Question

Your firm is considering a project that would require purchasing $7.7 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 20% using the alternative depreciation methods below. Note that because the depreciation tax shield is essentially a riskless cash flow​ (assuming the​ firm's tax rate remains​ constant), the appropriate cost of capital to evaluate the benefit from accelerated depreciation is the​ risk-free rate; assume this rate is 9% for all maturities.

a.​ Straight-line over a​ 10-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.​ 100% bonus depreciation​ (all the depreciation expense occurs when the asset is put into​ use, in this case​ immediately).

Answer 1

1-
Year	Annual depreciation =7700000/10	tax rate=20%	depreciation tax shield=annual depreciation*tax rate	present value of depreciation tax shield = depreciation tax shield/(1+r)^n r =9% n=1,2,3…...............10
1	770000	20%	154000	141284.4
2	770000	20%	154000	129618.72
3	770000	20%	154000	118916.26
4	770000	20%	154000	109097.48
5	770000	20%	154000	100089.43
6	770000	20%	154000	91825.168
7	770000	20%	154000	84243.274
8	770000	20%	154000	77287.407
9	770000	20%	154000	70905.878
10	770000	20%	154000	65051.264
Present value of sum of present value of depreciation tax shield =sum of present value of depreciation tax shield				988319.29
2-
Year	Annual depreciation =7700000/5	tax rate=20%	depreciation tax shield=annual depreciation*tax rate	present value of depreciation tax shield = depreciation tax shield/(1+r)^n r =9% n=1,2,3…...............10
1	1540000	20%	308000	282568.81
2	1540000	20%	308000	259237.44
3	1540000	20%	308000	237832.51
4	1540000	20%	308000	218194.97
5	1540000	20%	308000	200178.87
Present value of sum of present value of depreciation tax shield =sum of present value of depreciation tax shield				1198012.6
3-
Year	cost of equipment	MACRS rate of depreciation	Annual depreciation=cost of equipment*macrs rate	tax rate=20%	depreciation tax shield=annual depreciation*tax rate	present value of depreciation tax shield = depreciation tax shield/(1+r)^n r =9% n=0,1,2,3…...............10
0	7700000	20%	1540000	20%	308000	308000
1	7700000	32%	2464000	20%	492800	282568.8073
2	7700000	19.20%	1478400	20%	295680	259237.4379
3	7700000	11.52%	887040	20%	177408	237832.5119
4	7700000	11.52%	887040	20%	177408	218194.965
5	7700000	5.76%	443520	20%	88704	200178.867
Present value of sum of present value of depreciation tax shield =sum of present value of depreciation tax shield						1506012.59
4-
Year	cost of equipment	rate of depreciation	Annual depreciation=cost of equipment*macrs rate	tax rate=20%	depreciation tax shield=annual depreciation*tax rate	present value of depreciation tax shield = depreciation tax shield/(1+r)^n r =9% n=0
0	7700000	100%	7700000	20%	1540000	1540000