Question

Your firm is considering a project that would require purchasing $7.3 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 7%, 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. Straight-line over a ten-year period, with the first deduction starting in one year. The present value of the depreciation tax shield associated with this equipment is $

b. Straight-line over a five-year period, with the first deduction starting in one year. The present value of the depreciation tax shield associated with this equipment is $

C. The present value of the depreciation tax shield associated with this equipment is $

d. Fully as an immediate deduction.
The present value of the depreciation tax shield is $ million.

PLEASE SHOW THE DETAILED FORMULA(NOT IN EXCEL). THANK YOU

Answer 1

SLM with 10 years						7.00%
						NPV@ 0.07
Year	Machine Cost	Dep rate	Depreciation	Tax rate	Dep Shield	PV factor	PV-Cash flow
0	7,300,000	0	-	33%	-	1.000	-
1	7,300,000	10%	730,000	33%	240,900	0.935	225,140
2	7,300,000	10%	730,000	33%	240,900	0.873	210,411
3	7,300,000	10%	730,000	33%	240,900	0.816	196,646
4	7,300,000	10%	730,000	33%	240,900	0.763	183,781
5	7,300,000	10%	730,000	33%	240,900	0.713	171,758
6	7,300,000	10%	730,000	33%	240,900	0.666	160,522
7	7,300,000	10%	730,000	33%	240,900	0.623	150,020
8	7,300,000	10%	730,000	33%	240,900	0.582	140,206
9	7,300,000	10%	730,000	33%	240,900	0.544	131,034
10	7,300,000	10%	730,000	33%	240,900	0.508	122,461
						Total PV	1,691,981
SLM with 5 years						7.00%
						NPV@ 0.07
Year	Machine Cost	Dep rate	Depreciation	Tax rate	Dep Shield	PV factor	PV-Cash flow
0	7,300,000	0	-	33%	-	1.000	-
1	7,300,000	20%	1,460,000	33%	481,800	0.935	450,280
2	7,300,000	20%	1,460,000	33%	481,800	0.873	420,823
3	7,300,000	20%	1,460,000	33%	481,800	0.816	393,292
4	7,300,000	20%	1,460,000	33%	481,800	0.763	367,563
5	7,300,000	20%	1,460,000	33%	481,800	0.713	343,517
						Total PV	1,975,475
Macars starting today						7.00%
						NPV@ 0.07
Year	Machine Cost	Dep rate	Depreciation	Tax rate	Dep Shield	PV factor	PV-Cash flow
0	7,300,000	20.00%	1,460,000	33%	481,800	1.000	481,800
1	7,300,000	32.00%	2,336,000	33%	770,880	0.935	720,449
2	7,300,000	19.20%	1,401,600	33%	462,528	0.873	403,990
3	7,300,000	11.52%	840,960	33%	277,517	0.816	226,536
4	7,300,000	11.52%	840,960	33%	277,517	0.763	211,716
5	7,300,000	5.76%	420,480	33%	138,758	0.713	98,933
						Total PV	2,143,424
Macars starting today						7.00%
						NPV@ 0.07
Year	Machine Cost	Dep rate	Depreciation	Tax rate	Dep Shield	PV factor	PV-Cash flow
0	7,300,000	100.00%	7,300,000	33%	2,409,000	1.000	2,409,000
						Total PV	2,409,000