Bill Clinton reportedly was paid an advance of $$$$10\mathrm{.}0$ million to write his book My Life. Suppose the book took $3$ years to write. In the time he spent$$ writing, Clinton could have been paid to make speeches. Given his$$ popularity, assume that he could earn $$$$8\mathrm{.}2$ million a year$($paid at the end of the$$ year$)$ speaking instead of writing. Assume his cost of capital is $10\mathrm{.}2\%$ 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 $$$$4\mathrm{.}8$ million in the first year$($paid at the end of the$$ 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?