Case 1

(1)

1 Andriyanto

2 Ruth

3 Rasyed

4 Filco

5 Anggraini

(2)

1

End of Year Annual Return Policy Payment 0 (55,000) 1 6% 58,300 3,300 2 6% 61,798 3,498 3 6% 65,506 3,708 4 6% 69,436 3,930 5 6% 73,602 4,166 6 6% 78,019 4,416 7 6% 82,700 4,681 8 6% 87,662 4,962 9 6% 92,921 5,260 10 6% 98,497 5,575 11 6% 104,406 5,910 12 6% 110,671 6,264 13 6% 117,311 6,640 14 6% 124,350 7,039 15 6% 131,811 7,461 16 6% 139,719 7,909 17 6% 148,103 8,383 18 6% 156,989 8,886 19 6% 166,408 9,419 20 6% 176,392 9,984

Morton notes that the $55,000 invested in the single-premium life insurance policy would grow to $176,392 in 20 years for a return of 6 percents a year. Explain how this return was calculated.

Menurut Morton uang senilai $55,000 untuk asuransi jiwa premium, dapat Studebarker peroleh dari "kelebihan" dana dari reksadanannya sebesar $30,000 dan dana simpanan dari pengajuan hipotek baru sebesar $25,000. Tiap tahunnya, polis asuransi menghasilkan 6% dan menghasilkan akumulasi nilai selama 20 tahun. Ditahun pertama, jumlah nilai yang ditambahkan sebesar $3,300 dari awalnya $55,000, sehingga menjadi $58,300. Dan, nilai tersebut meningkat setiap tahunnya hingga tahun ke 20 sebesar $176,392.

Accumulation Value

Increase in Accumulation

(3)

2

End of Year Annual Return Policy Payment

Annual Cost

0 (55,000) 1 6% 58,300 3,300 3,052 2 6% 61,798 3,498 3,052 3 6% 65,506 3,708 3,052 4 6% 69,436 3,930 3,052 5 6% 73,602 4,166 3,052 6 6% 78,019 4,416 3,052 7 6% 82,700 4,681 3,052 8 6% 87,662 4,962 3,052 9 6% 92,921 5,260 3,052 10 6% 98,497 5,575 3,052 11 6% 104,406 5,910 3,052 12 6% 110,671 6,264 3,052 13 6% 117,311 6,640 3,052 14 6% 124,350 7,039 3,052 15 6% 131,811 7,461 3,052 16 6% 139,719 7,909 3,052 17 6% 148,103 8,383 3,052 18 6% 156,989 8,886 3,052 19 6% 166,408 9,419 3,052 20 6% 176,392 9,984 3,052

In order to reposition the equity in his home, Studebaker would have to take out a 30-year, $75,000 mortgage at 9 percent. Explain how the yearly mortgage payments on this loan were obtained

Sebelumnya nilai hipotek Studebaker sebesar $45.000 bunga 7% selama 20 tahun, dengan pembayaran per tahun sebesar $4,248. Dengan pengambilan hipotek $75,000 bunga 9% selama 30 tahun dengan pembayaran $7,300 per tahun. Ada biaya tambahan yang harus ditanggung Studebaker tiap tahunnya sekitar $3,052. Selisih biaya ini, menurut ilustrasi Morton's dapat ditutup oleh peningkatan pendapatan tiap tahun dari asuransi jiwa. Dan di tahun ke-20 ketika Studebacker mendapatkan hasil dari asuransi, dia dapat melunasi hutang di tahun 21 sampai 30.

Accumulation Value

(4)

Earn /Year

Value

Loan Term Mortagage Payment 30 9% (75,000) 7,300

248 55,248

20 7% (45,000) 4,248

446 55,694

Biaya tambahan per tahun

3,052

656 56,350

878 57,228

1,114 58,342

1,364 59,707

1,629 61,336

1,910 63,246

2,208 65,453

2,523 67,977

2,858 70,834

3,212 74,047

3,588 77,635

3,987 81,622

4,409 86,031

4,857 90,887

5,331 96,219

5,834 102,053

6,367 108,420

6,932

115,352

Annual Interest

(5)

