Your firm is considering a project that would require purchasing $7.9 million worth of new equipment. Determine the present value of the depreciation tax shield associated with this equipment if the? firm's tax rate is 33%?, the appropriate cost of capital is 8 %?, and the equipment can be? depreciated:
a.? Straight-line over a? ten-year period, with the first deduction starting in one year.
b.? Straight-line over a? five-year period, with the first deduction starting in one year.
c. Using MACRS depreciation with a? five-year recovery period and starting immediately.
d. Fully as an immediate deduction.
a)
Year | Dep | Tax shield(.33*.79) | Discount factor | PV |
1 | .79 | .26 | .926 | .24 |
2 | .79 | .26 | .857 | .22 |
3 | .79 | .26 | .794 | .21 |
4 | .79 | .26 | .735 | .19 |
5 | .79 | .26 | .681 | .18 |
6 | .79 | .26 | .630 | .16 |
7 | .79 | .26 | .583 | .15 |
8 | .79 | .26 | .540 | .14 |
9 | .79 | .26 | .500 | .13 |
10 | .79 | .26 | .463 | .12 |
Total NPV=1.74
b)
Year | Dep | Tax shield(.33*.79) | Discount factor | PV |
1 | 1.58 | .52 | .926 | .48 |
2 | 1.58 | .52 | .857 | .45 |
3 | 1.58 | .52 | .794 | .41 |
4 | 1.58 | .52 | .735 | .38 |
5 | 1.58 | .52 | .681 | .35 |
Total NPV=2.07
c)MACRS percent dep PV
Year 0 20% .52 .52
Year 1 32% .83 .77
Year 2 19.20% .50 .43
Year 3 11.52% .30 .24
Year 4 11.52% .30 .22
Year 5 5.76% .15 .10
Total 2.28
d) 7.9 *.33=2.61
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