Loose-Leaf Essentials of Investments
Loose-Leaf Essentials of Investments
10th Edition
ISBN: 9781259604966
Author: Kane, Alex, Marcus Professor, Alan J., Bodie Professor, Zvi
Publisher: McGraw-Hill Education
Question
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Chapter 21, Problem 10PS
Summary Introduction

To determine:

The effect on real consumption during retirement of a 1% increase in the rate of inflation to a 1% increase in the tax rate as per given spread sheet 21.5.

Introduction:

Tax shelters are ways and means by which it is possible to postpone the payment of liability for as long as possible.

Expert Solution & Answer
Check Mark

Answer to Problem 10PS

To determine the effect of desired revision and compare the results of such changes, first we will consider the spreadsheet 21.5 as it will form the base of our answer.

This sheet is prepared with the assumption that desired real consumption is taken as input from previous spreadsheet. Taxes are then calculated on nominal consumption minus the necessary exemption. Thus, savings comes as a residuary information nominal income minus the tax minus the nominal consumption. The retirement section specifies that all funds in the retirement account are subject to tax.

Explanation of Solution

Given Information:

Following spreadsheet is given:

Loose-Leaf Essentials of Investments, Chapter 21, Problem 10PS

The detailed spreadsheet of the same would be produced as under:

    Retirement years Income growth Rate of inflation Exemption now Tax rate Savings rate ROR rROR
    25 0.07 0.03 15,000 0.25 0.15 0.06 0.0291
    AGE INCOME DEFLATOR EXEMPTION TAXES SAVINGS CUMMULATIVE SAVINGS CONSUMPTION
    30
    50,000
    1.00
    15,000
    5,016
    9,922
    9,922
    35,063
    31
    53,500
    1.03
    15,450
    5,465
    10,724
    21,242
    36,224
    32
    57,245
    1.06
    15,914
    5,949
    11,589
    34,105
    37,428
    33
    61,252
    1.09
    16,391
    6,468
    12,519
    48,671
    38,678
    34
    65,540
    1.13
    16,883
    7,027
    13,522
    65,112
    39,974
    35
    70,128
    1.16
    17,389
    7,628
    14,600
    83,620
    41,319
    36
    75,037
    1.19
    17,911
    8,273
    15,762
    104,399
    42,713
    37
    80,289
    1.23
    18,448
    8,966
    17,012
    127,674
    44,160
    38
    85,909
    1.27
    19,002
    9,710
    18,357
    153,692
    45,661
    39
    91,923
    1.30
    19,572
    10,509
    19,804
    182,718
    47,218
    40
    98,358
    1.34
    20,159
    11,367
    21,362
    215,043
    48,834
    41
    105,243
    1.38
    20,764
    12,288
    23,037
    250,982
    50,509
    42
    112,610
    1.43
    21,386
    13,277
    24,840
    290,881
    52,248
    43
    120,492
    1.47
    22,028
    14,337
    26,778
    335,113
    54,052
    44
    128,927
    1.51
    22,689
    15,475
    28,864
    384,083
    55,923
    45
    137,952
    1.56
    23,370
    16,695
    31,106
    438,234
    57,864
    46
    147,608
    1.60
    24,071
    18,004
    33,517
    498,044
    59,878
    47
    157,941
    1.65
    24,793
    19,408
    36,109
    564,036
    61,968
    48
    168,997
    1.70
    25,536
    20,913
    38,896
    636,775
    64,136
    49
    180,826
    1.75
    26,303
    22,526
    41,892
    716,874
    66,386
    50
    193,484
    1.81
    27,092
    24,256
    45,113
    804,999
    68,720
    51
    207,028
    1.86
    27,904
    26,110
    48,574
    901,873
    71,141
    52
    221,520
    1.92
    28,742
    28,097
    52,295
    1,008,281
