Compute the payback period for each of these two separate investments (round the payback period to two decimals): a. a new operating system for an existing machine is expected to cost $520,000 and have a useful life of six years. the system yields an incremental after-tax income of $150,000 each year after deducting its straight-line depreciation. the predicted salvage value of the system is $10,000.b. a machine costs $380,000, has a $20,000 salvage value, is expected to last eight years, and will generate an after-tax income of $60,000 per year after straight-line depreciation. nb: i need a detailed and well explained answer. full points would be awarded for a detailed and well explained answer

a. 2.21 years

b. 3.62 years

Explanation:

The payback period measures how long it takes for the amount invested in a project to be recovered from the cummulative cash flows.

To find the payback period of the machine, first we need to calculate the depreciation expense.

Straight line depreciation = ( Cost of asset - Salvage value) / useful life

Investment a's depreciation expense = ($520,000 - $10,000) / 6 = $85,000

Because depreciation is a non cash expense, it would be added back to cash flow = $85,00 + $150,000 = $235,000

Deprecation expense for investment b = ($380,000-$20,000) / 8 = $45,000

Because depreciation is a non cash expense, it would be added back to cash flow = $45,000 + $60,000 = $105,000

Explanations on how the payback periods were calculated can be found in the attached images.

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