Application of Time Value of Money Skills

Flynn Fireballer 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 Roswell Extraterrestrials; last year, he was the first runner$-$up for the Minor League Player

of the Year award. Using his $96mph$ fastball, an impeccable curve ball and slider, and a reliable changeup pitch, he achieved a $16-3$ win$-$loss record,

an earned run average $($ERA$)$ of $2\mathrm{.}98,$ and $146$ strikeouts in $117\mathrm{.}0$ innings pitched. He is also your best friend.

Two weeks ago, on his three$-$year anniversary with the team, Flynn received the following email from his agent, Marty Fineprint, indicating that he is

being called up to the Mobile Bayhoppers, the Extraterrestrials's corresponding Major League Baseball $($MLB$)$ team. Moreover, Flynn$\text{'}$s contract is being

revised to reflect his new status. The email describes the general terms and conditions of Flynn$\text{'}$s revised contract.

Flynn is so excited! According to Marty, the contract is worth $$3,054,400-$ assuming receipt of all possible bonuses. After rereading the email twice

and calling his family, Flynn called you to review the terms of the contract and verify Marty's calculations. After an extended conversation about what

he'll do with his newfound wealth, you and Flynn have agreed that any funds received could be invested to earn $7\mathrm{.}50\%,$ 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.

Flynn Fireballer's Contract Evaluation Worksheet$12$

$13$ Time$-$in$-$League Bonus

$14$ Discount factor $($based on $0\mathrm{.}9633$

Cell B$4$ above$)$

$15$ Discounted Time$-$in$-$League

Bonus

$16$

$17$ Milestone Bonus

$18$ Discount factor $($based on

$0\mathrm{.}9280$

$0\mathrm{.}8611$

$0\mathrm{.}7991$

$0\mathrm{.}7415$

Cell B$5$ above$)$

$19$ Discounted Milestone Bonus

$20$

$21$ Performance Bonus

$

$22$ Discount factor $($based on

$0\mathrm{.}9280$

$0\mathrm{.}8611$

$0\mathrm{.}7991$

$0\mathrm{.}7415$

Cell B$5$ above$)$

$23$ Discounted Performance

Bonus

$24$

$25$ Monthly Endorsement

Contract Payment

$26$ Discount factor $($based on

$11\mathrm{.}5264$

$10\mathrm{.}6960$

Cell B$4$ above$)$

$27$ Discounted Monthly

Endorsement Payment

$28$

$29$ Contract's Total NominalCell B$4$ above$)$

$27$ Discounted Monthly

Endorsement Payment

$28$

$29$ Contract's Total Nominal

Value

$30$ Contract's Total Discounted

Value

Given your worksheet calculations, which of the following statements is accurate? Is Marty's estimate of the value of Flynn$\text{'}$s contract accurate on

either a nominal or discounted basis? Check all that apply.

Marty's estimate of the value of Flynn$\text{'}$s contract is incorrect on a nominal basis, and the error is $$59,814.$

It is appropriate and necessary to discount the endorsement contract using the bank account's effective annual interest rate because of

differences in the timing of the compounding of the bank account and that of the payments on the endorsement contract.

It is appropriate and necessary to discount the performance bonus using the bank account's effective annual interest rate because of

differences in the timing of the compounding of the bank account and that of the payments for the performance bonus.

Related Question: The local car dealer creating Flynn$\text{'}$s endorsement opportunity can earn $6\%($compounded quarterly$)$ on his deposited funds. She

would have to deposit $,$ each quarter, starting exactly two years before the day Flynn signs his contract, to fund her endorsement

contract. $[$Note: The future value interest factor of $6\%$ compounded quarterly for eight quarterly periods is $8\mathrm{.}4328.]$