A company is considering replacing an old machine with a new one. The old machine is completely depreciated and can be sold for $$150,000$ in the market. The company intends to keep this old machine for its spare parts. The new machine costs $$450,000.$ The replacement of the machine will require an increase in inventories by $$250,000,$ and at the same time, accounts payable will increase by $$100,000.$

The new machine is going to be depreciated over $4$ years to zero salvage value.

The new machine will increase annual revenue by $$150,000,$ and in addition, it will reduce annual operating costs by $$75,000.$ This new machine can be sold for $$150,000$ in $4$ years. The project$$s life span is $4$ years. The company$$s tax rate is $21\%,$ and the cost of capital is $12\%.$

$1.$ What is the initial investment, CF$0?$

$2.$ What is the first cash flow, CF$1,$ that will be used for the NPV calculations?

$3.$ What is the terminal value in year $4?$

$4.$ What is the NPV of this project?