16. Application of Time Value of Money Skills 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 96 mph 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 2.98, and 146 strikeouts in 117.0 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, George Get-d'Bucks, indicating that he is being called up to the Boston Back Bay Boys, 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: George Get-d'Bucks To: Colin Closer Subject: New Team, New Contract Proposal Colin, Congratulations! You've been called up to the Boston Back Bay Boys. 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! Salary and Incentives: Colin Closer hereafter referred to as the "Player," is offered a four-year contract with an annual salary of $594,000 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 payable at the end of the operating year if he is selected to play in the All-Star game. 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 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 Back Bay Boys, I've also been able to secure the following endorsement opportunity: A local car dealer has offered you a contract that will pay $750 per month for two years. This contract is contingent on your accepting the contract with the Back Bay Boys 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, George George Get-d'Bucks Sports Agent, R&R Talent Management Inc. | Boston Colin is so excited! According to George, the contract is worth $3,412,400-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 George'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 5.00%, 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. 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. Colin Closer's Contract Evaluation Worksheet B D E F TI 1 2. Assumptions and Calculated Values Bank Rate Information: Colin's Bank Account Rate (compounded monthly) Monthly Bank Rate Effective Annual Interest Rate 3 % 4 4 % 5 % 6 7 Year 1 Year 2 Year 3 Year 4 Total value 8 9 Salary and Bonus Information: Annual Salary (4% COLA) Monthly Salary Discount factor (based on Cell B4 above) Discounted Annual Salary 10 11.6812 11.1127 10.5718 10.0573 11 12 13 14 0.9754 Time-in-League Bonus Discount factor (based on Cell B4 above) Discounted Time-in-League Bonus 15 16 17 18 0.9513 0.9050 0.8610 0.8191 Milestone Bonus Discount factor (based on Cell B5 above) Discounted Milestone Bonus 19 20 21 22 Performance Bonus Discount factor (based on Cell B5 above) 0.9513 0.9050 0.8610 0.8191 23 Discounted Performance Bonus $ 24 11.6812 11.1127 25 Monthly Endorsement Contract Payment 26 Discount factor (based on Cell B4 above) 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 George's estimate of the value of Colin's contract accurate on either a nominal or discounted basis? Check all that apply. George's estimate of the nominal value of Colin's contract is correct. 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. George's estimate of the value of Colin's contract is incorrect on a nominal basis, and the error is $50,389. 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.] 16. Application of Time Value of Money Skills 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 96 mph 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 2.98, and 146 strikeouts in 117.0 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, George Get-d'Bucks, indicating that he is being called up to the Boston Back Bay Boys, 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: George Get-d'Bucks To: Colin Closer Subject: New Team, New Contract Proposal Colin, Congratulations! You've been called up to the Boston Back Bay Boys. 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! Salary and Incentives: Colin Closer hereafter referred to as the "Player," is offered a four-year contract with an annual salary of $594,000 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 payable at the end of the operating year if he is selected to play in the All-Star game. 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 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 Back Bay Boys, I've also been able to secure the following endorsement opportunity: A local car dealer has offered you a contract that will pay $750 per month for two years. This contract is contingent on your accepting the contract with the Back Bay Boys 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, George George Get-d'Bucks Sports Agent, R&R Talent Management Inc. | Boston Colin is so excited! According to George, the contract is worth $3,412,400-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 George'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 5.00%, 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. 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. Colin Closer's Contract Evaluation Worksheet B D E F TI 1 2. Assumptions and Calculated Values Bank Rate Information: Colin's Bank Account Rate (compounded monthly) Monthly Bank Rate Effective Annual Interest Rate 3 % 4 4 % 5 % 6 7 Year 1 Year 2 Year 3 Year 4 Total value 8 9 Salary and Bonus Information: Annual Salary (4% COLA) Monthly Salary Discount factor (based on Cell B4 above) Discounted Annual Salary 10 11.6812 11.1127 10.5718 10.0573 11 12 13 14 0.9754 Time-in-League Bonus Discount factor (based on Cell B4 above) Discounted Time-in-League Bonus 15 16 17 18 0.9513 0.9050 0.8610 0.8191 Milestone Bonus Discount factor (based on Cell B5 above) Discounted Milestone Bonus 19 20 21 22 Performance Bonus Discount factor (based on Cell B5 above) 0.9513 0.9050 0.8610 0.8191 23 Discounted Performance Bonus $ 24 11.6812 11.1127 25 Monthly Endorsement Contract Payment 26 Discount factor (based on Cell B4 above) 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 George's estimate of the value of Colin's contract accurate on either a nominal or discounted basis? Check all that apply. George's estimate of the nominal value of Colin's contract is correct. 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. George's estimate of the value of Colin's contract is incorrect on a nominal basis, and the error is $50,389. 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.]