3

For the 9 percent mortgage in Exhibit 4, find the loan balance at the end of years 19 and 20

Year Payment Interest Principal

Balance

0 75,000 1 7,300 6,750 550 74,450 2 7,300 6,700 600 73,850 3 7,300 6,647 654 73,196 4 7,300 6,588 713 72,484 5 7,300 6,524 777 71,707 6 7,300 6,454 847 70,860 7 7,300 6,377 923 69,938 8 7,300 6,294 1,006 68,932 9 7,300 6,204 1,096 67,835 10 7,300 6,105 1,195 66,640 11 7,300 5,998 1,303 65,338 12 7,300 5,880 1,420 63,918 13 7,300 5,753 1,548 62,370 14 7,300 5,613 1,687 60,684 15 7,300 5,462 1,839 58,845 16 7,300 5,296 2,004 56,841 17 7,300 5,116 2,185 54,656 18 7,300 4,919 2,381 52,275 19 7,300 4,705 2,595 49,679 20 7,300 4,471 2,829 46,850 21 7,300 4,217 3,084 43,767 22 7,300 3,939 3,361 40,405 23 7,300 3,636 3,664 36,742 24 7,300 3,307 3,993 32,748 25 7,300 2,947 4,353 28,395 26 7,300 2,556 4,745 23,651 27 7,300 2,129 5,172 18,479 28 7,300 1,663 5,637 12,842 29 7,300 1,156 6,144 6,697 30 7,300 603 6,697 0 219,007 144,007 75,000

(6)

4

End of Year

Earn /Year

0 (55,000) 1 6% 58,300 3,300 3,052

248

2 6% 61,798 3,498 3,052

446

3 6% 65,506 3,708 3,052

656

4 6% 69,436 3,930 3,052

878

5 6% 73,602 4,166 3,052

1,114

6 6% 78,019 4,416 3,052

1,364

7 6% 82,700 4,681 3,052

1,629

8 6% 87,662 4,962 3,052

1,910

9 6% 92,921 5,260 3,052

2,208

10 6% 98,497 5,575 3,052

2,523

11 6% 104,406 5,910 3,052

2,858

12 6% 110,671 6,264 3,052

3,212

13 6% 117,311 6,640 3,052

3,588

14 6% 124,350 7,039 3,052

3,987

15 6% 131,811 7,461 3,052

4,409

16 6% 139,719 7,909 3,052

4,857

17 6% 148,103 8,383 3,052

5,331

18 6% 156,989 8,886 3,052

5,834

19 6% 166,408 9,419 3,052

6,367

20 6% 176,392 9,984 3,052

6,932

Sisa Utang

Exhibit 3 indicates that $176,392 will be accumulated after 20 years in the life insurance policy. Is this really true? ( Hint: If Studebaker were to make this investment, what would his debt position look like in year 20?)

Menurut perhitungan morton menggunakan rumus future value, dari dana yang diinvestasikan sebesar $55,000 selama 20 tahun akan terakumulasi menjadi $176,392 adalah benar. Namun, bila Morton mengatakan kenaikan akumulasi nilai tiap tahunnya dapat menutupi annual cost, maka di tahun ke-20, Studebaker hanya menerima $115,352, dan dia dapat melunasi hutang tahun ke 21-30 sebesar $73,000 dan tetap menghasilkan keuntungan $42,352.

Annual

Return PaymentPolicy Accumulation Value

Value

Annual

Cost

(7)

Value

Year 0 75,000

55,248

1

55,694

2

56,350

3

57,228

4

58,342

5

59,707

6

61,336

7

63,246

8

65,453

9

67,977

10

70,834

11

74,047

12

77,635

13

81,622

14

86,031

15

90,887

16

96,219

17

102,053

18

108,420

19

115,352

20

73,000

21

42,352

22 23 7,300 3,636 24 7,300 3,307 Payment Interest Principal

Balance

7,300 6,750 550 74,450 7,300 6,700 600 73,850 7,300 6,647 654 73,196 7,300 6,588 713 72,484 7,300 6,524 777 71,707 7,300 6,454 847 70,860 7,300 6,377 923 69,938 7,300 6,294 1,006 68,932 7,300 6,204 1,096 67,835 7,300 6,105 1,195 66,640 7,300 5,998 1,303 65,338 7,300 5,880 1,420 63,918 7,300 5,753 1,548 62,370 7,300 5,613 1,687 60,684 7,300 5,462 1,839 58,845 7,300 5,296 2,004 56,841 7,300 5,116 2,185 54,656 7,300 4,919 2,381 52,275 7,300 4,705 2,595 49,679 7,300 4,471 2,829 46,850 7,300 4,217 3,084 43,767

