Question

Suppose that the present value of lifetime earnings is S20 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 ri-10%, T2-8%, T3-696, etc). b) How masy years ldth phe ls rationalY c) If the player decides to stay the amount that was decided in part b, what would be his expected lifetime earnings?

Answer 1

This is a question on perpetuity.

As we know the Present value of perpetuity = Each year payment / Difference of growth rate and interest rate

Here if PV = 20 Million, then Each year payment = PV X (Difference between growth rate and interest rate )

= 20 million x (0.10-.05)

= 1 million

So if a student goes to college for only 1 year, his expected earnings are 1 million only.

b) If the player is rational, he will continue playing till the growth rate becomes zero. That means till period when the growth rate is 0%, he will continue. Hence r1=8%,r2 =6% , r3=4%,r2= 2 %. So the player will attend 4 years of college if growth rate decreases at the above rate.

c)Expected earnings if he stays for 4 years =

= P1/r-g + P2/r-g + p3/r-g + p4/r-g

= 1 mn /(0.10-0.05) + 1 mn/ (0.8-0.05) + 1 mn/ (0.6-.05) + 1 mn/(0.4-.05) + 1 mn/(0.2-.05)

= 20 mn +1.3 mn+ 1.82 mn+2.86 mn+6.7 mn

= 32.68 mn