Question

Consider an asset that costs $680,000 and is depreciated straight-line to zero over its eight-year tax life. The asset is to be used in a five-year project; at the end of the project, the asset can be sold for $143.000. The relevant tax rate is 21 percent. Suppose the fixed asset actually qualifies for 100 percent bonus depreciation in the first year. All the other facts are the same. What is the project's Year 1 net cash flow now? Year 2? Year 3? What is the new NPV?

Answer 1

Case 1; Without bonus tax

In this case the asset is depreciated over useful life of 8yrs using straight line method. So depreciation for each year is 85,000 (680,000/8) assuming zero salvage value at the end of 8th year. The book value of the asset will keep on reducing by the amount of depreciation each year.

The depreciation schedule and cash flow for each year is as follows:

Year	0	1	2	3	4	5	6	7	8
Depreciation	-	85,000	85,000	85,000	85,000	85,000	85,000	85,000	85,000
Book Value	6,80,000	5,95,000	5,10,000	4,25,000	3,40,000	2,55,000	1,70,000	85,000	-
Cash flow	-6,80,000	17,850	17,850	17,850	17,850	1,84,370

In the first year the asset was purchased, so an outflow of that amount. In every year subsequent to that, tax benefit on depreciation is earned which is equal to (depreciation*Tax). Thus cash flow of 85,000*0.21=17,850.

Also at the end of project in year 5, the asset can be sold at 143,000. Thus the post tax benefit on selling is calculated as Market Value - (Market Value - Book Value)*Tax.

which is 143,000 - (143,000 - 255,000)*0.21 = 184,370.

The NPV can be calculated as per the given compounding rate by discounting each year cash flow.

Case 1; With bonus tax

Here an additional depreciation of 100% of book value can be claimed in the year the asset is purchased. The left over book value of the asset is then depreciated over the remaining useful life of the asset as is done usually.

Thus at the beggining itself, a depreciation of 680,000 * 100% * 0.21 = 142,800. Then the remaining book value of 680,000 - 142,800 = 537,200. is depreciated over the remaining life of 8 yrs. The annual depreciation is thus 537,000/8=67,150

The depreciation schedule and cash flows are as follows:

Year	0	1	2	3	4	5	6	7	8
Depreciation	1,42,800	67,150	67,150	67,150	67,150	67,150	67,150	67,150	67,150
Book Value	5,37,200	4,70,050	4,02,900	3,35,750	2,68,600	2,01,450	1,34,300	67,150	-
Cash flow	-6,50,012	14,102	14,102	14,102	14,102	1,69,376

The cash outflow for 1st year is purchase cost plus the tax benefit on bonus depreciation which is (-680,000)+(142,800*0.21) = -650,012. Rest of the process remains the same. Each year for Year2 to year 5, we will earn tax benefit on depreciation, 67,150*0.21 = 14,102. And the in the last year additional cash flow from selling the asset in year 5 can be earned which is 143,000 - (143,000 - 168,600)*.21 = 169,376

The NPV can then be calculated as per the given compounding rate by discounting each year cash flow