7,300 3,939 3,361 40,405 3,664 36,742 3,993 32,748

(8)

25 7,300 2,947 4,353 28,395 26 7,300 2,556 4,745 23,651 27 7,300 2,129 5,172 18,479 28 7,300 1,663 5,637 12,842 29 7,300 1,156 6,144 6,697 30 7,300 603 6,697 0

(9)

(10)

5.a

5.b

5.a

5.b

End of Year Annual Return Policy Payment n

0 (30,000) 0 1 8% 32,400 2,400 1 2 8% 34,992 2,592 2 3 8% 37,791 2,799 3 4 8% 40,815 3,023 4 5 8% 44,080 3,265 5 6 8% 47,606 3,526 6 7 8% 51,415 3,808 7 8 8% 55,528 4,113 8 9 8% 59,970 4,442 9 10 8% 64,768 4,798 10 11 8% 69,949 5,181 11 12 8% 75,545 5,596 12 13 8% 81,589 6,044 13 14 8% 88,116 6,527 14

If the excess $30,000 were invested in a long-term asset yielding 8 percent a year, how much would be accumulated after 20 years?

Suppose Studebaker place $3,052 a year into a long-term investment paying 8 percent a year. How much would be accumulated after 20 years (amounts invested at the end of each year)?

Setelah 20 tahun, investasi $30,000 akan terakumulasi menjadi sebesar $139,829

Dari investasi jangka panjang sebesar $3,052 tiap tahunnya, Studebacker akan menghasilkan sebesar $139,666 di tahun ke 20. Bila digabungkan dengan investasi aset jangka panjang sebesar $30.000, jumlah akumulasi yang akan diterima oleh Studebacker sebesar $279,494

Accumulation Value

(11)

15 8% 95,165 7,049 15 16 8% 102,778 7,613 16 17 8% 111,001 8,222 17 18 8% 119,881 8,880 18 19 8% 129,471 9,590 19 20 8% 139,829 10,358 20

(12)

r PMT Fv of annuity Accumuated 8% (3,052) 3,296 35,696 8% (3,052) 6,856 41,848 8% (3,052) 10,701 48,492 8% (3,052) 14,853 55,668 8% (3,052) 19,337 63,417 8% (3,052) 24,180 71,787 8% (3,052) 29,411 80,826 8% (3,052) 35,060 90,588 8% (3,052) 41,161 101,131 8% (3,052) 47,750 112,518 8% (3,052) 54,866 124,815 8% (3,052) 62,552 138,097 8% (3,052) 70,852 152,441 8% (3,052) 79,816 167,932

(13)

8% (3,052) 89,498 184,663 8% (3,052) 99,954 202,732 8% (3,052) 111,246 222,247 8% (3,052) 123,442 243,323 8% (3,052) 136,614 266,085 8% (3,052) 139,666 279,494

(14)

6

Repeat problem 5 but assume a 7 percent return can be earned

0 (30,000) 0 1 7% 32,100 2,100 1 2 7% 34,347 2,247 2 3 7% 36,751 2,404 3 4 7% 39,324 2,573 4 5 7% 42,077 2,753 5 6 7% 45,022 2,945 6 7 7% 48,173 3,152 7 8 7% 51,546 3,372 8 9 7% 55,154 3,608 9 10 7% 59,015 3,861 10 11 7% 63,146 4,131 11 12 7% 67,566 4,420 12 13 7% 72,295 4,730 13 14 7% 77,356 5,061 14 15 7% 82,771 5,415 15 16 7% 88,565 5,794 16 17 7% 94,764 6,200 17

