A. A new operating system for an existing machine is expected to cost $616,000 and have a useful life of six years. The system yields an incremental after-tax income of $180,000 each year after deducting its straight-line depreciation. The predicted salvage value of the system is $40,000. b. b. A machine costs $440,000, has a $32,000 salvage value, is expected to last eight years, and will generate an after-tax income of $90,000 per year after straight-line depreciation. Assume the company requires a 12% rate of return on its investments.

Required:
Compute the net present value of each potential investment.

a. Net present value = $539,013.67

b. Net present value = $273,361.47

Explanation:

a. A new operating system for an existing machine is expected to cost $616,000 and have a useful life of six years. The system yields an incremental after-tax income of $180,000 each year after deducting its straight-line depreciation. The predicted salvage value of the system is $40,000.

Annual depreciation = (Expected machine cost – Predicted salvage value) / Number of useful life = ($616,000 - $40,000) / 6 = $96,000

Annual cash inflows = Annual incremental after-tax income + annual depreciation = $180,000 + $96,000 = $276,000

Present value of the annual cash inflow = Annual cash inflows * ((1 - [1 / (1 + required rate of return)]^Number of years) / required rate of return) = $276,000 * ((1 - [1 / (1 + 0.12)]^6) / 0.12) = $276,000 * 4.11140732352233 = $1,134,748.42

Present value of predicted salvage value = Predicted salvage value / (1 + required rate of return)^Number of years = $40,000 / (1 + 0.12)^6 =  $20,265.24

Net present value = Present value of the annual cash inflow + Present value of predicted salvage value - Expected machine cost) = $1,134,748.42 + $20,265.24 - $616,000 = $539,013.67

b. A machine costs $440,000, has a $32,000 salvage value, is expected to last eight years, and will generate an after-tax income of $90,000 per year after straight-line depreciation.

Annual depreciation = (Machine cost – Salvage value) / Number of useful life = ($440,000 - $32,000) / 8 = $51,000

Annual cash inflows = Annual incremental after-tax income + annual depreciation = $90,000 + $51,000 = $141,000

Present value of the annual cash inflow = Annual cash inflows * ((1 - [1 / (1 + required rate of return)]^Number of years) / required rate of return) = $141,000 * ((1 - [1 / (1 + 0.12)]^8) / 0.12) = $141,000 * 4.96763976683859 = $700,437.21

Present value of salvage value = Salvage value / (1 + required rate of return)^Number of years = $32,000 / (1 + 0.12)^8 = $12,924.26

Net present value = Present value of the annual cash inflow + Present value of salvage value - Machine cost) = $700,437.21 + $12,924.26 - $440,000 = $273,361.47