    73,654
    53
    237,026
    1.97
    29,604
    30,226
    56,293
    1,125,070
    76,261
    54
    253,618
    2.03
    30,492
    32,507
    60,589
    1,253,163
    78,966
    55
    271,372
    2.09
    31,407
    34,952
    65,205
    1,393,559
    81,773
    56
    290,368
    2.16
    32,349
    37,571
    70,165
    1,547,337
    84,685
    57
    310,693
    2.22
    33,319
    40,376
    75,494
    1,715,671
    87,707
    58
    332,442
    2.29
    34,319
    43,381
    81,218
    1,899,829
    90,843
    59
    355,713
    2.36
    35,348
    46,599
    87,367
    2,101,186
    94,097
    60
    380,613
    2.43
    36,409
    50,046
    93,972
    2,321,229
    97,474
    61
    407,256
    2.50
    37,501
    53,738
    101,066
    2,561,568
    100,978
    62
    435,764
    2.58
    38,626
    57,691
    108,684
    2,823,947
    104,614
    63
    466,267
    2.65
    39,785
    61,923
    116,866
    3,110,250
    108,387
    64
    498,906
    2.73
    40,979
    66,455
    125,653
    3,422,517
    112,302
    65
    533,829
    2.81
    42,208
    71,307
    135,087
    3,762,956
    116,365
    TOTAL 944,536 1,773,854 REAL ANNUITY 76,052
    RETIREMENT
    AGE WITHDRAWN DEFLATOR EXEMPTION TAXES SAVINGS ROR rROR
    66
    220,420
    2.90
    43,474
    44,236
    3,768,313
    60,789
    67
    227,033
    2.99
    44,778
    45,564
    3,767,379
    60,789
    68
    233,844
    3.07
    46,122
    46,930
    3,759,578
    60,789
    69
    240,859
    3.17
    47,505
    48,338
    3,744,294
    60,789
    70
    248,085
    3.26
    48,931
    49,789
    3,720,867
    60,789
    71
    255,527
    3.36
    50,398
    51,282
    3,688,592
    60,789
    72
    263,193
    3.46
    51,910
    52,821
    3,646,715
    60,789
    73
    271,089
    3.56
    53,468
    54,405
    3,594,429
    60,789
    74
    279,221
    3.67
    55,072
    56,037
    3,530,873
    60,789
    75
    287,598
    3.78
    56,724
    57,719
    3,455,127
    60,789
    76
    296,226
    3.90
    58,426
    59,450
    3,366,209
    60,789
    77
    305,113
    4.01
    60,178
    61,234
    3,263,069
    60,789
    78
    314,266
    4.13
    61,984
    63,071
    3,144,587
    60,789
    79
    323,694
    4.26
    63,843
    64,963
    3,009,568
    60,789
    80
    333,405
    4.38
    65,759
    66,912
    2,856,737
    60,789
    81
    343,407
    4.52
    67,731
    68,919
    2,684,734
    60,789
    82
    353,709
    4.65
    69,763
    70,987
    2,492,108
    60,789
    83
    364,321
    4.79
    71,856
    73,116
    2,277,314
    60,789
    84
    375,250
    4.93
    74,012
    75,310
    2,038,703
    60,789
    85
    386,508
    5.08
    76,232
    77,569
    1,774,517
    60,789
    86
    398,103
    5.23
    78,519
    79,896
    1,482,885
    60,789
    87
    410,046
    5.39
    80,875
    82,293
    1,161,812
    60,789
    88
    422,347
    5.55
    83,301
    84,762
    809,174
    60,789
    89
    435,018
    5.72
    85,800
    87,304
    422,706
    60,789
    90
    448,068
    5.89
    88,374
    89,924
    -
    60,789
    TOTAL 8,036,350 1,612,828

For the first part of the answer where we have to calculate effect of 1% increase in inflation on real consumption, we have considered the following assumption:

    Number of retirement years
    25
    Income growth rate
    7%
    Rate of return
    6%
    Income at age 30
    50,000
    Savings Rate
    15%
    Inflation Rate
    4%
    Exemption
    $15,000
    Tax rate
    25%

The ANSWER will be as followed:

