Poor Alex Rodriguez! The newspapers claim that he is making $5.7 million a year.
ID: 2613527 • Letter: P
Question
Poor Alex Rodriguez! The newspapers claim that he is making $5.7 million a year. He claims that this is not true in a present value sense and that he will really be making the following amounts for the next 5 years:
Year | Amount
0 (now) | $ 5.5 million (Sign up Bonus)
1 | $ 4 million
2 | $ 4 million
3 | $ 4 million
4 | $ 4 million
5 | $ 7 million
If you wanted to raise the nominal value of his contract to $30 million, while preserving the present value, how would you do it? (You can adjust only the sign up bonus and the final year's cash flow.)
7% is the discount rate
Explanation / Answer
We have to reduce sigb up Nonus by 3.73 million and the final year's cash flow by 5.23 million(3.73+1.5) to raise the nominal value of his contract to $30 million, while preserving the present value 24.04.
7% Year Nominal Value PV of $1 @ 7% PV of Cash Flows 0 5.5 1 5.5 1 4 0.9346 3.74 2 4 0.8734 3.49 3 4 0.8163 3.27 4 4 0.7629 3.05 5 7 0.7130 4.99 Total 28.5 24.04 Let the sign up bonus be reduced by X, Then the cash flowin year 5 will have to be raised by X+1.5 (7.5-5) to raise the nominal valueof his contract to 30million, while preserving PV X-(X+1.5)/((1+0.07)^5)=0 X=1.5/((1.07)^5)-1) X=1.5/((1.07)^5)-1) X=3.73 million