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A company is considering buying a new system, the cost of the system is $25,000 , and the system will serve for 4 years, and the devices for the system are then sold for $3,000
A company is considering buying a new system, the cost of the system is $25,000 , and the system will serve for 4 years, and the devices for the system are then sold for $3,000 . The Income Tax Law allows for the full depreciation of the assets' value, and in an accelerated manner, within four years and by using the sum of years numbers method. The system needs to hire a programmer with an annual salary of $3,500 , and the savings that the system will give are $12,000 annually. The company is subject to an income tax rate of 15% and the company requires an annual return on investment of 20%. Required:
1- Determining the current value of the tax savings resulting from using the sum of years numbers method instead of the fixed-section method, assuming that there is no residual value for the asset at the end of its useful life in both methods.
2- Determining the net present value after income tax for the amount collected from the sale of the asset at the end of its useful life.
3- Determining the net present value of the project and whether the company should invest in it or not.
Expert Solution
-
1.
- in fixed section
Annual depreciation= (Cost of asset -salvage value) / life in years
Annual depreciation =25,000 / 4= 6250
Annual tax savings=Annual depreciation * tax rate= 6250 * 0.15= 937.5
Present value factor of annuity (4 years and 20% discount rate)=2.589
Present value of tax savings in fixed section method= Annual tax savings*Present value factor of annuity
Present value of tax savings in fixed section method= 937.5 * 2.589= 2427.1875
- in sum of years numbers
sum of years numbers= 1+2+3+4=10
Calculation of depreciation for each year is shown below
Year 1: 25,000 * 4/10=10,000
Year 2: 25,000 * 3/10=7,500
Year 3: 25,000 * 2/10=5,000
Year 4: 25,000 * 1/10=2,500
Year Depreciation Tax savings
(Depreciation * tax rate)
Present value factor
20% rate of return
Present value of tax savings 1 10,000 1500 0.833 1249.5 2 7,500 1125 0.694 780.75 3 5,000 750 0.579 434.25 4 2500 375 0.482 180.75 Total 2645.25 current value of the tax savings resulting from using the sum of years numbers = 2645.25
current value of the tax savings resulting from using the fixed rate method= 2427.1875
current value of the tax savings resulting from using the sum of years numbers method instead of the fixed-section method= 2645.25 - 2427.1875=218.0625
2.
Selling price= 3,000
Tax = (selling price -book value value) * tax rate
Book value at the end of fourth year is zero,fully depreciated
Tax= (3000-000) *0.15= 450
amount collected from the sale of the asset after tax=selling price - tax=3,000 -450=2,550
Present value factor (4 periode and 20% discount rate)=0.482
Present value of amount collected from the sale of the asset after tax= 2550 * 0.482=1229.1
3.
Annual cash flow from the project= annual cash savings-annual salary=12,000 -3500=8500
After tax Annual cash flow from the project=Annual cash flow from the project *(1-tax rate)=8500 *0.85=7225
Present value factor of annuity (4 years and 20% discount rate)=2.589
Present value of After tax Annual cash flow from the project= Present value factor of annuity*After tax Annual cash flow from the project
Present value of After tax Annual cash flow from the project= 7225 * 2.589=18,705.525
Present value of amount collected from the sale of the asset after tax=1229.1
Present value of cashflow from the project=Present value of After tax Annual cash flow from the project +Present value of amount collected from the sale of the asset after tax+ current value of the tax savings resulting from using the sum of years numbers
Present value of cashflow from the project=18,705.525 + 1229.1 + 2645.25=22,579.875
Initial investment= Cost of system 25,000
Net present value=Present value of cashflow from the project-Initial investment
Net present value=22,579.875 - 25000= -2,420.125
Net present value is negative, company should not invest in this project
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