    Retirement years Income growth Rate of inflation Exemption now Tax rate Savings rate ROR rROR
    25 0.07 0.04 15,000 0.25 0.15 0.06 0.0192
    AGE INCOME DEFLATOR EXEMPTION TAXES SAVINGS CUMMULATIVE SAVINGS CONSUMPTION
    30
    50,000
    1.00
    15,000
    5,016
    9,922
    9,922
    35,063
    31
    53,500
    1.04
    15,600
    5,518
    10,309
    20,826
    36,224
    32
    57,245
    1.08
    16,224
    6,065
    10,698
    32,774
    37,428
    33
    61,252
    1.12
    16,873
    6,659
    11,086
    45,826
    38,678
    34
    65,540
    1.17
    17,548
    7,304
    11,472
    60,048
    39,974
    35
    70,128
    1.22
    18,250
    8,005
    11,852
    75,503
    41,319
    36
    75,037
    1.27
    18,980
    8,767
    12,224
    92,257
    42,713
    37
    80,289
    1.32
    19,739
    9,593
    12,584
    110,376
    44,160
    38
    85,909
    1.37
    20,529
    10,490
    12,928
    129,927
    45,661
    39
    91,923
    1.42
    21,350
    11,464
    13,253
    150,976
    47,218
    40
    98,358
    1.48
    22,204
    12,521
    13,551
    173,586
    48,834
    41
    105,243
    1.54
    23,092
    13,666
    13,819
    197,820
    50,509
    42
    112,610
    1.60
    24,015
    14,909
    14,050
    223,739
    52,248
    43
    120,492
    1.67
    24,976
    16,256
    14,236
    251,400
    54,052
    44
    128,927
    1.73
    25,975
    17,716
    14,370
    280,854
    55,923
    45
    137,952
    1.80
    27,014
    19,299
    14,442
    312,148
    57,864
    46
    147,608
    1.87
    28,095
    21,014
    14,443
    345,320
    59,878
    47
    157,941
    1.95
    29,219
    22,872
    14,361
    380,400
    61,968
    48
    168,997
    2.03
    30,387
    24,885
    14,183
    417,407
    64,136
    49
    180,826
    2.11
    31,603
    27,065
    13,896
    456,348
    66,386
    50
    193,484
    2.19
    32,867
    29,427
    13,484
    497,213
    68,720
    51
    207,028
    2.28
    34,182
    31,983
    12,930
    539,976
    71,141
    52
    221,520
    2.37
    35,549
    34,751
    12,215
    584,590
    73,654
    53
    237,026
    2.46
    36,971
    37,748
    11,317
    630,982
    76,261
    54
    253,618
    2.56
    38,450
    40,991
    10,213
    679,054
    78,966
    55
    271,372
    2.67
    39,988
    44,501
    8,877
    728,674
    81,773
    56
    290,368
    2.77
    41,587
    48,300
    7,280
    779,674
    84,685
    57
    310,693
    2.88
    43,251
    52,411
    5,390
    831,845
    87,707
    58
    332,442
    3.00
    44,981
    56,858
    3,172
    884,927
    90,843
    59
    355,713
    3.12
    46,780
    61,669
    587
    938,610
    94,097
    60
    380,613
    3.24
    48,651
    66,874
    -2,408
    992,519
    97,474
    61
    407,256
    3.37
    50,597
    72,504
    -5,859
    1,046,211
    100,978
    62
    435,764
    3.51
    52,621
    78,592
    -9,819
    1,099,164
    104,614
    63
    466,267
    3.65
    54,726
    85,177
    -14,346
    1,150,768
    108,387
    64
    498,906
    3.79
    56,915
    92,299
    -19,502
    1,200,312
    112,302
    65
    533,829
    3.95
    59,191
    99,999
    -25,356
    1,246,974
    116,365
    TOTAL 1,203,168 265,856 REAL ANNUITY 16,040
    RETIREMENT
    AGE WITHDRAWN DEFLATOR EXEMPTION TAXES SAVINGS ROR rROR
    66
    65,827
    4.10
    61,559
    1,067
    1,255,966
    15,780
    67
    68,460
    4.27
    64,021
    1,110
    1,262,864
    15,780
    68
    71,199
    4.44
    66,582
    1,154
    1,267,437
    15,780
    69
    74,046
    4.62
    69,245
    1,200
    1,269,437
    15,780
    70
    77,008
    4.80
    72,015
    1,248
    1,268,594
    15,780
    71
    80,089
    4.99
    74,896
    1,298
    1,264,621
    15,780
    72
    83,292
    5.19
    77,892
    1,350
    1,257,206
    15,780
    73
    86,624
    5.40
    81,007
    1,404
    1,246,015
    15,780
    74
    90,089
    5.62
    84,248
    1,460
    1,230,687
    15,780
    75
    93,692
    5.84
    87,618
    1,519
    1,210,836
    15,780
    76
    97,440
    6.07
    91,122
    1,579
    1,186,046
    15,780
    77
    101,338
    6.32
    94,767
    1,643
    1,155,871
    15,780
    78
    105,391
    6.57
    98,558
    1,708
    1,119,832
    15,780
    79
    109,607
    6.83
    102,500
    1,777
    1,077,415
    15,780
    80
    113,991
    7.11
    106,600
    1,848
    1,028,069
    15,780
    81
    118,551
    7.39
    110,864
    1,922
    971,202
    15,780
    82
    123,293
    7.69
    115,299
    1,999
    906,181
    15,780
    83
    128,225
    7.99
    119,911
    2,078
    832,327
    15,780
    84
    133,354
    8.31
    124,707
    2,162
    748,914
    15,780
    85
    138,688
    8.65
    129,696
    2,248
    655,161
    15,780
    86
    144,235
    8.99
    134,883
    2,338
    550,235
    15,780
    87
    150,005
    9.35
    140,279
    2,431
    433,245
    15,780
    88
    156,005
    9.73
    145,890
    2,529
    303,235
    15,780
    89
    162,245
    10.12
    151,725
    2,630
    159,184
    15,780
    90
    168,735
    10.52
    157,794
    2,735
    -
    15,780
    TOTAL 2,741,427 44,437

