This is a deferred annuity question. The cash flow diagram looks like this:
Year: 19 |
20 |
21 |
22 … |
31 |
0 |
0 |
0 |
5 … |
5 |
IN YEAR 21, the Value of the annuity of 10 payments of $5M is
311.2
Assume that a particular college basketball player is certain to go pro. He is 19 now and will likely earn $5 million per year for 10 years once he turns pro at the age of 22. If his first paycheck of $5 million dollars is due 3 years from today, what is the value today of his future earnings as a professional basketball player? Assume a discount rate of 15% per year. (3 pts)
This is a deferred annuity question. The cash flow diagram looks like this:
Year: 19
20
21
22 …
31
0
0
0
5 …
5
IN YEAR 21, the Value of the annuity of 10 payments of $5M is
If the discount rate is lower would the value today be lower or higher? WHY?
Higher. A lower discount rate means we put more value on future cash flows. Our current opportunities to invest our money are less attractive, so money today is relatively less valuable that it used to be, meaning future cash flows are worth more money today. Finally, another way of thinking about it is that at a lower interest rate, it would take you more money today to recreate the cash flows that would come from this annuity.
If he expects to turn pro earlier, but still plans to play only 10 years, will the value of his earnings today be lower or higher? WHY?
Higher. He will still be paid the same amount of money, but he will be getting it sooner, which is always more valuable than getting it later.