Bill Clinton reportedly was paid $ $15\mathrm{.}0$ million to write his book My Life. 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 $ $8\mathrm{.}7$ million per year$($paid at the end of the$$ year$)$ speaking instead of writing. Assume his cost of capital is $9\mathrm{.}9\%$ 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 $ $4\mathrm{.}7$ 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?