Question

In: Finance

A 100,000 loan can be obtained at a 10 percent rate with monthly payments over a 15 year term.

A 100,000 loan can be obtained at a 10 percent rate with monthly payments over a 15 year term.
a. What is the after tax effective interest rate on the loan, assuming the borrower is in a 30 percent tax bracket and the loan is only held three years? Assume that the benefit of interest deductions for tax purposes occurs at the same time payments are made.
b. Calculate the after tax effective cost for the above loan, assuming that 5 points are charged and that the points are tax deductible at the time they are paid.
c. How does the after tax cost in part (b) compare with the pretax effective cost of the loan?

Expert Solution

After tax effective interest rate has a vital role in analyzing the cost of mortgages. As the interest paid on mortgages is tax deductible, the deductibles of interest payments reduce the after tax cost of debt. The interest payments made in year is deductible for the same year. The after tax cost is product of pre tax cost and complement of borrowers tax rate.

a. The following table shows the calculation of detailed interest payment structure before and after tax implication:

Amount Borrowed	100000
Period	180
Rate	0.008333333
Payment	₹ 1,074.61
Month	Before tax Payment	Interest	Principal	Balance	After tax value of Deduction	At Payment
0	100000
1	₹ 1,074.61	833.333	-241.27	99758.728	250	₹ 824.61
2	₹ 1,074.61	₹ 831.32	-243.28	99515.446	249.4	₹ 825.21
3	₹ 1,074.61	₹ 829.30	-245.31	99270.136	248.79	₹ 825.82
4	₹ 1,074.61	₹ 827.25	-247.35	99022.782	248.18	₹ 826.43
5	₹ 1,074.61	₹ 825.19	-249.42	98773.367	247.56	₹ 827.05
6	₹ 1,074.61	₹ 823.11	-251.49	98521.873	246.93	₹ 827.68
7	₹ 1,074.61	₹ 821.02	-253.59	98268.284	246.3	₹ 828.31
8	₹ 1,074.61	₹ 818.90	-255.7	98012.581	245.67	₹ 828.94
9	₹ 1,074.61	₹ 816.77	-257.83	97754.747	245.03	₹ 829.58
10	₹ 1,074.61	₹ 814.62	-259.98	97494.765	244.39	₹ 830.22
11	₹ 1,074.61	₹ 812.46	-262.15	97232.616	243.74	₹ 830.87
12	₹ 1,074.61	₹ 810.27	-264.33	96968.283	243.08	₹ 831.53
13	₹ 1,074.61	₹ 808.07	-266.54	96701.747	242.42	₹ 832.19
14	₹ 1,074.61	₹ 805.85	-268.76	96432.99	241.75	₹ 832.86
15	₹ 1,074.61	₹ 803.61	-271	96161.993	241.08	₹ 833.53
16	₹ 1,074.61	₹ 801.35	-273.26	95888.738	240.4	₹ 834.21
17	₹ 1,074.61	₹ 799.07	-275.53	95613.205	239.72	₹ 834.89
18	₹ 1,074.61	₹ 796.78	-277.83	95335.377	239.03	₹ 835.58
19	₹ 1,074.61	₹ 794.46	-280.14	95055.233	238.34	₹ 836.27
20	₹ 1,074.61	₹ 792.13	-282.48	94772.755	237.64	₹ 836.97
21	₹ 1,074.61	₹ 789.77	-284.83	94487.923	236.93	₹ 837.68
22	₹ 1,074.61	₹ 787.40	-287.21	94200.717	236.22	₹ 838.39
23	₹ 1,074.61	₹ 785.01	-289.6	93911.118	235.5	₹ 839.11
24	₹ 1,074.61	₹ 782.59	-292.01	93619.106	234.78	₹ 839.83
25	₹ 1,074.61	₹ 780.16	-294.45	93324.66	234.05	₹ 840.56
26	₹ 1,074.61	₹ 777.71	-296.9	93027.76	233.31	₹ 841.30
27	₹ 1,074.61	₹ 775.23	-299.37	92728.386	232.57	₹ 842.04
28	₹ 1,074.61	₹ 772.74	-301.87	92426.518	231.82	₹ 842.79
29	₹ 1,074.61	₹ 770.22	-304.38	92122.134	231.07	₹ 843.54
30	₹ 1,074.61	₹ 767.68	-306.92	91815.213	230.31	₹ 844.30
31	₹ 1,074.61	₹ 765.13	-309.48	91505.735	229.54	₹ 845.07
32	₹ 1,074.61	₹ 762.55	-312.06	91193.677	228.76	₹ 845.85
33	₹ 1,074.61	₹ 759.95	-314.66	90879.019	227.98	₹ 846.63
34	₹ 1,074.61	₹ 757.33	-317.28	90561.739	227.2	₹ 847.41
35	₹ 1,074.61	₹ 754.68	-319.92	90241.815	226.4	₹ 848.21
36	₹ 90,993.83	₹ 752.02	-322.59	₹ 89,919.22	225.6	₹ 90,768.20

