Question

Bill ClintonBill Clinton

reportedly was paid an advance of

$ 10.0$10.0

million to write his book

My LifeMy 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

$ 8.1$8.1

million a year​ (paid at the end of the​ year) speaking instead of writing. Assume his cost of capital is

10.2 %10.2%

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

$ 4.9$4.9

million in the first year​ (paid at the end of the​ year) and these royalties are expected to decrease at a rate of

30 %30%

per year in perpetuity. What is the NPV of the book with the royalty​ payments?

Answer 1

Answer

a. NPV = $-10.073 million

b. NPV = $-964739.92

Explanation

a.

Cash Inflow in year 0 = $10 million

Opportunity cost from year 1 to 3 = $8.1 million each year

NPV = Initial cash inflow - Present value of opportunity cost

Present Value factor =  (1 - (1 + cost of capital) ^-years ) / cost of capital

Present Value factor =  (1 - (1 + 10.2%) ^-3 ) / 10.2%

Present Value factor =  2.47812179170518

Present value of opportunity cost = 8100000 * 2.47812179170518 = 20072786.512812

NPV = 10000000 - 20072786.512812 = -10072786.51

NPV = $-10.073 million

Note: Cash flow timeline

0		1		2		3
10		–8.1		–8.1		–8.1

b.

Cash Flow Timeline

0		1		2		3		4		5		6
10		–8.1		–8.1		–8.1		4.9		4.9(1 – 0.3)		4.9(1 – 03)2

Cash flow for first 3 years will be same and next 3 years royalty will be received at $4.9 million in year 4 and decreasing 30% in year 5 and year 6.

Value of royalty at the end of 3 years = Royalty in year 4 / (cost of capital - growth rate)

Value of royalty at the end of 3 years = 4900000 / (.102 - (-.3))

Value of royalty at the end of 3 years = 4900000 / .402 = 12189054.7263682

Present Value of royalty = 12189054.7263682 / (1+10.2%)^3 = 9108046.58832279

Now add this to the NPV from part a)

NPV = -10072786.51 + 9108046.59

NPV = $-964739.92

Conclusion

The NPV rule indicates that by writing the book ignoring royalties, you will decrease the value of the firm today by $10.073 million, and by writimg the book including royalties, you will decrease the value of the firm by only $964,740 and therefore Bill should not undertake either project because both will decrease the value.