$1.$ You are considering opening a new plant. The plant will cost $$100$ million upfront. After that, it is expected to produce profits of $$30$ million at the end of every year. The cash flows are expected to last forever. Calculate the NPV of this investment opportunity if your cost of capital is $8\%.$ Should you make the investment? Calculate the IRR and use it to determine the maximum deviation allowable in the cost of capital estimate to leave the decision unchanged.

$2.$ Bill Clinton reportedly was paid $$15$ million to write his book My Life. Suppose the book took three years to write. In the time he spent writing, Clinton could have been paid to make speeches. Given his popularity, assume that he could earn $$8$ million per year $($paid at the end of the year$)$ speaking instead of writing. Assume his cost of capital is $10\%$ per year.

a$.$ What is the NPV of agreeing to write the book $($ignoring any royalty payments$)?$

b$.$ Assume that, once the book is finished, it is expected to generate royalties of $$5$ million in the first year $($paid at the end of the year$)$ and these royalties are expected to decrease at a rate of $30\%$ per year in perpetuity. What is the NPV of the book with the royalty payments?

$3.$ You are considering making a movie. The movie is expected to cost $$10$ million upfront and take a year to make. After that, it is expected to make $$5$ million in the first year it is released and $$2$ million per year for the following four years. What is the payback period of this investment? If you require a payback period of two years, will you make the movie? Does the movie have positive NPV if the cost of capital is $10\%?$

$4.$ You are deciding between two mutually exclusive investment opportunities. Both require the same initial investment of $$10$ million. Investment A will generate $$2$ million per year $($starting at the end of the first year$)$ in perpetuity. Investment B will generate $$1\mathrm{.}5$ million at the end of the first year and its revenues will grow at $2\%$ per year for every year after that.

a$.$ Which investment has the higher IRR?

b$.$ Which investment has the higher NPV when the cost of capital is $7\%?$