Case 1 - financial planing : time value of money
December 3, 2017 | Author: Ahmad Bjoe Hariadi | Category: N/A
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case 1 financial managing...
Description
CASE 1 1 2 3 4 5
Andriyanto Ruth Rasyed Filco Anggraini
1
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.
End of Year Annual Return Policy Payment 0
Accumulation Value
Increase in Accumulation Value
(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
2
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.
End of Year Annual Return Policy Payment 0
Accumulation Value
Increase in Accumulation Annual Cost Value
(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
Earn /Year
Value
Annual Loan Term Interest
Mortagage
Payment
30
9%
(75,000)
7,300
7%
(45,000)
4,248
248
55,248
20
446
55,694
Biaya tambahan per tahun
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
3,052
3
For the 9 percent mortgage in Exhibit 4, find the loan balance at the end of years 19 and 20
Year
Payment
Interest
Balance
Principal
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
4
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.
End of Year
Annual Return
0
Policy Payment
Accumulation Value
Increase in Accumulation Value
Annual Cost
Earn /Year
(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
Value
Year
Payment
Interest
Principal
0
Balance 75,000
55,248
1
7,300
6,750
550
74,450
55,694
2
7,300
6,700
600
73,850
56,350
3
7,300
6,647
654
73,196
57,228
4
7,300
6,588
713
72,484
58,342
5
7,300
6,524
777
71,707
59,707
6
7,300
6,454
847
70,860
61,336
7
7,300
6,377
923
69,938
63,246
8
7,300
6,294
1,006
68,932
65,453
9
7,300
6,204
1,096
67,835
67,977
10
7,300
6,105
1,195
66,640
70,834
11
7,300
5,998
1,303
65,338
74,047
12
7,300
5,880
1,420
63,918
77,635
13
7,300
5,753
1,548
62,370
81,622
14
7,300
5,613
1,687
60,684
86,031
15
7,300
5,462
1,839
58,845
90,887
16
7,300
5,296
2,004
56,841
96,219
17
7,300
5,116
2,185
54,656
102,053
18
7,300
4,919
2,381
52,275
108,420
19
7,300
4,705
2,595
49,679
115,352
20
7,300
4,471
2,829
46,850
73,000
21
7,300
4,217
3,084
43,767
42,352
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
the excess $30,000 were invested in a long-term asset yielding 8 percent a 5.a If year, how much would be accumulated after 20 years?
5.b
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)?
5.a
Setelah 20 tahun, investasi $30,000 akan terakumulasi menjadi sebesar $139,829
5.b
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
Increase in End of Year Annual Return Policy Payment Accumulation Accumulation Value Value 0
(30,000)
n 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
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
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
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
6
Repeat problem 5 but assume a 7 percent return can be earned
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
Increase in End of Year Annual Return Policy Payment Accumulation Accumulation Value Value 0
(30,000)
n 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
18
7%
101,398
6,634
18
19
7%
108,496
7,098
19
20
7%
116,091
7,595
20
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
7%
(3,052)
111,029
212,427
7%
(3,052)
122,066
230,562
7%
(3,052)
125,118
241,209
7
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.
End of Year
Increase in Annual Return Policy Payment Accumulation Accumulation Value Value
0
Annual Cost
(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
Earn /Year
Value
NPV (Earn/year) (27,742)
248
55,248
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
NPV < 0
4,409
86,031
4,857
90,887
5,331
96,219
5,834
102,053
6,367
108,420
6,932
115,352
Suppose Studebaker's goal is to accumulate $400,000 in 20 years. Assume the is invested at 8%. How much will he have to save in equal amounts at 8.a $30,000 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
8.b to 20. This is, he will save an equal amount at the end of years 1 to 12 and nothing thereafter.
harus menyiapkan dana sebesar $5,685 tiap tahunnya, agar 8.a Studebacker dapat memperoleh uang senilai $400,000 di tahun ke 20
harus menyiapkan dana sebesar $13,709 tiap tahunnya di tahun 8.b Studebacker 1 sampai ke 12, agar dapat memperoleh uang senilai $400,000 di tahun ke 20
Loan Term Annual Interest 20
8%
Mortagage (260,171)
Inv/year 5,685
Increase in End of Year Annual Return Policy Payment Accumulation Accumulation Value Value 0
(30,000)
n 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
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
Increase in End of Year Annual Return Policy Payment Accumulation Accumulation Value Value
n
Loan Term Annual Interest 12
8%
0
Mortagage (260,171)
Inv/year 13,709.7
(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
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
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
9
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.
Loan Term
Annual Interest
30 Tahun
9% /tahun
(75,000)
7,300 /tahun
360 Bulan
0.75% /bulan
(75,000)
603 /bulan
Year
Payment
Interest Principal
0
Mortagage
Balance
Payment
Month
75,000
0
$7,242
Payment
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
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
12
603
Interest 1 tahun pertama
/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
559
6,729
44
74,488
10
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
End of Year Annual Return
Annual Cost
Increase in Accumulation Accumulation Cost Value
Year
1
7%
(5,152)
5,152
5,152
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
20
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
Annual Interest
7%
Invest
(30,000)
Earning interest
2,100 /year
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