Question

A professional baseball player signs a contract for $164 million to play with a team for 7 years. He and his team agree that the contract will be spread out so that the player is paid beyond the 7 years. The payment plan for the contract is as follows:
$17 million each year for years 1 through 7.
$3.1 million each year for the next 9 years.
$1.4 million each year for the next 7 years.
You should assume that the baseball team will pay the player annually at the end of each year and that he will receive the first $17 million at the end of the first year. The player receives money for 23 years.
The player had previously rejected a contract that would have paid $152 million for 7 years in which the $152 million would be paid in 7 equal installments (i.e., $21.71 million per year). The first payment would be made at the end of the first year.
Assume the player will invest every dollar that he receives in an account that pays 4.7% interest compounded annually. Enter the amount in millions of dollars of the contract that would result in the most money at the end of 23 years for the player."

Answer 1

OPTION 1 - Payment for 23 years PV of future receipts from contract Years Amount (per year) Annuity factor PV of Income Annuity factor explanation 1 to 7 17,000,000 3.482059,193,447.63 Cummulative PV at the end of 7 years @ 4.7% is used Cummulative PV at the end of 16 years @ 4.7% less 8 to 16 3,100,000 1.0034 3,110,585.31 Cummulative PV at the end of 7 years @ 4.7% is used Cummulative PV at the end of 23 years @ 4.7% less 17 to 23 1,400,000 0.1590 222,597.76 Cummulative PV at the end of 16 years @ 4.7% is used PV of future receipts 62,526,630.69

PV of future receipts from Interest Compound interest Receipt Year o/g Principal (A) closing principal (D=A+B+C) B = (A * 4.7%) received (C) 17,000,000 17,000,000 799,000 17,000,000 34,799,000 1,635,553 17,000,000 53,434,553 2,511,424 17,000,000 72,945,977 3,428,461 17,000,000 93,374,438 4,388,599 17,000,000 114,763,036 5,393,863 17,000,000 137,156,899 6,446,374 3,100,000 146,703,273 6,895,054 3,100,000 156,698,327 7,364,821 3,100,000 167,163,149 7,856,668 3,100,000 178,119,817 8,371,631 3,100,000 189,591,448 8,910,798 3,100,000 201,602,246 9,475,306 3,100,000 15 214,177,552 10,066,345 3,100,000 227,343,897 10,685,163 3,100,000 241,129,060 11,333,066 1,400,000 253,862,126 11,931,520 1,400,000 267,193,645 12,558,101 1,400,000 20 281,151,747 13,214,132 1,400,000 21 295,765,879 13,900,996 1,400,000 22 311,066,875 14,620,143 1,400,000 327,087,018 15,373,090 1,400,000 PV of interest receipts Annuity factor PV of Interest Income @ 4.7% € (B*E) 17,000,000 0.8246 34,799,000 0.6799 543,241 53,434,553 0.5606 916,925 72,945,977 0.4623 1,160,946 93,374,438 0.3812 1,306,815 114,763,036 0.3143 1,379,316 137,156,899 0.2592 1,397,851 146,703,273 0.2137 1,377,525 156,698,327 0.1762 1,214,912 167,163,149 0.1453 1,070,021 178,119,817 0.1198 941,221 189,591,448 0.0988 826,963 201,602,246 0.0815 725,798 214,177,552 0.0672 636,378 227,343,897 0.0554 557,464 241,129,060 0.0457 487,921 253,862, 126 0.0377 426,716 267,193,645 0.0310 370,433 281,151,747 0.0256 321,485 295,765,879 0.0211 278,932 311,066,875 0.0174 241,952 327,087,018 0.0144 209,825 343,860,108 0.0118 181,924 16,574,564 14 18 23

Benefit from Option 1 Particulars PV of future receipts PV of interest receipts Total Amount 62,526,631 16,574,564 79,101,195

- OPTION 2 - Payment for 7 years Years 11 to 7 PV of future receipts from contract Amount (per year) Annuity factor PV of Income Annuity factor explanation 21,710,000 3.4820 75,593,514.59 Cummulative PV at the end of 7 years @ 4.7% is used

PV of future receipts from Interest Compound interest Receipt Year o/g Principal (A) B=(A* 4.7%) closing principal (D=A+B+C) received (C) 21,710,000 21,710,000 1,020,370 21,710,000 44,440,370 2,088,697 21,710,000 68,239,067 3,207,236 21,710,000 93,156,304 4,378,346 21,710,000 119,244,650 5,604,499 21,710,000 146,559,148 6,888,280 21,710,000 175,157,428 8,232,399 183,389,827 8,619,322 192,009,149 9,024,430 201,033,579 9,448,578 210,482,158 9,892,661 220,374,819 10,357,616 230,732,436 10,844,424 241,576,860 11,354,112 252,930,972 11,887,756 264,818,728 12,446,480 277,265,208 13,031,465 290,296,673 13,643,944 20 303,940,617 14,285,209 21 318,225,826 14,956,614 22 333,182,440 15,659,575 23 348,842,014 16,395,575 PV of interest receipts Annuity factor PV of Interest Income @ 4.7% € (BTE) 21,710,000 0.8246 44,440,370 0.6799 693,751 68,239,067 0.5606 1,170,967 93,156,304 0.4623 1,482,596 119,244,650 0.3812 1,668,880 146,559,148 0.3143 1,761,468 175,157,428 0.2592 1,785,138 183,389,827 0.2137 1,759,181 192,009, 149 0.1762 1,518,728 201,033,579 0.1453 1,311,142 210,482,158 0.1198 1,131,930 220,374,819 0.0988 977,213 230,732,436 0.0815 843,643 241,576,860 0.0672 728,331 252,930,972 0.0554 628,779 264,818,728 0.0457 542,835 277,265,208 0.0377 468,638 290,296,673 0.0310 404,583 303,940,617 0.0256 349,283 318,225,826 0.0211 301,541 333,182,440 0.0174 260,325 348,842,014 0.0144 224,743 365,237,589 0.0118 194,024 20,207,719 17

Benefit from Option 2 Particulars PV of future receipts PV of interest receipts Total Amount 75,593,515 20,207,719 95,801,234

Conclusion -

Obtaining receipts of $ 152 million for 7 years is more beneficial, as it yield more income at the end of 23 years.

* I am not able to paste the excel as characters are more than 65k, hence working screenshots are attached.