Application of Time Value of Money Skills

Harry Hurler 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

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

to reflect his new status. The email describes the general terms and conditions of Harry's revised contract.

bonus: a $$250,000$ 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

the beginning of the next contract year. Although this proposal describes only

one milestone, the actual contract contains several progressive milestones.

Exceeding one milestone creates the opportunity to exceed another.

Harry is so excited! According to Noah, the contract is worth $$3,772,400-$assuming receipt of all possible bonuses. After rereading the email twice

he'll do with his newfound wealth, you and Harry have agreed that any funds received could be invested to earn $8\mathrm{.}00\%,$ 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.

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.

Harry Hurler's Contract Evaluation Worksheet

A

B

Assumptions and

Calculated Values

$2$ Bank Rate Information:

$3$ Harry's Bank Account Rate

$($compounded monthly$)$

$4$ Monthly Bank Rate $\%$

$5$ Effective Annual Interest

Rate

$6$

$7$ Salary and Bonus

Year $1$

Year $2$

Year $3$

$11\mathrm{.}495781801$

$10\mathrm{.}61476181$

$9\mathrm{.}801261902$

$5$

$\%$

$\%$

$\%$

Information:

$8$ Annual Salary $(4\%$ COLA$)$

$9$ Monthly Salary

$10$ Discount factor $($based on

Cell B$4$ above$)$

$11$ Discounted Annual Salary

$12$

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

$14$ Discount factor $($based on

$0\mathrm{.}9609$

Cell B$4$ above$)$

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

Bonus

$16$

$17$ Milestone Bonus

$18$ Discount factor $($based on

$0\mathrm{.}9234$

$0\mathrm{.}8526$

$0\mathrm{.}7873$

$0\mathrm{.}7269$

Cell B$5$ above$)$

$19$ Discounted Milestone Bonus

C

D

E

F$19$ Discounted Milestone Bonus

$20$

$21$ Performance Bonus

Cell B$5$ above$)$

$23$ Discounted Performance

Bonus

$24$

$25$ Monthly Endorsement

Contract Payment

$26$ Discount factor $($based on $,11\mathrm{.}4958,10\mathrm{.}6148$

Cell 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 Noah's estimate of the value of Harry's contract accurate on

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

Noah's estimate of the value of Harry's contract is incorrect on a nominal basis, and the error is $$80,389.$

Noah's estimate of the nominal value of Harry's contract is correct.

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.

would have to deposit

each quarter, starting exactly two years before the day Harry signs his contract, to fund her endorsement

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