Setelah 20 tahun, investasi $30,000 akan terakumulasi menjadi sebesar $116,091

Dari investasi jangka panjang sebesar $3,052 tiap tahunnya, Studebacker akan menghasilkan sebesar $125,118 di tahun ke 20. Bila digabungkan dengan investasi aset jangka panjang sebesar $30.000, jumlah akumulasi yang akan diterima oleh Studebacker sebesar $241,209

Accumulation Value

(15)

18 7% 101,398 6,634 18

19 7% 108,496 7,098 19

(16)

r PMT Fv of annuity Accumuated 7% (3,052) 3,266 35,366 7% (3,052) 6,760 41,107 7% (3,052) 10,499 47,250 7% (3,052) 14,499 53,823 7% (3,052) 18,780 60,856 7% (3,052) 23,360 68,382 7% (3,052) 28,261 76,434 7% (3,052) 33,505 85,050 7% (3,052) 39,116 94,270 7% (3,052) 45,120 104,134 7% (3,052) 51,544 114,689 7% (3,052) 58,417 125,983 7% (3,052) 65,772 138,067 7% (3,052) 73,642 150,998 7% (3,052) 82,062 164,833 7% (3,052) 91,072 179,637 7% (3,052) 100,713 195,478

(17)

7% (3,052) 111,029 212,427

7% (3,052) 122,066 230,562

(18)

7

End of Year Annual Return Policy Payment

0 (55,000) 1 6% 58,300 3,300 3,052 2 6% 61,798 3,498 3,052 3 6% 65,506 3,708 3,052 4 6% 69,436 3,930 3,052 5 6% 73,602 4,166 3,052 6 6% 78,019 4,416 3,052 7 6% 82,700 4,681 3,052 8 6% 87,662 4,962 3,052 9 6% 92,921 5,260 3,052 10 6% 98,497 5,575 3,052 11 6% 104,406 5,910 3,052 12 6% 110,671 6,264 3,052 13 6% 117,311 6,640 3,052 14 6% 124,350 7,039 3,052

Comer's critisms implied that the single-premium life insurance policy is an unttractive investment for Studebaker. What do your previous answers suggest?

Sebaiknya Studebacker tidak melanjutkan untuk menginvestasikan uangnya di asuransi premium yang diajukan oleh Morton. Karena dilihat dari pendapatan setelah 20 tahun, dikurangi utang yang harus ditanggung, Studebacker hanya menghasilkan $42,352 selama 20 tahun. Berbeda halnya, bila dia menginvestasikan $30,000, tetap menggunakan mortgage $45,000, dan menginvestasikan biaya $3,052/tahun, total hasilnya Studebacker akan mendapatkan keuntungan hampir 5 kali lipat lebih besar dibandingkan penawaran yang diajukan Morton.

Accumulation Value Increase in Accumulation Value

Annual

Cost

(19)

15 6% 131,811 7,461 3,052 16 6% 139,719 7,909 3,052 17 6% 148,103 8,383 3,052 18 6% 156,989 8,886 3,052 19 6% 166,408 9,419 3,052 20 6% 176,392 9,984 3,052

(20)

Earn /Year

Value

NPV (Earn/year)

(27,742)

248 55,248

NPV < 0

446 55,694

656 56,350

878 57,228

1,114 58,342

1,364 59,707

1,629 61,336

1,910 63,246

2,208 65,453

2,523 67,977

2,858 70,834

3,212 74,047

3,588 77,635

3,987 81,622

(21)

4,409 86,031

4,857 90,887

5,331 96,219

5,834 102,053

6,367 108,420

6,932

115,352

(22)

8.a

8.b

8.a

8.b

Loan Term Annual Interest Mortagage Inv/year 20 8% (260,171) 5,685

0 (30,000) 0 1 8% 32,400 2,400 1 2 8% 34,992 2,592 2 3 8% 37,791 2,799 3 4 8% 40,815 3,023 4 5 8% 44,080 3,265 5 6 8% 47,606 3,526 6 7 8% 51,415 3,808 7 8 8% 55,528 4,113 8 9 8% 59,970 4,442 9 10 8% 64,768 4,798 10 11 8% 69,949 5,181 11 12 8% 75,545 5,596 12 13 8% 81,589 6,044 13

Suppose Studebaker's goal is to accumulate $400,000 in 20 years. Assume the $30,000 is invested at 8%. How much will he have to save in equal amounts at the end of each of the next 20 years if he can earn 8 percent per year on any investment?

