Question

Colin Closer 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 Moab Mountain Goats; last year, he was the first runner-up for the Minor League Player of the Year award. Using his 93 mph 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 2.76, and 123 strikeouts in 99.1 innings pitched. He is also your best friend.

Two weeks ago, on his three-year anniversary with the team, Colin received the following email from his agent, Michael Make-d’Team, indicating that he is being called up to the Mobile Bayhoppers, the Mountain Goats’s corresponding Major League Baseball (MLB) team. Moreover, Colin’s contract is being revised to reflect his new status. The email describes the general terms and conditions of Colin’s revised contract.

From: Michael Make-d’Team

To: Colin Closer

Subject: New Team, New Contract Proposal

Congratulations! You’ve been called up to the Mobile Bayhoppers. Below are the offered terms and conditions of your new contract. After you review them and think about the offer, call me and we’ll discuss your options. Congrats again!

Colin Closer hereafter referred to as the “Player,” is offered a four-year contract with an annual salary of $504,000 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.

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 $75,000 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.

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.

In addition to the proposal offered by the Bayhoppers, I’ve also been able to secure the following endorsement opportunity:

A local car dealer has offered you a contract that will pay $800 per month for two years. This contract is contingent on your accepting the contract with the Bayhoppers and will take effect immediately upon signing your MLB contract. In return for these payments, you will participate in the dealer’s promotional events, such as signing autographs and allowing photographs as requested.

I’ve also attached a worksheet that you can use to analyze the deal. I’m in negotiations for the rest of the day, so let’s discuss your thoughts on the contract proposal tomorrow. I’m proud of you!

Take care,

Colin is so excited! According to Michael, the contract is worth $2,678,400—assuming receipt of all possible bonuses. After rereading the email twice and calling his family, Colin called you to review the terms of the contract and verify Michael’s calculations. After an extended conversation about what he’ll do with his newfound wealth, you and Colin have agreed that any funds received could be invested to earn 7.50%, 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.

COLLIN CLOSERS EVALUATION WORKSHEET

Assumptions and Calculated Values
2	Bank Rate Information:
3	Colin's Bank Account Rate (compounded monthly)	%
4	Monthly Bank Rate	%
5	Effective Annual Interest Rate	%
6
7	Salary and Bonus Information:	Year 1	Year 2	Year 3	Year 4	Total value
8	Annual Salary (4% COLA)
9	Monthly Salary
10	Discount factor (based on Cell B4 above)	11.5264	10.6960	9.9255	9.2105
11	Discounted Annual Salary
12
13	Time-in-League Bonus
14	Discount factor (based on Cell B4 above)	0.9633
15	Discounted Time-in-League Bonus
16
17	Milestone Bonus
18	Discount factor (based on Cell B5 above)	0.9280	0.8611	0.7991	0.7415
19	Discounted Milestone Bonus
20
21	Performance Bonus
22	Discount factor (based on Cell B5 above)	0.9280	0.8611	0.7991	0.7415
23	Discounted Performance Bonus
24
25	Monthly Endorsement Contract Payment
26	Discount factor (based on Cell B4 above)	11.5264	10.6960
27	Discounted Monthly Endorsement Payment
28
29	Contract’s Total Nominal Value
30	Contract’s Total Discounted Value

1. Given your worksheet calculations, which of the following statements is accurate? Is Michael’s estimate of the value of Colin’s contract accurate on either a nominal or discounted basis? Check all that apply.

Michael’s estimate of the value of Colin’s contract is incorrect on a nominal basis, and the error is $48,663.

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 Colin'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 Colin signs his contract, to fund her endorsement contract. [Note: The future value interest factor of 6% compounded quarterly for eight quarterly periods is 8.4328.] How much would she have to deposit?

Answer 1

Evaluation worksheet:

1). The correct statements are:

- Michael’s estimate of the value of Colin’s contract is incorrect on a nominal basis, and the error is $48,663. (Contract nominal value is 2,727,063 and Michael's estimated value is 2,678,400, so difference is 48,663.)

- 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. (Bank account has monthly compounding where as performance bonus is paid at the beginning of a contract year.)

2). Amount to be deposited each quarter in order to have $19,200 after two years will be 19,200/8.4328 = 2,276.82 (or 2,277).