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