Repeat part (a) but assume he will not be able to save any money in years 13 to 20. This is, he will save an equal amount at the end of years 1 to 12 and nothing thereafter.

Studebacker harus menyiapkan dana sebesar $5,685 tiap tahunnya, agar dapat memperoleh uang senilai $400,000 di tahun ke 20

Studebacker harus menyiapkan dana sebesar $13,709 tiap tahunnya di tahun 1 sampai ke 12, agar dapat memperoleh uang senilai $400,000 di tahun ke 20

Accumulation Value

(23)

14 8% 88,116 6,527 14 15 8% 95,165 7,049 15 16 8% 102,778 7,613 16 17 8% 111,001 8,222 17 18 8% 119,881 8,880 18 19 8% 129,471 9,590 19 20 8% 139,829 10,358 20

Loan Term Annual Interest Mortagage Inv/year 12 8% (260,171) 13,709.7

0 (30,000) 0 1 8% 32,400 2,400 1 2 8% 34,992 2,592 2 3 8% 37,791 2,799 3 4 8% 40,815 3,023 4 5 8% 44,080 3,265 5 6 8% 47,606 3,526 6 7 8% 51,415 3,808 7 8 8% 55,528 4,113 8 9 8% 59,970 4,442 9 10 8% 64,768 4,798 10 11 8% 69,949 5,181 11 12 8% 75,545 5,596 12 13 8% 81,589 6,044 14 8% 88,116 6,527 15 8% 95,165 7,049 16 8% 102,778 7,613 17 8% 111,001 8,222 18 8% 119,881 8,880 19 8% 129,471 9,590 20 8% 139,829 10,358 Accumulation Value Increase in Accumulation Value

(24)

r PV Fv of annuity Accumuated 8% (5,685) 6,140 38,540 8% (5,685) 12,771 47,763 8% (5,685) 19,933 57,725 8% (5,685) 27,668 68,483 8% (5,685) 36,022 80,102 8% (5,685) 45,044 92,650 8% (5,685) 54,787 106,202 8% (5,685) 65,310 120,838 8% (5,685) 76,675 136,645 8% (5,685) 88,949 153,717 8% (5,685) 102,206 172,155 8% (5,685) 116,522 192,067 8% (5,685) 131,984 213,573

(25)

8% (5,685) 148,683 236,799 8% (5,685) 166,718 261,883 8% (5,685) 186,195 288,973 8% (5,685) 207,231 318,231 8% (5,685) 229,950 349,830 8% (5,685) 254,486 383,957 8% (5,685) 260,171 400,000 r FV Fv of annuity 8% (13,709.7) 14,806 8% (13,709.7) 30,798 8% (13,709.7) 48,068 8% (13,709.7) 66,720 8% (13,709.7) 86,864 8% (13,709.7) 108,619 8% (13,709.7) 132,115 8% (13,709.7) 157,491 8% (13,709.7) 184,897 8% (13,709.7) 214,495 8% (13,709.7) 246,461 8% (13,709.7) 260,171

Accumulated

400,000

(26)

(27)

(28)

9

Loan Term Annual Interest Mortagage Payment

30 Tahun 9% /tahun (75,000) 7,300

/tahun

360 Bulan 0.75% /bulan (75,000) 603

/bulan

$7,242

Year Payment Interest Principal

Balance

Month Payment

0 75,000 0 1 7,300 6,750 550 74,450 1 603 2 7,300 6,700 600 73,850 2 603 3 7,300 6,647 654 73,196 3 603 4 7,300 6,588 713 72,484 4 603 5 7,300 6,524 777 71,707 5 603 6 7,300 6,454 847 70,860 6 603 7 7,300 6,377 923 69,938 7 603 8 7,300 6,294 1,006 68,932 8 603 9 7,300 6,204 1,096 67,835 9 603 10 7,300 6,105 1,195 66,640 10 603 11 7,300 5,998 1,303 65,338 11 603

The yearly payment on the new 30-year, $75,000 mortgage is $7,300. This assume one payment is made at the end of each of the next 30 years. Suppose that payments must be made at the end of each month. Would 12 of these monthly payments be equal to one of the yaerly payments? Explain.

