your company purchased equipment for 50000 that will reduce materials and labor

Question

your company purchased equipment for 50000 that will reduce materials and labor costs by 14000 each year for n years. after n years, there will be no further need for the machine, and because the machine is specially designed, it will have no mv at any time. the irs, however has ruled that you must depreciate the equipment on a sl basis with a tax life of five years. if the effective income tax rate is 40%, what is the minimum number of years your firm must operate the equipment to earn 10% per year after taxes on its investment?

Explanation / Answer

Depreciation = 50,000/ 5 = $ 10,000 / year

so for first five years Cash flows = 4000*0.6 + 10000 = $ 12400

After five years cash flow = 14000*0.6 = $8400

so

50,000 = 12,400/1.1 + 12,400/1.1^2+ 12400/1.1^3 + 12400/1.1^4 + 12400/1.1^5 + 8400/1.1^6 +.....uptil n years

50,000 = 3.79*12400 +  8400/1.1^6 +.....uptil n years

50,000 = 47005.756 +8400/1.1^6 +.....uptil n years

2994.25 = 8400/1.1^6 +.....uptil n years

now 8400/1.1^6 = 4741.58 > 2994.25

so we will recover investment in the sixth year.

So minimum no of years = 6 years

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