Question

Bill Clinton reportedly was paid $15.0 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 $8.5 million per year (paid at the end of the year) speaking instead of writing. Assume his cost of capital is 9.8% 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 $5.4 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?

Answer 1

We can compute the NPV of agreeing to write the book, ignoring any royalty payments, using an approach similar to Eq. 8.3. The cash flows are an immediate $10 million outflow followed by an annuity inflow of $8 million per year for three years and a discount rate of 10%. We can compute the NPV of the book with the royalty payments by first computing the present value of the royalties at year 3. Once we compute the royalties at year 3 we can compute the present value of the royalties today and add that number to the NPV of agreeing to write the book ignoring any royalty payments.

a. Timeline: 0 1 2 3 10 –8 –8 –8 381NPV101$9.895 million0.1(1.1)ΛΞ=−−=−ΜΟΝΠ

b. Timeline: 0 1 2 3 4 5 6 10 –8 –8 –8 5 5(1 –0.3) 5(1 – 0.3)2 First, calculate the PV of the royalties at year 3. The royalties are a declining perpetuity: PV3=50.1−(−0.3)=50.4=12.5 million
so the value today is royalties312.5PV(1.1)square=9.391
Now add this to the NPV from part

(a), NPV9.895+9.391=$503,381.
The NPV rule indicates that by agreeing to write the book (ignoring any royalties), you will decrease the value of Clinton’s wealth today by $9.895 million, and by agreeing to write the book including royalties, you will decrease the value of the firm by only $503,381 and therefore Bill should not undertake either project because both will decrease the value of the firm