323.3
3.Kevin Brown, a pitcher for the Dodgers, became
baseball's first "$100 million man". His contract called for a $15
million payment upon signing, $10 million in the first year,
and $15 million per year for 6 years after that, adding up to $115
million. Assume that all of his salary payments except for the
signing bonus are paid at the ends of the years. What is the
actual value of his contract if the appropriate discount rate is
10%? (6)
This employs a deferred annuity. In order to answer this question you should start with a cash flow diagram!
| Signing | 1 | 2 … | 7 |
| $15M | $10M | $15M … | $15M |
There are 2 cash flows followed by a deferred annuity of 6 payments of $15M each. The deferred annuity starts in year 2, so our annuity formula will give us the value of that annuity in year 1. We will then need to discount it back 1 more year to the present. At a 10% discount rate, the present value of his contract is:
Guess he’s not the $100 million man after all.
