“ClearWater, a nonprofit organization, is considering purchasing a water treatment system for $250,000 that will produce uniform after-tax cash inflows of $90,000 for five years. The system has an expected useful life of five years and an after-tax residual value of $25,000. ClearWater uses straight-line depreciation and has a 30% tax rate. ClearWater evaluates capital projects using discounted cash flows at a cost of capital of 12 percent per year. Based on the following table, what is the net present value of the water treatment system?”

Future value of $1 for 5 years at 12%: 1.762 Present value of $1 for 5 years at 12%: 0.567 Future value of $1 ordinary annuity for 5 years at 12%: 6.353 Present value of $1 ordinary annuity for 5 years at 12%: 3.605

To calculate the net present value (NPV), we need to consider the uniform cash inflows of $90,000, the depreciation tax shield (depreciation expense X tax rate), and the present value of the residual value ($25,000).

Depreciation expense per year = (Initial cost – Residual value) / Useful life = ($250,000 – $25,000) / 5 = $45,000

Depreciation tax shield per year = Depreciation expense per year X Tax rate = $45,000 X 0.30 = $13,500

Total annual cash inflows = Uniform cash inflows + Depreciation tax shield = $90,000 + $13,500 = $103,500

Present value of total annual cash inflows = Total annual cash inflows X Present value of $1 ordinary annuity for 5 years at 12% = $103,500 X 3.605 = $373,167.50

Present value of residual value = Residual value X Present value of $1 for 5 years at 12% = $25,000 X 0.567 = $14,175

NPV = Present value of total annual cash inflows + Present value of residual value – Initial cost = $373,167.50 + $14,175 – $250,000 = $387,342.50 – $250,000 = $137,342.50

Since all of the cash amounts were given as post-tax, then we didn’t have to subtract the taxes from the present value of the cash inflows.