Question

Your firm is considering a project that would require purchasing $ 7.4 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 31 %​, the appropriate cost of capital is 10 %​, 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. Fully as an immediate deduction.

Questions:

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. ​ (Round the final answer to three decimal places.​ Round all intermediate values to four decimal places as​ needed.)

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. ​ (Round the final answer to three decimal places.​ Round all intermediate values to four decimal places as ​needed.)

c. Fully as an immediate deduction. The present value of the depreciation tax shield is ​$ *** million. ​ (Round the final answer to three decimal places.​ Round all intermediate values to four decimal places as​ needed.)  

Answer 1

a. Annual depreciation expense = $ 7,400,000 / 10 = $ 740,000

Depreciation tax shield per year = $ 740,000 x 0.31 = $ 229,400.

Present value of the tax shield = Annual depreciation tax shield x PVA _{10%, 10 years} = $ 229,400 x 6.1446 = $ 1,409,571.24.

b. Annual depreciation = $ 7,400,000 / 5 = $ 1,480,000

Depreciation tax shield per year = $ 1,480,000 x 0.31 = $ 458,800.

Present value of the tax shield = Annual depreciation tax shield x PVA _{10%, 5 years} = $ 458,800 x 3.7908 = $ 1,739,219.04.

c. Annual depreciation = $ 0.

Therefore there would be no depreciation tax shield.