Homework Answers
| Incremental PV of tax savings using SYD depreciation calculation |
SYD excel formula=(cost, salvage, life, per)
for eg: year 1 depreciation =(200,000,0,4,1)
SLD excel formula= (cost, salvage, life)
CALCULATION:
| Method | year 1 | year 2 | year 3 | year 4 | Total | |
| SYD depreciation | [1] | $80,000 | $60,000 | $40,000 | $20,000 | |
| tax benefit@40% | [2] | $32,000 | $24,000 | $16,000 | $8,000 | |
| PV for $1 factor for 11% | [3] | 0.901 | 0.812 | 0.731 | 0.659 | |
| PV [2]*[3] | [4] | 28832 | 19488 | $11,696 | $5,272 | $65288 |
| Straight Line Depreciation (SLD) | [1] | $50,000 | $50,000 | $50,000 | $50,000 | |
| tax benefit | [2] | $20,000 | $20,000 | $20,000 | $20,000 | |
| PV for $1 | [3] | $0.901 | 0.812 | 0.731 | 0.659 | |
| PV [2]*[3] | [4] | $18020 | $16240 | $14,620 | $13,180 | $62060 |
| Incremental PV of tax savings using SYD depreciation | [$65288-$62060] | $3228 |
2) Incremental PV of tax savings using DDB depreciation
DDB excel formula=(cost, salvage, life, period)
for eg:- for year 1 depreciation=(200000,0,4,1)
| Method | year 1 | year 2 | year 3 | year 4 | Total | |
| DDB depreciation | [1] | $100,000 | $50,000 | $25,000 | $12,500 | |
| tax benefit@40% | [2] | $40,000 | $20,000 | $10,000 | $5,000 | |
| PV for $1 factor for 11% | [3] | 0.901 | 0.812 | 0.731 | 0.659 | |
| PV [2]*[3] | [4] | $36,040 | $16,240 | $7,310 | $3,295 | $62,885 |
| Straight Line Depreciation (SLD) | [1] | $50,000 | $50,000 | $50,000 | $50,000 | |
| tax benefit | [2] | $20,000 | $20,000 | $20,000 | $20,000 | |
| PV for $1 | [3] | $0.901 | 0.812 | 0.731 | 0.659 | |
| PV [2]*[3] | [4] | $18,020 | $16,240 | $14,620 | $13,180 | $62,060 |
| Incremental PV of tax savings using DDB depreciation | [$62885-$62060] | $825 | ||||
| 3) Incremental PV of tax savings using MACRS over SYD |
Asset is going to depreciate over 3 years using half-year convention. The MACRS rate for each of the 4 years are:
| year 1 | 33.33% |
| year 2 | 44.45% |
| year 3 | 14.81% |
| year 4 | 7.41% |
All these rates add unto 100%. It means asset will be fully depreciated and MACRS don't consider salvage value. for Now let's see how to calculate depreciation using the above rate. For eg:- depreciation for year 1 is calculated as: $200,000*33.33%= $66,660.
[Note: the rate was not given in the question, so I took it from public source.]
| 3.a) Incremental PV of tax savings using MACRS over SYD |
| Method | year 1 | year 2 | year 3 | year 4 | Total | |
| SYD depreciation | [1] | $80,000 | $60,000 | $40,000 | $20,000 | |
| tax benefit@40% | [2] | $32,000 | $24,000 | $16,000 | $8,000 | |
| PV for $1 factor for 11% | [3] | 0.901 | 0.812 | 0.731 | 0.659 | |
| PV [2]*[3] | [4] | $28,832 | $19,488 | $11,696 | $5,272 | $65,288 |
| MACRS depreciation | [1] | $66,660 | $88,900 | $29,620 | $14,820 | |
| tax benefit@40% | [2] | $26,664 | $35,560 | $11,848 | $5,928 | |
| PV for $1 | [3] | $0.901 | 0.812 | 0.731 | 0.659 | |
| PV [2]*[3] | [4] | $24,024 | $28,875 | $8,661 | $3,907 | $65,466 |
| Incremental PV of tax savings using MACRS over SYD | [$65,466-$65288] | $178 |
| 3.B) Incremental PV of tax savings using MACRS over DDB |
| Method | year 1 | year 2 | year 3 | year 4 | Total | |
| DDB depreciation | [1] | $100,000 | $50,000 | $25,000 | $12,500 | |
| tax benefit@40% | [2] | $40,000 | $20,000 | $10,000 | $5,000 | |
| PV for $1 factor for 11% | [3] | 0.901 | 0.812 | 0.731 | 0.659 | |
| PV [2]*[3] | [4] | $36,040 | $16,240 | $7,310 | $3,295 | $62,885 |
| MACRS depreciation | [1] | $66,660 | $88,900 | $29,620 | $14,820 | |
| tax benefit@40% | [2] | $26,664 | $35,560 | $11,848 | $5,928 | |
| PV for $1 | [3] | $0.901 | 0.812 | 0.731 | 0.659 | |
| PV [2]*[3] | [4] | $24,024 | $28,875 | $8,661 | $3,907 | $65,466 |
| Incremental PV of tax savings using MACRS over DDB | [$62885-$62060] | $2,581 |
Add Answer to:
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estimated life at time of purchase was 4 years, with no estimated
salvage value. Assume a discount rate of 7% and an income tax rate
of 40%. (Use Exhibit 12.4, Appendix C, TABLE 1 and Appendix C,
TABLE 2.)
Required: 1. What is the incremental present value of the tax
benefits resulting from calculating depreciation using the
sum-of-the-years’-digits (SYD) method rather than the straight-line
(SLN) method on this asset? Use the...
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i tried to answer 996,-996,292,-292,3201,-3201, all these were
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Freedom Corporation acquired a fixed asset for $220,000. Its estimated life at time of purchase was 4 years, with no estimated salvage value. Assume a discount rate of 7% and an income tax rate of 40%. (Use Exhibit 12.4, Appendix C, TABLE 1 and Appendix C, TABLE 2.) TABLE 2 Present Value of Annuity of $1 Periods 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 20% 25%...
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