An asset is being considered whose first cost, life, recovery period, salvage va
ID: 1122092 • Letter: A
Question
An asset is being considered whose first cost, life, recovery period, salvage value, and annual operating expenses, respectively, are estimated at $15,000, 12 years, 10 years, zero, and $800. The asset, classified as 10-year property, 24. Chap. 12 Income Taxes in Economic Analysis will be depreciated by the MACRS (GDS) straight-line method of depreciation The effective income tax is 40%. Determine the AE(i) cost at 12% for the after- tax cash flow if a. The initial investment is made from retained earnings. b. The initial investment is borrowed at 8% with repayment of principal and interest in 10 equal annual amounts. The initial investment is borrowed at 8% with repayment of interest at the end of each period and repayment of the loan principal at the end of 10 years.Explanation / Answer
Answer::
Given:
Cost of Life = $15,000
Life = 12 years
Recovery period = 10 years
Salvage Value = Nil
Annual operating expenses = $800
Rate of return = 12%
Tax rate = 40%
Depreciation = MACRS (GDS) straight-line method 10 years
Calculation of tax savings on depreciation:
Rate of depreciation (MACRS 10 year asset class)
Depreciation ($)
Tax Savings on Depreciation ($)
10.00%
1500
600
18.00%
2700
1080
14.40%
2160
864
11.52%
1728
691
9.22%
1383
553
7.37%
1105.5
442
6.55%
982.5
393
6.55%
982.5
393
6.56%
984
394
6.55%
982.5
393
3.28%
492
197
a. Aggregate Expenditure (AE) when the initial investment is made from retained earnings:
After tax operating expenses = operating expenses x (1-tax rate) = $800 x (1-0.4) = $ 480
AE = Initial investment + Present value of operating expenses – Present value of tax savings on depreciation
Now calculate the Present Value of operating expenses and tax savings on depreciation:
Present Value of $480 for 12 years at 12% rate of interest = $ 480 x PVAF, 12 years at 12% = $ 480 x 6.19437 = $2,973.3
Present value tax saving on depreciation:
Year
Present Value Factor @ 12%
Tax savings on depreciation
Present value of tax savings on depreciation
1
0.8929
$ 600
$ 535.71
2
0.7972
$ 1,080
$ 860.97
3
0.7118
$ 864
$ 614.98
4
0.6355
$ 691
$ 439.14
5
0.5674
$ 553
$ 313.79
6
0.5066
$ 442
$ 223.93
7
0.4523
$ 393
$ 177.77
8
0.4039
$ 393
$ 158.73
9
0.3606
$ 394
$ 142.08
10
0.3220
$ 393
$ 126.54
11
0.2875
$ 197
$ 56.63
Total Present Value
$ 3,650.27
Hence Aggregate Expenditure (AE) = $ 15,000 + $ 2,973.3 - $ 3,650.27 = $ 14,323.03
b. Aggregate Expenditure (AE) when the initial investment is borrowed at 8% with repayment of principal interest in 10 equal annual amounts.
AE = Present Value of principal payment + Present value of after tax interest + Present value of operating expenses – Present value of tax savings on depreciation
Calculation of present value of principal payment and after tax interest:
Formula for Installment = P[{r(1+r)n}/{(1+r)n-1}]
Now P = Loan amount = $15,000, r= 8%, n = 10 years
Putting all the above figures in formula, we get installment = 15,000 x [{0.08(1+0.08)10)}/{(1+0.08)10-1}] = 15,000 x (0.1727 / 1.1589)
= 15,000 x 0.149 = $2,235
(Figures in $)
Year
Opening Principal
Int. payment @ 8% (A)
Installment
Principal Payment (B)
Closing principal
After tax int. C = (A x 0.6)
PV Factor @ 12% (D)
PV of Principal (B x D)
PV of Interest (C x D)
1
15000.00
1200.00
2235.00
1035.00
13965.00
720.00
0.89
924.11
642.86
2
13965.00
1117.20
2235.00
1117.80
12847.20
670.32
0.80
891.10
534.38
3
12847.20
1027.78
2235.00
1207.22
11639.98
616.67
0.71
859.28
438.93
4
11639.98
931.20
2235.00
1303.80
10336.17
558.72
0.64
828.59
355.08
5
10336.17
826.89
2235.00
1408.11
8928.07
496.14
0.57
799.00
281.52
6
8928.07
714.25
2235.00
1520.75
7407.31
428.55
0.51
770.46
217.12
7
7407.31
592.59
2235.00
1642.41
5764.90
355.55
0.45
742.95
160.83
8
5764.90
461.19
2235.00
1773.81
3991.09
276.72
0.40
716.41
111.76
9
3991.09
319.29
2235.00
1915.71
2075.38
191.57
0.36
690.83
69.08
10
2075.38
166.03
2235.00
2075.00
0
99.62
0.32
668.09
32.07
Total
7,890.81
2,843.63
Hence Aggregate Expenditure (AE) = $ 7,890.81 + $ 2,843.63 + $ 2,973.3 - $ 3,650.27 = $ 10,057.47
c. Aggregate Expenditure (AE) when the initial investment is borrowed at 8% with repayment of interest at the end of each period and repayment of the loan principal at the end of 10 years:
AE = Present Value of principal payment + Present value of after tax interest + Present value of operating expenses – Present value of tax savings on depreciation
Principal of $15,000 is paid at the end of 10th year. Present value = Principal X PVF, 12%, 10 years = $ 15,000 * 0.322 = $4,830
Present Value of after tax interest = (Principal X int. rate) x (1 - tax rate) x (PVAF, 12%, 10 years) = (15000 x 8%) x (1-0.4) x (5.650) = $ 4,068
Hence Aggregate Expenditure (AE) = $ 4,830 + $ 4,068 + $ 2,973.3 - $ 3,650.27 = $ 8221.03
Rate of depreciation (MACRS 10 year asset class)
Depreciation ($)
Tax Savings on Depreciation ($)
10.00%
1500
600
18.00%
2700
1080
14.40%
2160
864
11.52%
1728
691
9.22%
1383
553
7.37%
1105.5
442
6.55%
982.5
393
6.55%
982.5
393
6.56%
984
394
6.55%
982.5
393
3.28%
492
197
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