Application of Time Value of Money Skills

Gavin Goldenarm has been playing baseball since he was five years old and has always dreamed of playing in the big leagues. Last season, he was a starting pitcher for a double$-$A $($AA$)-$level baseball team, the Ketchum Baldies; last year, he was the first runner$-$up for the Minor League Player of the Year award. Using his $93mph$ fastball, an impeccable curve ball and slider, and a reliable changeup pitch, he achieved a $15-2$ win$-$loss record, an earned run average $($ERA$)$ of $2\mathrm{.}76,$ and $123$ strikeouts in $99\mathrm{.}1$ innings pitched. He is also your best friend.

Two weeks ago, on his three$-$year anniversary with the team, Gavin received the following email from his agent, Steven Sign'em$-$Now, indicating that he is being called up to the Wichita Wizards, the Baldies's corresponding Major League Baseball $($MLB$)$ team. Moreover, Gavin's contract is being revised to reflect his new status. The email describes the general terms and conditions of Gavin's revised contract.

Salary and Incentives:

Gavin Goldenarm hereafter referred to as the "Player," is offered a four$-$year contract with an annual salary of $$414,000$ per year, to be paid at the end of each month in the contract term.

Under the league's collective bargaining agreement, the Player will receive a $4\%$ cost$-$of$-$living adjustment $($COLA$)$ to his annual salary at the beginning of every other year. This means that the Player's annual salary will increase at the beginning of year $2$ and year $4,$ as applicable.

In addition, the Player will receive a one$-$time $$15,000$ time$-$in$-$league bonus after six months of participation with an MLB team. This bonus will be paid immediately on completion of the six$-$month period.

The Player is offered a performance$-$based bonus, as well as a milestone bonus. Both are intended to encourage outstanding performance.

The Player is offered the following award$-$based performance incentive: a $15\%$ bonus if he is designated as the Most Valuable Player $($MVP$)$ in the league. The Player is also offered the following milestone bonus: a $$150,000$ bonus if he ties Nolan Ryan's $1973$ single$-$season strikeout record $(383$ strikeouts$).$

The Player is eligible for each potential bonus each year that the contract is in effect and, if expressed as a percentage, will be based on the value of the Player's base annual salary for the corresponding year. If earned, the performance and milestone bonuses will be distributed in a single payment at

Gavin is so excited! According to Steven, the contract is worth $$2,564,400-$assuming receipt of all possible bonuses. After rereading the email twice and calling his family, Gavin called you to review the terms of the contract and verify Steven's calculations. After an extended conversation about what he'll do with his newfound wealth, you and Gavin have agreed that any funds received could be invested to earn $5\mathrm{.}50\%,$ compounded monthly.

Contract Evaluation Worksheet

Complete the following worksheet by inserting the appropriate values to evaluate the contract and answer the related questions.

Note: To clarify possible sources of confusion and simplify your calculations:

Assume that all bonuses are earned in each of the years for which they are available and are paid at the end of the corresponding year$($s$),$ unless specifically stated differently. Their value should be based on the salary in effect at the time the bonuses were earned.

The endorsement proceeds are paid in accordance with the terms of the deal.

Remember that the timing of a cash flow affects the interest rate that is used to discount the cash flow. For example, annual interest rates should be used to discount annual cash flows, and monthly interest rates are used to discount monthly cash flows. Therefore, it may be necessary to compute the appropriate interest rate that should be used in a discounting calculation.

Round all dollar amounts to the nearest whole dollar and carry out all interest rate factors to four decimal places.

When entering intermediate values as answer choices, be sure to round them to the nearest dollar, however when using those same values to calculate another answer, do not round.

$16$

$17$ Milestone Bonus

$18$ Discount factor $($based on

$0\mathrm{.}9466$

$0\mathrm{.}8961$

$0\mathrm{.}8482$

$0\mathrm{.}8029$

Cell B$5$ above$)$

$19$ Discounted Milestone Bonus

$20$

$21$ Performance Bonus

$22$ Discount factor $($based on

$0\mathrm{.}9466$

$0\mathrm{.}8961$

$0\mathrm{.}8482$

$0\mathrm{.}8029$

Cell B$5$ above$)$

$23$ Discounted Performance

Bonus

$24$

$25$ Monthly Endorsement

Contract Payment

$26$ Discount factor $($based on $11\mathrm{.}6500,11\mathrm{.}0280$

Cell B$4$ above$)$

$27$ Discounted Monthly

Endorsement Payment

$28$

$29$ Contract's Total Nominal

Value

Endorsement Payment

$28$

$29$ Contract's Total Nominal

Value

$30$ Contract's Total Discounted

Value

Given your worksheet calculations, which of th