Untuk pembayaran yang dilakukan tiap bulan berbeda (tidak sama) dengan pembayaran tiap tahun. Dilihat dari bunga (interest) pembayaran tahunan (tahun ke-1) sebesar $6,750, yang jauh lebih besar dibanding bunga pembayaran bulanan dengan total (akumulasi tahun-1) sebesar $6,729. Dengan pembayaran per bulan, nilai pokok pinjaman tiap bulannya semakin mengecil begitu pula bunganya. Sehingga lebih ringan cicilan dengan metode bulanan dibanding tahunan.

(29)

12 7,300 5,880 1,420 63,918 12 603 13 7,300 5,753 1,548 62,370 Interest 1 tahun pertama

14 7,300 5,613 1,687 60,684 15 7,300 5,462 1,839 58,845 16 7,300 5,296 2,004 56,841 17 7,300 5,116 2,185 54,656 18 7,300 4,919 2,381 52,275 19 7,300 4,705 2,595 49,679 20 7,300 4,471 2,829 46,850 21 7,300 4,217 3,084 43,767 22 7,300 3,939 3,361 40,405 23 7,300 3,636 3,664 36,742 24 7,300 3,307 3,993 32,748 25 7,300 2,947 4,353 28,395 26 7,300 2,556 4,745 23,651 27 7,300 2,129 5,172 18,479 28 7,300 1,663 5,637 12,842 29 7,300 1,156 6,144 6,697 30 7,300 603 6,697 0

(30)

/tahun

Interest Principal

Balance

75,000 563 41 74,959 562 41 74,918 562 42 74,876 562 42 74,834 561 42 74,792 561 43 74,750 561 43 74,707 560 43 74,664 560 43 74,620 560 44 74,576 559 44 74,532

(31)

559 44 74,488

(32)

10

End of Year Annual Return Annual Cost Year

- 1 7% (5,152) 5,152 5,152 20 2 7% (5,152) 10,665 5,513 3 7% (5,152) 16,563 5,899 4 7% (5,152) 22,875 6,311 5 7% (5,152) 29,628 6,753 6 7% (5,152) 36,854 7,226 7 7% (5,152) 44,586 7,732 8 7% (5,152) 52,859 8,273 9 7% (5,152) 61,711 8,852 10 7% (5,152) 71,182 9,472 11 7% (5,152) 81,317 10,135 12 7% (5,152) 92,161 10,844 13 7% (5,152) 103,765 11,603

Exhibit 3 suggest that the annual cost of the life insurance policy is $3,052. With the adjustments mentioned in the case, Comer calculated the cost to be $5,152 in year 1 and $18,632 by year 20 assuming a 7 percent annual return. Explain how these were determined.

Comer melihat ada kehilangan pendapatan ketika Studebacker menarik uang $30,000 dari reksadananya. Dengan perhitungan bunga 7%/tahun dari $30,000, corner menyimpulkan Studebacker kehilangan pendapatan $2,100/tahun. Karena itu, bila $30,000 diambil untuk di investasikan ke jalur yang lain, akan ada penambahan annual cost sebesar $2,100 ditambah perkiraan annual cost yang disebutkan oleh Morton sebesar $3,052. Sehingga dana yang harus disediakan Studebacker tiap tahun seharusnya sebesar $5,152 ($3,052 + $2,100)

Bila annual cost ini di asumsikan berbunga 7% tiap tahunnya, maka di tahun ke 20, biaya yang seharusnya disediakan Studebacker bukan lagi $3,052 (menurut Morton) tetapi senilai $18,632

Accumulation Cost

(33)

14 7% (5,152) 116,180 12,416 15 7% (5,152) 129,465 13,285 16 7% (5,152) 143,679 14,215 17 7% (5,152) 158,889 15,210 18 7% (5,152) 175,163 16,274 19 7% (5,152) 192,576 17,413 20 7% (5,152) 211,209 18,632

(34)

Invest Earning interest

7% (30,000) 2,100

/year

Annual