Your firm is considering a project that would require purchasing $7.8 million wo

Question

Your firm is considering a project that would require purchasing $7.8 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 36%, 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.

The present value of the depreciation tax shield associated with this equipment is ?million.

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 ?million.

c. Using MACRS depreciation with a five-year recovery period and starting immediately.

The present value of the depreciation tax shield associated with this equipment is ?million.

d. Fully as an immediate deduction.

The present value of the depreciation tax shield is ? million

Explanation / Answer

Answer :-

Asset cost = $ 7.8 million

Tax rate = 36%

cost of capital = 7%

a.) year = 10 years

Depreciation = (7.8 - 0) / 10

= .78

Depreciation Tax Shield = Depreciation amount * Tax rate

= .78 * 36%

= .2808

Present value of Depreciation Tax Shield = Depreciation Tax Shield * PVIFA at (r,n)

= .2808 * PVIFA at (7%,10year)

= .2808 * 7.024

= $ 1.97 million

b.) year = 5 years

Depreciation = (7.8 - 0) / 5

= 1.56

Depreciation Tax Shield = Depreciation amount * Tax rate

= 1.56 * 36%

= .5616

Present value of Depreciation Tax Shield = Depreciation Tax Shield * PVIFA at (r,n)

= .5616 * PVIFA at (7%,5year)

= .5616 * 4.100

= $ 2.30 million

c.)

=7.8*20%

=1.56

=7.8*32%

=2.496

=1.4976

=.8986

=.8986

=.4493

=1.56*36%

=.5616

=.8986

=.5391

=.3235

=.3235

=.1617

=.5616*.935

=.525

=.784

=.440

=.247

=.231

=.108

Present value of Depreciation Tax Shield = $ 2.335 million

d.) Year = 0 year

Depreciation = 7.8 fully immediate deduction

Depreciation Tax Shield = 7.8 * 36%

= 2.808

Present value of Depreciation Tax Shield = 2.808 * PVIFA at (7%,0year)

= $ 2.808 million

Year 0 1 2 3 4 5 Asset cost 7.8 MACRS Depreciation Rate 20% 32% 19.20% 11.52% 11.52% 5.76% Depreciation amount

=7.8*20%

=1.56

=7.8*32%

=2.496

=1.4976

=.8986

=.8986

=.4493

Depreciation Tax Shield

=1.56*36%

=.5616

=.8986

=.5391

=.3235

=.3235

=.1617

PVIF at 7% .935 .873 .816 .763 .713 .666 Present Value

=.5616*.935

=.525

=.784

=.440

=.247

=.231

=.108

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