Bayleaf Inc is considering the purchase of a machine that costs $250,000. The machine is expected to generate revenues of $85,000 per year for five years. The machine would be depreciated using the straight-line method over a five-year life and have no salvage value. The company considers the impact of income taxes in all of its capital investment decisions. The company has a 40 percent income tax rate and desires an after-tax rate of return of 12 percent on its investment Compute the net present value of the machine.

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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

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