When Patrick purchased his home, he borrowed $150,000 from his bank at 6% intere

Question

When Patrick purchased his home, he borrowed $150,000 from his bank at 6% interest rate per year to be repaid in 180 equal annual end-of-month payments in 15 years. After making 120 payments, Patrick found he could refinance the balance due on his loan at 5% interest for the remaining 5 years. To refinance the loan, Patrick must pay the original lender the balance due on the loan, plus a penalty charge of 2% of the balance due for this new 5-year loan. To the new lender, he also must pay a $1,000 service charge to obtain the loan. The new loan would be made equal to the balance due on the old loan, plus the 2% penalty charge of the amount owed to be paid to the previous lender, and the $1,000 service charge to the new lender. Should Patrick refinance the loan, assuming that he will keep the house for the next 5 years? Use an annual cash flow analysis for solving this problem?

Explanation / Answer

Let us first find EMI

EMI = Loan amount/PVIFA(0.5%,180months)

=150,000/118.5035

=1265.79$

NOw let us check balance at end of 120 months

Now he has two option

1) to continue his loan

2) to refinance his loan

If he chosses to refinance the loan then

New loan = 65473 + (65473*2%) + 1000 = 67782.46

EMI = loan/PVIFA(0.4167%,60 months)

=67782.46/52.9902

1279.15$

Repayment schedule

If he had continued his old loan

Thus we need to find NPV of this decision

Thus he should not refinance the loan

Towards Period opening balance Installment Principal Interest @0.5% Closing balance 1 150000 1265.8 516 750 149484 2 149484 1265.8 518 747 148966 3 148966 1265.8 521 745 148445 4 148445 1265.8 524 742 147921 5 147921 1265.8 526 740 147395 6 147395 1265.8 529 737 146866 7 146866 1265.8 531 734 146335 8 146335 1265.8 534 732 145801 9 145801 1265.8 537 729 145264 10 145264 1265.8 539 726 144724 11 144724 1265.8 542 724 144182 12 144182 1265.8 545 721 143637 13 143637 1265.8 548 718 143090 14 143090 1265.8 550 715 142539 15 142539 1265.8 553 713 141986 16 141986 1265.8 556 710 141431 17 141431 1265.8 559 707 140872 18 140872 1265.8 561 704 140310 19 140310 1265.8 564 702 139746 20 139746 1265.8 567 699 139179 21 139179 1265.8 570 696 138609 22 138609 1265.8 573 693 138037 23 138037 1265.8 576 690 137461 24 137461 1265.8 578 687 136882 25 136882 1265.8 581 684 136301 26 136301 1265.8 584 682 135717 27 135717 1265.8 587 679 135130 28 135130 1265.8 590 676 134539 29 134539 1265.8 593 673 133946 30 133946 1265.8 596 670 133350 31 133350 1265.8 599 667 132751 32 132751 1265.8 602 664 132149 33 132149 1265.8 605 661 131544 34 131544 1265.8 608 658 130936 35 130936 1265.8 611 655 130325 36 130325 1265.8 614 652 129711 37 129711 1265.8 617 649 129094 38 129094 1265.8 620 645 128473 39 128473 1265.8 623 642 127850 40 127850 1265.8 627 639 127223 41 127223 1265.8 630 636 126594 42 126594 1265.8 633 633 125961 43 125961 1265.8 636 630 125325 44 125325 1265.8 639 627 124686 45 124686 1265.8 642 623 124043 46 124043 1265.8 646 620 123398 47 123398 1265.8 649 617 122749 48 122749 1265.8 652 614 122097 49 122097 1265.8 655 610 121442 50 121442 1265.8 659 607 120783 51 120783 1265.8 662 604 120121 52 120121 1265.8 665 601 119456 53 119456 1265.8 669 597 118787 54 118787 1265.8 672 594 118116 55 118116 1265.8 675 591 117440 56 117440 1265.8 679 587 116762 57 116762 1265.8 682 584 116080 58 116080 1265.8 685 580 115394 59 115394 1265.8 689 577 114706 60 114706 1265.8 692 574 114013 61 114013 1265.8 696 570 113318 62 113318 1265.8 699 567 112618 63 112618 1265.8 703 563 111916 64 111916 1265.8 706 560 111209 65 111209 1265.8 710 556 110500 66 110500 1265.8 713 552 109786 67 109786 1265.8 717 549 109070 68 109070 1265.8 720 545 108349 69 108349 1265.8 724 542 107625 70 107625 1265.8 728 538 106897 71 106897 1265.8 731 534 106166 72 106166 1265.8 735 531 105431 73 105431 1265.8 739 527 104693 74 104693 1265.8 742 523 103950 75 103950 1265.8 746 520 103204 76 103204 1265.8 750 516 102454 77 102454 1265.8 754 512 101701 78 101701 1265.8 757 509 100944 79 100944 1265.8 761 505 100183 80 100183 1265.8 765 501 99418 81 99418 1265.8 769 497 98649 82 98649 1265.8 773 493 97876 83 97876 1265.8 776 489 97100 84 97100 1265.8 780 485 96320 85 96320 1265.8 784 482 95536 86 95536 1265.8 788 478 94747 87 94747 1265.8 792 474 93955 88 93955 1265.8 796 470 93159 89 93159 1265.8 800 466 92359 90 92359 1265.8 804 462 91555 91 91555 1265.8 808 458 90747 92 90747 1265.8 812 454 89935 93 89935 1265.8 816 450 89119 94 89119 1265.8 820 446 88299 95 88299 1265.8 824 441 87475 96 87475 1265.8 828 437 86646 97 86646 1265.8 833 433 85814 98 85814 1265.8 837 429 84977 99 84977 1265.8 841 425 84136 100 84136 1265.8 845 421 83291 101 83291 1265.8 849 416 82442 102 82442 1265.8 854 412 81588 103 81588 1265.8 858 408 80730 104 80730 1265.8 862 404 79868 105 79868 1265.8 866 399 79002 106 79002 1265.8 871 395 78131 107 78131 1265.8 875 391 77256 108 77256 1265.8 880 386 76376 109 76376 1265.8 884 382 75492 110 75492 1265.8 888 377 74604 111 74604 1265.8 893 373 73711 112 73711 1265.8 897 369 72814 113 72814 1265.8 902 364 71912 114 71912 1265.8 906 360 71006 115 71006 1265.8 911 355 70095 116 70095 1265.8 915 350 69180 117 69180 1265.8 920 346 68260 118 68260 1265.8 924 341 67336 119 67336 1265.8 929 337 66406 120 66406 1265.8 934 332 65473

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