Question

Your firm is considering a project that would require purchasing $ 7.2 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 38 %?, the appropriate cost of capital is 8 %?, and the equipment can be? depreciated:

please round all answers to 4 decimal points

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.

Answer 1

Present Value can be calculated using PV function on a calculator

a) Annual Depreciation = 7.2m / 10 = 720,000, Tax Shield = 38% x 720,000 = 273,600

N = 10, I/Y = 8%, PMT = 273,600, FV = 0 => Compute PV = $1,835,878

b) Depreciation = 7.2/5 = 1,440,000, Tax Shield = 38% x 1,440,000 = 547,200

=> N = 5, I/Y = 8%, PMT = 547,200, FV = 0 => Compute PV = $3,671,757

c)

	0	1	2	3	4	5
MACRS %	20%	32%	19.20%	11.52%	11.52%	5.76%
Depreciation	1440000	2304000	1382400	829440	829440	414720
Tax Shield	547200	875520	525312	315187.2	315187.2	157593.6
PV	$2,397,370

d) As an immediate deduction, tax shield = 0.38 x 7.2m = $2,736,000