For the second part of the answer where we have to calculate effect of 1% increase in tax rate on real consumption, we have considered the following assumption:

    Number of retirement years
    25
    Income growth rate
    7%
    Rate of return
    6%
    Income at age 30
    50,000
    Savings Rate
    15%
    Inflation Rate
    3%
    Exemption
    $15,000
    Tax rate
    26%
    Retirement years Income growth Rate of inflation Exemption now Tax rate Savings rate ROR rROR
    25 0.07 0.03 15,000 0.26 0.15 0.06 0.0291
    AGE INCOME DEFLATOR EXEMPTION TAXES SAVINGS CUMMULATIVE SAVINGS CONSUMPTION
    30
    50,000
    1.00
    15,000
    5,216
    9,721
    9,721
    35,063
    31
    53,500
    1.03
    15,450
    5,684
    10,506
    20,810
    36,224
    32
    57,245
    1.06
    15,914
    6,187
    11,351
    33,410
    37,428
    33
    61,252
    1.09
    16,391
    6,727
    12,261
    47,675
    38,678
    34
    65,540
    1.13
    16,883
    7,308
    13,240
    63,776
    39,974
    35
    70,128
    1.16
    17,389
    7,933
    14,295
    81,898
    41,319
    36
    75,037
    1.19
    17,911
    8,604
    15,431
    102,243
    42,713
    37
    80,289
    1.23
    18,448
    9,324
    16,653
    125,030
    44,160
    38
    85,909
    1.27
    19,002
    10,099
    17,969
    150,501
    45,661
    39
    91,923
    1.30
    19,572
    10,930
    19,384
    178,915
    47,218
    40
    98,358
    1.34
    20,159
    11,822
    20,907
    210,557
    48,834
    41
    105,243
    1.38
    20,764
    12,780
    22,546
    245,736
    50,509
    42
    112,610
    1.43
    21,386
    13,808
    24,309
    284,789
    52,248
    43
    120,492
    1.47
    22,028
    14,911
    26,205
    328,082
    54,052
    44
    128,927
    1.51
    22,689
    16,094
    28,245
    376,011
    55,923
    45
    137,952
    1.56
    23,370
    17,363
    30,438
    429,010
    57,864
    46
    147,608
    1.60
    24,071
    18,724
    32,797
    487,547
    59,878
    47
    157,941
    1.65
    24,793
    20,184
    35,333
    552,133
    61,968
    48
    168,997
    1.70
    25,536
    21,749
    38,060
    623,320
    64,136
    49
    180,826
    1.75
    26,303
    23,427
    40,991
    701,711
    66,386
    50
    193,484
    1.81
    27,092
    25,226
    44,143
    787,956
    68,720
    51
    207,028
    1.86
    27,904
    27,154
    47,530
    882,764
    71,141
    52
    221,520
    1.92
    28,742
    29,221
    51,171
    986,900
    73,654
    53
    237,026
    1.97
    29,604
    31,435
    55,084
    1,101,198
    76,261
    54
    253,618
    2.03
    30,492
    33,808
    59,289
    1,226,559
    78,966
    55
    271,372
    2.09
    31,407
    36,350
    63,807
    1,363,959
    81,773
    56
    290,368
    2.16
    32,349
    39,074
    68,662
    1,514,459
    84,685
    57
    310,693
    2.22
    33,319
    41,991
    73,879
    1,679,205
    87,707
    58
    332,442
    2.29
    34,319
    45,116
    79,483
    1,859,440
    90,843
    59
    355,713
    2.36
    35,348
    48,463
    85,503
    2,056,510
    94,097
    60
    380,613