The general formula to evaluate the after tax effective interest rate on loan is:

After-tax cost=(Pre - tax cost)(1-taxrate)

After-tax cost=(0.10)(1-0.30)

=0.1*0.7

=0.07%

b. By assuming the charge of 5% points which were deductible when they are paid the after tax effective cost would be:

Month	Before tax Payment	Interest	Principal	Balance	After tax value of Deduction	At Payment
0	95000
1	₹ 1,074.61	833.33	-241.272	94758.73	250	824.61
2	1074.605118	789.66	-284.949	94473.78	236.9	837.71
3	1074.605118	787.28	-287.324	94186.46	236.18	838.43
4	1074.605118	784.89	-289.718	93896.74	235.47	839.14
5	1074.605118	782.47	-292.132	93604.61	234.74	839.87
6	1074.605118	780.04	-294.567	93310.04	234.01	840.60
7	1074.605118	777.58	-297.021	93013.02	233.28	841.33
8	1074.605118	775.11	-299.497	92713.52	232.53	842.08
9	1074.605118	772.61	-301.992	92411.53	231.78	842.83
10	1074.605118	770.10	-304.509	92107.02	231.03	843.58
11	1074.605118	767.56	-307.047	91799.97	230.27	844.34
12	1074.605118	765.00	-309.605	91490.37	229.5	845.11
13	1074.605118	762.42	-312.185	91178.18	228.73	845.88
14	1074.605118	759.82	-314.787	90863.39	227.95	846.66
15	1074.605118	757.19	-317.41	90545.98	227.16	847.45
16	1074.605118	754.55	-320.055	90225.93	226.36	848.25
17	1074.605118	751.88	-322.722	89903.21	225.56	849.05
18	1074.605118	749.19	-325.412	89577.8	224.76	849.85
19	1074.605118	746.48	-328.123	89249.67	223.94	850.67
20	1074.605118	743.75	-330.858	88918.81	223.12	851.49
21	1074.605118	740.99	-333.615	88585.2	222.3	852.31
22	1074.605118	738.21	-336.395	88248.8	221.46	853.15
23	1074.605118	735.41	-339.198	87909.61	220.62	853.99
24	1074.605118	732.58	-342.025	87567.58	219.77	854.84
25	1074.605118	729.73	-344.875	87222.7	218.92	855.69
26	1074.605118	726.86	-347.749	86874.96	218.06	856.55
27	1074.605118	723.96	-350.647	86524.31	217.19	857.42
28	1074.605118	721.04	-353.569	86170.74	216.31	858.30
29	1074.605118	718.09	-356.516	85814.22	215.43	859.18
30	1074.605118	715.12	-359.487	85454.74	214.54	860.07
31	1074.605118	712.12	-362.482	85092.25	213.64	860.97
32	1074.605118	709.10	-365.503	84726.75	212.73	861.88
33	1074.605118	706.06	-368.549	84358.2	211.82	862.79
34	1074.605118	702.99	-371.62	83986.58	210.9	863.71
35	1074.605118	699.89	-374.717	83611.87	209.97	864.64
36	90993.83	696.77	-377.84	83234.03	209.03	90784.80-

here in this case with the application of IRR rule for the values in after tax payment column the essective cost after tax is found to be 8.56%.

c. The before tax eefective cost due to increase on 5% points is not 12.09% and this also resulted in increased after tax effective cost with affect to 5% points. The approximate after tax effective cost would be around,

After tax effective cost=0.1209*(1-0.30)

= 0.1209*0.70

=0.0846

but however with the increase in 5% points after tax effective cost is 0.0846 , thus the percentage of 5points increase resulted in an increase of before and after effective costs.

jeff jeffy answered 2 years ago

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