You are working with a consumer product company on estimating the expected

cash flows from a new brand of toothpaste that they plan to introduce. From your

prior experiences with earlier introductions of similar products, you have

collected the following information:

$$ You are likely to sell $8$ million tubes in the first year that you introduce the project,

$10$ million in the second year, $12$ million in the third year and back down to $8$

million in the fourth year. At the end of the fourth year, you will have to replace

the brand with a new one.

$$ You price toothpaste at $ $3$ a tube currently, and expect to increase prices at $5\%$ a

year for the next $4$ years.

$$ You will have to advertise most heavily in the first year, spending $ $10$ million on

advertising, but you expect this to drop to $ $6$ million in year $2,$ $ $4$ million in year

$3$ and $ $2$ million in year $4.$

$$ Your costs associated with producing the toothpaste are $ $0\mathrm{.}50$ a tube currently, and

you expect this to increase at $5\%$ a year for the next $4$ years.

$$ You will have to invest $ $10$ million in new equipment at an old plant to create the

manufacturing facilities and you expect to depreciate this expenditure straight line

over the $4$ years down to zero.

$$ You have a $40\%$ tax rate.

$$ The firm$$s weighted average cost of capital is $12\%.$ This is the required return on

the project.

What is the NPV$?$

Please exlpain with formulas included thank you!