Question 18.3: A company has purchased a small pickup truck for $20,000. Co...
A company has purchased a small pickup truck for $20,000. Compare writing the truck off in the year it was purchased under Section 179 (see Chapter 5) versus depreciating it using 200% declining balance and the half-year convention. The company’s marginal tax rate is 34% and its MARR is 15%.
If the truck were to be written off during the year it was purchased the company’s tax savings would be as follows:
Tax_1 = -$20,000(0.34) = -$6,800
The cash flow for writing the truck off is as follows:
Cash Flow_1 = -$20,000 – (-$6,800) = -$13,200
The after-tax net present cost for writing the truck off is calculated using Eq. (15-3) as follows:
P = F/(1 + i)^n (15-3)
NPV = -$13,200/(1 + 0.15)^1 = -$11,478
Using Table 5-6, the annual depreciation for the truck is as follows:
| TABLE 5-6^{18} Depreciation Rates for 200% Declining Balance Using the Half-Year Convention | ||||
| YEAR | 3 YEARS (%) | 5 YEARS (%) | 7 YEARS (%) | 10 YEARS (%) |
| 1 | 33.33 | 20.00 | 14.29 | 10.00 |
| 2 | 44.45 | 32.00 | 24.49 | 18.00 |
| 3 | 14.81 | 19.20 | 17.49 | 14.40 |
| 4 | 7.41 | 11.52 | 12.49 | 11.52 |
| 5 | NA | 11.52 | 8.93 | 9.22 |
| 6 | NA | 5.76 | 8.92 | 7.37 |
| 7 | NA | NA | 8.93 | 6.55 |
| 8 | NA | NA | 4.46 | 6.55 |
| 9 | NA | NA | NA | 6.56 |
| 10 | NA | NA | NA | 6.55 |
| 11 | NA | NA | NA | 3.28 |
Depreciation_1 = $20,000(0.2000) = $4,000
Depreciation_2 = $20,000(0.3200) = $6,400
Depreciation_3 = $20,000(0.1920) = $3,840
Depreciation_4 = $20,000(0.1152) = $2,304
Depreciation_5 = $20,000(0.1152) = $2,304
Depreciation_6 = $20,000(0.0576) = $1,152
The annual tax savings are as follows:
Tax_1 = $4,000(0.34) = $1,360
Tax_2 = $6,400(0.34) = $2,176
Tax_3 = $3,840(0.34) = $1,306
Tax_4 = $2,304(0.34) = $783
Tax_5 = $2,304(0.34) = $783
Tax_6 = $1,152(0.34) = $392
The annual cash flows are as follows:
Cash Flow_1 = -$20,000 – (-$1,360) = -$18,640
Cash Flow_2 = $2,11,440.00 – $5,000.00)(0.34)/4 = -$302.60
Cash Flow_3 = $1,306
Cash Flow_4 = $783
Cash Flow_5 = $783
Cash Flow_6 = $392
The after-tax net present cost for depreciating the truck is calculated using Eq. (15-3) as follows:
NPV = -$18,640/(1 + 0.15)^1 + $2,176/(1 + 0.15)^2 + $1,306/
(1 + 0.15)^3 + $783/(1 + 0.15)^4 + $783/
(1 + 0.15)^5 + $392/(1 + 0.15)^6
NPV = -$12,698
We see that by depreciating the truck the net present cost has increased by $1,220 ($12,698 – $11,478).