Question

Oxygen Optimization is considering buying a new purification system. The new system would be purchased today for 18,400 dollars. It would be depreciated straight-line to 1,000 dollars over 2 years. In 2 years, the system would be sold and the after-tax cash flow from capital spending in year 2 would be 1,900 dollars. The system is expected to reduce costs by 6,700 dollars in year 1 and by 14,800 dollars in year 2. If the tax rate is 50 percent and the cost of capital is 9.06 percent, what is the net present value of the new purification system project?

Answer 1

Cost of New Machine = 18,400  

Salvage Value = 1,000

Usefule Life = 02 Years

Depreciation each Year = ( Cost of New Machine - Salvage Value ) / Usefule Life

   = ( 18,400 - 1,000) / 02 = 8,700

Tax Saving Due to Depreciation each year = Depreciation * Tax Rate = 8,700 * 50% = 4,350

After-Tax Savings in Cost = Savings in Cost Each Year * Tax Rate

For Year 01 :

After-Tax Savings in Cost = 6,700 * 50% = 3,350

For Year 02 :

After-Tax Savings in Cost = 14,800 * 50% = 7,400

Cash Flow in Year 0 :

CF0 = - Initial Investment in Machine = -18,400

Cash Flow in Year 1 :

CF1 = After-Tax Savings in Cost +  Tax Saving Due to Depreciation each year = 3350 + 4350 = 7,700

Cash Flow in Year 2 :

CF2 = After-Tax Savings in Cost +  Tax Saving Due to Depreciation each year + after-tax cash flow from capital spending in year 2  

= 7,400 +  4,350 + 1,900 = 13,650

Now Net Present Value of the Project will be

Here r =  cost of capita = 9.06% = 0.0906

= - 18,400 + 7060.33 + 11,363.48

= 23.81

~24

the net present value of the new purification system project is $ 24