We have been provided with the information as under
Machine that costs $250,000.
Revenues of $85,000 per year
Life = five years.
The machine would be depreciated using the straight-line method over a five-year life
no salvage value.
Tax rate = 40 %
after-tax rate of return =12%
Now we will find NPV as under
Depreciation
=250,000-0 /5 year
=$ 50,000 depreciation each year
Now we will find the cash flow each year
Revenue
85,000
Less: depreciation
50,000
Before tax revenue
35,000
Less: tax at 40%
14000
After tax revenue
21,000
Add: depreciation
50,000
Net cash flow each year
71,000
NPV calculation
year
Cashflow
Presentvalue factor at12%
Presentvalue
A
b
c=a*b
0
-250,000
1
-250000
1
71,000
0.892857143
63392.86
2
71,000
0.797193878
56600.77
3
71,000
0.711780248
50536.40
4
71,000
0.635518078
45121.78
5
71,000
0.567426856
40287.31
5939.11
NPV of the project is $ 5939.11
Two main equations are required to solve this problem, the first has to do with depreciation rate, and the second with after-tax revenue.
As to the first, if a $250,000 investment has no salvage value after 5 years, it's depreciate rate is $50,000/year. We use this alongside the annual revenue to calculate general income before tax, as follows: $85,000-$50,000=$35,000.
Taxable revenue=before tax revenue * (tax rate).
Thus, taxable revenue = $35,000 * (.4) =$14,000.
So, each year will have an annual net revenue of $85,000-$14,000 = $71,000
We now use those figures to compute the present value:
future value = $71,000+$71,000*1.12+$71,000*1.12^2+$71,000*1.12^3+$71,000*1.12^4 = $451,000
present value = future value/(1+r)^n, where r is the interest rate, and n is the number of years. Thus, the present value is $451,000/(1.12)^5 = $255,909
Net present value = present value - cost = $255,909-$250,000 = $5,909
https://www.mathsisfun.com/money/net-present-value.html
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