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

d.nothing happens by chance.

When the tragic plot events of a Greek belief are connected in various relationships, it is usually due to the fact that the Greeks did not believe in things happening by chance. Instead, they believed that the gods influenced everything that happened in the world, including the private lives of people.