John Howard reportedly was paid $ $420$ comma $000$ to write his book Lazarus Rising. The book took three years to write. In the time he spent$$ writing, Howard could have been paid to make speeches. Given his significance as$$ Australia's second$-$longest serving Prime$$ Minister, assume that he could earn $ $320$ comma $000$ per year$($paid at the end of the$$ year$)$ speaking instead of writing. Assume his cost of capital is $9\mathrm{.}5\%$ per year. Assume also that once the book is$$ finished, it is expected to generate royalties of $ $210$ comma $000$ in the first year$($paid at the end of the$$ year$)$ and these royalties are expected to decrease at $30\%$ per year in perpetuity. The NPV of the book with the royalty payments is negative $ $382$ comma $850.$ How many IRRs are there in this$$ problem? Does the IRR rule work in this$$ case?