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 Ketchum Baldies; 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 Springfield Dusties, the Baldies'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 In addition, the Player will receive a one-time $10,000 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: $250,000 bonus if he ties Nolan Ryan's 1973 single-season strikeout record (383 strikeouts) The Plaver is eligible for each potential bonus each vear that the contract is in Gavin is so excited! According to Noah, the contract is worth $3,220,400-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 5.50%, compounded monthly Gavin is so excited! According to Noah, the contract is worth $3,220,400-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 5.50%, 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 month ly 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 E A C D 1 Assumptions and Calculated Values 2 Bank Rate Information: Gavin's Bank Account Rate (compounded monthly) Monthly Bank Rate 4 % % Effective Annual Interest Rate 6 Year 1 Year 4 7 Salary and Bonus Information: Year 2 Year 3 Total value Annual Salary (4% COLA) 8 Monthly Salary $ $ 10 Discount factor (based on Cell B4 11.6500 11.0280 10.4391 9.8817 above) Discounted Annual Salary 11 S 12 13 Time-in-League Bonus Discount factor (based on Cell B4 14 0.9729 above) Discounted Time-in-League Bonus 15 $ 16 17 Milestone Bonus Discount factor (based on Cell B5 18 0.9466 0.8961 0.8482 0.8029 above) 19 Discounted Milestone Bonus $ $ 20 21 Performance Bonus 22 Discount factor (based on Cell B5 0.9466 0.8961 0.8482 0.8029 above) Discounted Performance Bon us 23 S 24 25 Monthly Endorsement Contract S Payment 26 Discount factor (based on Cell B4 11.6500 11.0280 above) Discounted Monthly Endorsement $ Payment 28 Contract's Total Nominal Value 29 Contract's Total Discounted Value 30 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. Noah's estimate of the value of Gavin's contract is incorrect on a nominal basis, and the error is $58,088 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 Noah's estimate of the nominal value of Gavin's contract is correct. 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.] 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 Ketchum Baldies; 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 Springfield Dusties, the Baldies'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 In addition, the Player will receive a one-time $10,000 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: $250,000 bonus if he ties Nolan Ryan's 1973 single-season strikeout record (383 strikeouts) The Plaver is eligible for each potential bonus each vear that the contract is in Gavin is so excited! According to Noah, the contract is worth $3,220,400-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 5.50%, compounded monthly Gavin is so excited! According to Noah, the contract is worth $3,220,400-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 5.50%, 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 month ly 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 E A C D 1 Assumptions and Calculated Values 2 Bank Rate Information: Gavin's Bank Account Rate (compounded monthly) Monthly Bank Rate 4 % % Effective Annual Interest Rate 6 Year 1 Year 4 7 Salary and Bonus Information: Year 2 Year 3 Total value Annual Salary (4% COLA) 8 Monthly Salary $ $ 10 Discount factor (based on Cell B4 11.6500 11.0280 10.4391 9.8817 above) Discounted Annual Salary 11 S 12 13 Time-in-League Bonus Discount factor (based on Cell B4 14 0.9729 above) Discounted Time-in-League Bonus 15 $ 16 17 Milestone Bonus Discount factor (based on Cell B5 18 0.9466 0.8961 0.8482 0.8029 above) 19 Discounted Milestone Bonus $ $ 20 21 Performance Bonus 22 Discount factor (based on Cell B5 0.9466 0.8961 0.8482 0.8029 above) Discounted Performance Bon us 23 S 24 25 Monthly Endorsement Contract S Payment 26 Discount factor (based on Cell B4 11.6500 11.0280 above) Discounted Monthly Endorsement $ Payment 28 Contract's Total Nominal Value 29 Contract's Total Discounted Value 30 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. Noah's estimate of the value of Gavin's contract is incorrect on a nominal basis, and the error is $58,088 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 Noah's estimate of the nominal value of Gavin's contract is correct. 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.]