

$$8$ million for the next $10$ years.

$$ The costs of goods sold is expected to remain at $50\%$ of revenues.

$$ The tax rate is $40\%.$

$$ As a result of the computerized system, the firm will be able to cut its inventory from

$50\%$ of revenues to $25\%$ of revenues immediately. There is no change expected in

the other working capital components.

a$.$ What is your expected cash flow at time$=0?$

b$.$ What is the expected incremental annual cash flow from computerizing the

system?

c$.$ What is the net present value of this project?