Question

Declining Balance Depreciation 12-18 A firm is considering the following investment project: Before-Tax Cash Flow (thousands) Year 12 -$1000 0 500 1 340 2 244 3 100 4 100 5 125 Salvage value

Answer 1

To solve this problem, first we have to tind out the DDB depreciation schedule DDB depreciation in any year = (2/N)*(the last year's book value). The calculations are shown in the following table: Year DDB Book value 1000.00 1000-40/1-600.00 600-240-360.00 360-144=216.00 216-86.4=129.60 125.00 2/5*1000-400.00 2/5.600=240.00 2/5*360=144,00 2/5 +216-86.40 129.60-125-4.60*** *** Note the adjustment in the last year, where the depreciation is adjusted to match the Book Value to the salvage value. In case of DDB this adjustment is required when the Book Value and the salvage value is not the same aller last years depreciation. Once the depreciation is known, we can analyze the before and after tax cash flow in the following table, BTCF DDB ATCF Taxable Income "Tax a 24% -1000 400 240 -1000 500 340 244 100 100.00 125.00** 144 86.4 100 100 100 13.6 95.4 -3.26 96.74 4.6 -22.90 77.10+ 125.00** **Note that salvage value is not taxable, unless you sell it at a higher price, that is unless you make any profit by selling it. As DDB with salvage value of 125K is used to depreciate the ansel, thus, the book value and the market value is same and hence there will be no tax consequence at the last year due to the sale of the property. To examine if the After Tax Cash Flow is generating more than 10%, let us compute the NET PRESENT BENEFIT (NPB) at 10% rate. NPB-476(P/F, 10%,1)+316(P/F, 10%.2) + 220(P/F,10%.3) + 96.74(P/F, 10%,4) + 212.10(P/T.10%,5) - 1057.35 As NPB is more than the net present cost (NPC-$1000), the project is economically justificd.

To solve this problem, first we have to tind out the DDB depreciation schedule DDB depreciation in any year = (2/N)*(the last year's book value). The calculations are shown in the following table: Year DDB Book value 1000.00 1000-40/1-600.00 600-240-360.00 360-144=216.00 216-86.4=129.60 125.00 2/5*1000-400.00 2/5.600=240.00 2/5*360=144,00 2/5 +216-86.40 129.60-125-4.60*** *** Note the adjustment in the last year, where the depreciation is adjusted to match the Book Value to the salvage value. In case of DDB this adjustment is required when the Book Value and the salvage value is not the same aller last years depreciation. Once the depreciation is known, we can analyze the before and after tax cash flow in the following table, BTCF DDB ATCF Taxable Income "Tax a 24% -1000 400 240 -1000 500 340 244 100 100.00 125.00** 144 86.4 100 100 100 13.6 95.4 -3.26 96.74 4.6 -22.90 77.10+ 125.00** **Note that salvage value is not taxable, unless you sell it at a higher price, that is unless you make any profit by selling it. As DDB with salvage value of 125K is used to depreciate the ansel, thus, the book value and the market value is same and hence there will be no tax consequence at the last year due to the sale of the property. To examine if the After Tax Cash Flow is generating more than 10%, let us compute the NET PRESENT BENEFIT (NPB) at 10% rate. NPB-476(P/F, 10%,1)+316(P/F, 10%.2) + 220(P/F,10%.3) + 96.74(P/F, 10%,4) + 212.10(P/T.10%,5) - 1057.35 As NPB is more than the net present cost (NPC-$1000), the project is economically justificd.