Question

You have just been offered your dream job after graduating from Jacksonville University. In response to your negotiations concerning your compensation package, the company has offered you a couple of different stock options in addition to the agreed upon salary.
Under the first option, you would receive stocks with a value of $2,000,000 at the end of each year. This option also includes an additional $4,000,000 bonus that you would receive for staying at the company for 3 years.
Under the second option, you would receive stocks with a value of $1,000,000 at the end of each year. This option also includes an additional $8,000,000 bonus that you would receive for staying at the company for 3 years.
Assume that these stocks grow at a rate of 11% compounded monthly. Moreover, assume that you will leave the company at the end of your fourth year to start your own firm. Which option will you choose. (The more money you have to start your own firm, the better.)
Your formal solutions should include ...
⦁ The overall goal and/or purpose.
⦁ The given information
⦁ A time-line for each option
⦁ A future value for each individual stock payment provided you by the company
⦁ The total future value of each option at the time you plan to leave the company
⦁ Your conclusion

Answer 1

Answer:

Goal: maximize return at the end of the fourth year.

Future value of each option:

First choise:       $ 11,730,289.64

Second choise: $ 12,559,457.84‬

Conclusion:

It is better to pick the second option as yields a better return

Explanation:

We solve for the future value of the cashflow of each option:

First choise:

End of the first year:

$Principal \: (1+ r)^{time} = Amount$

Principal 2,000,000.00

time 36.00 (form end of the first to end of the fourth)

rate 0.00917 (11% / 12 months as it compounds monthly)

$2000000 \: (1+ 0.00916666666666667)^{36} = Amount$

Amount $2,777,757.26

End of the second year:

Principal 2,000,000.00

time 24.00

rate 0.00917

$2000000 \: (1+ 0.00916666666666667)^{24} = Amount$

Amount $2,489,657.04

End of the third year:

Principal 4,000,000.00

time 12.00

rate 0.00917

$4000000 \: (1+ 0.00916666666666667)^{12} = Amount$

Amount $4,462,875.34

End of the fourth year: $2,000,000

Total:  

$2,777,757.26

$2,489,657.04

$4,462,875.34

$2,000,000        

$ 11,730,289.64

Second choise:

First year

Principal 1,000,000.00

time 36.00

rate 0.00917

$1000000 \: (1+ 0.00916666666666667)^{36} = Amount$

Amount 1,388,878.63

Second year:

Principal 1,000,000.00

time 24.00

rate 0.00917

$1000000 \: (1+ 0.00916666666666667)^{24} = Amount$

Amount 1,244,828.52

Third Year

Principal 8,000,000.00

time 12.00

rate 0.00917

$8000000 \: (1+ 0.00916666666666667)^{12} = Amount$

Amount 8,925,750.69

Fourth year: 1,000,000

Total

1,388,878.63

1,244,828.52

8,925,750.69

1,000,000.00      

12,559,457.84‬