Question

2 Turning Pro

Suppose that the present value of lifetime earnings is $20 million. Assume that interest rate (i) is 5% and the growth rate for 1 year of college is 10% for a certain player.

a) If the player goes to college for 1 year, what is his expected lifetime earnings? Now suppose that this growth rate decreases 2 percentage points each year (so r1 = 10%, r2 = 8%, r3 = 6%, etc).

b) How many years of college would the player attend (assuming he is rational)?

c) If the player decides to stay the amount that was decided in part b, what would be his expected lifetime earnings?

Answer 1

a). Growth rate of college per year = 10%

So, PV of Lifetime Earnings after 1 year = $20 x 10% = $22

PV of $22 = $22/1.05 = $20.95 million

b). Below is the Table showing the Value of Life time earnings after every year at college with the given depreciating growth rate and the PV of those lifetime earnings today, calculated at 5% discount rate.

	T0	T1	T2	T3	T4	T5
Lifetie Earnings growth	20.00	22.00	23.76	25.19	26.19	26.72
PV @ 5% discount rate	20.00	20.95	21.55	21.76	21.55	20.93

Being a rational person, he will attend college untill the PV of his lifetime savings maximizes which happens after Year 3. After that the PV starts decreasing. Hence, he will attend 3 years of college.

c). expected Lifetime earnings if staying in college for 3 years = $21.76 million