16. 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 Dodge City Cowboys; last year, he was the first runner-up for the Minor League Player of the Year award. Using his 99 mph fastball, an impeccable curve ball and slider, and a reliable changeup pitch, he achieved a 18-2 win-loss record, an earned run average (ERA) of 2.23, and 166 strikeouts in 147.2 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, Noah Never-Enough, indicating that he is being called up to the Mobile Bayhoppers, the Cowboys'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. From: Noah Never-Enough To: Gavin Goldenarm Subject: New Team, New Contract Proposal Gavin, Congratulations! You've been called up to the Mobile Bayhoppers. Below are the Gavin is so excited! According to Noah, the contract is worth $2,522,400-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 Noah'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 9.00%, compounded monthly. Salary and Incentives: Gavin Goldenarm hereafter referred to as the "Player," is offered a four-year contract with an annual salary of $444,000 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 $20,000 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 $100,000 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 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 $3,000 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, Noah 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. Gavin Goldenarm's Contract Evaluation Worksheet B D E F 1 2 3 9.00% Assumptions and Calculated Values Bank Rate Information: Gavin's Bank Account Rate (compounded monthly) Monthly Bank Rate Effective Annual Interest Rate 4 96 5 9 6 7 Year 1 Year 2 Year 3 Year 4 Total value Salary and Bonus Information: 8 Annual Salary (4% COLA) IS $ S 9 S S Is 11.4349 10.4542 9.5577 8.7380 Monthly Salary 10 Discount factor (based on Cell B4 above) 11 Discounted Annual Salary $ S 12 13 Time-in-League Bonus S S 0.9562 14 Discount factor (based on Cell B4 above) ) 15 Discounted Time-in-League Bonus 16 17 $ S 0.9142 0.8358 0.7641 0.6986 Milestone Bonus 18 Discount factor (based on Cell B5 above) ) 19 Discounted Milestone Bonus 20 21 0.9142 0.8358 0.7641 0.6986 S S Performance Bonus 22 Discount factor (based on Cell B5 above) 23 Discounted Performance Bonus 24 25 Monthly Endorsement Contract Payment 26 Discount factor (based on Cell B4 above) 27 Discounted Monthly Endorsement Payment 11.4349 10.4542 s 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 Noah's estimate of the value of Gavin's contract accurate on either a nominal or discounted basis? Check all that apply. 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. Noah's estimate of the value of Gavin's contract is incorrect on a nominal basis, and the error is $22,513. 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. Related Question: The local car dealer creating Gavin'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 Gavin 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.]