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?

Solutions

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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