A company manufactures a variety of household products. Last year, they conducted a marketing study to collect consumers' perceptions about detergents existing in the market. The study cost them $$500,000.$ Today, the company is considering introducing a new detergent, Clean$-$it$-$All, which kills COVID$-19.$ The company's CFO has collected the following information about the proposed product.

The project has an anticipated economic life of $4$ years.

The company will have to purchase a new machine to produce the detergent. The machine has an up$-$front cost of $$2,500,000.$ The machine will be depreciated using the MACRS class of $3$ years $($MACRS $3-$year rates are $33\%,45\%,15\%,$ and $7\%).$ The company anticipates selling the machine at the end of four years for

$$175,000.$ If the company goes ahead with the proposed product, it will have an effect on the company's operating working capital. At the outset, $t=0,$ inventory will increase by $$350,000,$ and accounts payable will increase by $$150,000.$ The detergent is expected to generate sales revenue of $$1\mathrm{.}5$ million the first year $(t=1),$ $$2$ million the second year $(t=2),$ $$2$ million the third year $(t=3),$ and $$1\mathrm{.}5$ million the final year $(t=4).$ Each year the operating costs $($not including depreciation$)$ are expected to equal $35$ percent of sales revenue. The company's interest expense each year will be $$250,000.$ The new detergent is expected to reduce the after$-$tax cash flows of the company's existing products by

$$125,000$ a year for $4$ years. The company's overall cost of capital is $12$ percent. The company's tax rate is $21$ percent.

What is the initial investment, $CF0?$

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

What is the terminal value in year $4?$

What is the NPV of this project?

$***$PLEASE show work & the formulas used. Promise to upvote!