Your firm is considering a project that would require purchasing $7.8 million wo
ID: 2773828 • Letter: Y
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
a. Straight-line over a ten-year period, with the first deduction starting in one year.
Annual Depreciation = Cost/Usefullife
Annual Depreciation = 7800000/10
Annual Depreciation = 780000
Depreciation tax shield = Annual Depreciation*tax rate
Depreciation tax shield = 780000*36%
Depreciation tax shield = 280800
Present value of the depreciation tax shield = Depreciation tax shield*((1-(1+r)^-n)/r
Present value of the depreciation tax shield = 280800*((1-(1+7%)^-10)/7%
Present value of the depreciation tax shield = $ 1,972,221.70
The present value of the depreciation tax shield associated with this equipment is 1.97 million.
b. Straight-line over a five-year period, with the first deduction starting in one year.
Annual Depreciation = Cost/Usefullife
Annual Depreciation = 7800000/5
Annual Depreciation = 1560000
Depreciation tax shield = Annual Depreciation*tax rate
Depreciation tax shield = 1560000*36%
Depreciation tax shield = 561600
Present value of the depreciation tax shield = Depreciation tax shield*((1-(1+r)^-n)/r
Present value of the depreciation tax shield = 561600*((1-(1+7%)^-5)/7%)
Present value of the depreciation tax shield = $ 2,302,670.88
The present value of the depreciation tax shield associated with this equipment is 2.30 million.
c. Using MACRS depreciation with a five-year recovery period and starting immediately.
Depreciation Tax shield currently = 20%*7.8 Million*36% = 0.5616 Million
Depreciation in year 1 = 32%*7.8 Million * 36% = 0.89856 Million
Depreciation in year 2 = 19.2%*7.8 Million * 36% = 0.539136 Million
Depreciation in year 3= 11.52%*7.8 Million * 36% = 0.323482 Million
Depreciation in year 4 = 11.52%*7.8 Million * 36% = 0.323482 Million
Depreciation in year 5 = 5.76%*7.8 Million * 36% = 0.161741 Million
Present value of the depreciation tax shield = 0.5616 + 0.89856/1.07 + 0.539136/1.07^2 + 0.323482 /1.07^3 + 0.323482 /1.07^4 + 0.161741 /1.07^5
Present value of the depreciation tax shield = $ 2.498438 Million
The present value of the depreciation tax shield associated with this equipment is 2.50 million.
d. Fully as an immediate deduction.
Present value of the depreciation tax shield = 7,800,000*36%
Present value of the depreciation tax shield = $ 2,808,000
The present value of the depreciation tax shield is $ 2.81 million
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.