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.

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:

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.