    2.43
    36,409
    52,048
    91,970
    2,271,870
    97,474
    61
    407,256
    2.50
    37,501
    55,887
    98,916
    2,507,098
    100,978
    62
    435,764
    2.58
    38,626
    59,998
    106,377
    2,763,901
    104,614
    63
    466,267
    2.65
    39,785
    64,400
    114,389
    3,044,125
    108,387
    64
    498,906
    2.73
    40,979
    69,113
    122,994
    3,349,766
    112,302
    65
    533,829
    2.81
    42,208
    74,159
    132,235
    3,682,987
    116,365
    TOTAL 982,317 1,736,072 REAL ANNUITY 74,436
    RETIREMENT
    AGE WITHDRAWN DEFLATOR EXEMPTION TAXES SAVINGS ROR rROR
    66
    215,736
    2.90
    43,474
    44,788
    3,688,231
    58,983
    67
    222,208
    2.99
    44,778
    46,132
    3,687,317
    58,983
    68
    228,874
    3.07
    46,122
    47,516
    3,679,682
    58,983
    69
    235,740
    3.17
    47,505
    48,941
    3,664,723
    58,983
    70
    242,812
    3.26
    48,931
    50,409
    3,641,793
    58,983
    71
    250,097
    3.36
    50,398
    51,922
    3,610,204
    58,983
    72
    257,600
    3.46
    51,910
    53,479
    3,569,217
    58,983
    73
    265,328
    3.56
    53,468
    55,084
    3,518,042
    58,983
    74
    273,288
    3.67
    55,072
    56,736
    3,455,837
    58,983
    75
    281,486
    3.78
    56,724
    58,438
    3,381,701
    58,983
    76
    289,931
    3.90
    58,426
    60,191
    3,294,672
    58,983
    77
    298,629
    4.01
    60,178
    61,997
    3,193,724
    58,983
    78
    307,588
    4.13
    61,984
    63,857
    3,077,760
    58,983
    79
    316,815
    4.26
    63,843
    65,773
    2,945,610
    58,983
    80
    326,320
    4.38
    65,759
    67,746
    2,796,027
    58,983
    81
    336,109
    4.52
    67,731
    69,778
    2,627,679
    58,983
    82
    346,193
    4.65
    69,763
    71,872
    2,439,148
    58,983
    83
    356,578
    4.79
    71,856
    74,028
    2,228,918
    58,983
    84
    367,276
    4.93
    74,012
    76,249
    1,995,378
    58,983
    85
    378,294
    5.08
    76,232
    78,536
    1,736,806
    58,983
    86
    389,643
    5.23
    78,519
    80,892
    1,451,372
    58,983
    87
    401,332
    5.39
    80,875
    83,319
    1,137,122
    58,983
    88
    413,372
    5.55
    83,301
    85,818
    791,977
    58,983
    89
    425,773
    5.72
    85,800
    88,393
    413,723
    58,983
    90
    438,546
    5.89
    88,374
    91,045
    -
    58,983
    TOTAL 7,865,566 1,632,938

On comparing the above results, by keeping all the conditions remaining same, and revising the given rates we reach the following conclusion:

    AS PER ACTUAL STATED CONDITION
    AS PER ACTUAL STATED CONDITION AND INCREASING INFALTION RATE TO 4%
    AS PER ACTUAL STATED CONDITION AND INCREASING TAX RATE TO 26%
    REAL CONSUMPTION
    76,052.00
    16,040.00
    74,436.00
    REAL CONSUMPTION ON RETIREMENT
    60,789.00
    15,780.00
    58,983.00

Hence we can say, on increasing inflation rate by 1%, the real consumption decreases marginally.

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