Question

2. (30) In September 2017, Russell Westbrook has recently signed the richest contract in NBA history, a so-called “super-max” deal starting from the 2018-19 season and running for five years that would entitle him to a salary equal to 35% of the projected salary cap of $100 million that year, with 8% annual raises thereafter. For the sake of simplicity, assume that he receives the entirety of his annual salary as a lump sum at the beginning of each season, and that these payments grow at a constant rate, rather than increasing linearly as they do in actual NBA contracts.

(a) (10) Write Westbrook’s salary schedule, and compute the nominal value of the contract, as you would have seen it reported in the news.

(b) (10) Assuming an interest rate of 3%, calculate the present value, on the date of signing, of each annual payment and the contract as a whole.

(c) (10) Calculate the present value of the contract using the growing annuity formula. What restriction of the perpetuity formula does not apply to the annuity formula?

Answer 1

Part (a) The salary schedule & nominal value will be as below:

?Part (b) Using the inflation rate of 3% as the discount rate, the present value of the annual payment and contract as a whole will be, as below:

?Note that the first year salary has not been discounted since we are given that the payments are received at the begining of the season and not at the end. Accordingly even the Year 2 (and so on) payment has been discounted for 1 year only (and so on).

Part c: This payment stream is akin to a growing annuity due (since the payments are received in the beginning) with payment stream growing at the rate of 8% per annum. The formula for the same is as below:

PV_{annuity due growing}? = P * (1+r) * [(1-{(1+g)^t/(1+r)^t?})/(r-g)]

where P is the annuity payment or the first payment in this case, r is the discount rate of 3% and g is the growth rate of 8% and t is the time period . Now as we can see that this formula cannot be used since the term (r-g) for this case will be negative, hence instead of the formula we will do the following:

PV = P_{year 1} / (1+r)_?⁰? + (P_{year 1} * (1+g) )/ (1+r)^?1 + (P_{year 1} * (1+g)² )/ (1+r)^?2 + (P_{year 1} * (1+g)^?3 )/ (1+r)³ + (P_{year 1} * (1+g)^?4 )/ (1+r)^?4

^??Plugging in the values and solving we get:

PV = 35/(1) + 35*(1+8%)/(1+3%) + 35*(1+8%)²?/(1+3%)² + 35*(1+8%)³?/(1+3%)³ + 35*(1+8%)⁴/(1+3%)⁴? = $ 192.84 million