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18 January, 12:34

Compute the payback period for each of these two separate investments:

(a) A new operating system for an existing machine is expected to cost $260,000 and have a useful life of four years. The system yields an incremental after-tax income of $75,000 each year after deducting its straight-line depreciation. The predicted salvage value of the system is $10,000.

(b) A machine costs $170,000, has a $14,000 salvage value, is expected to last nine years, and will generate an after-tax income of $41,000 per year after straight-line depreciation.

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  1. 18 January, 12:51
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    1.89 years and 2.91 years

    Explanation:

    The formula to compute the payback period is shown below:

    = Initial investment : Net cash flow

    For first case

    The initial investment is $260,000

    And, the net cash flow is shown below:

    = Depreciation + incremental after tax income

    where,

    Depreciation equals to

    = (Original cost - residual value) : (useful life)

    = ($260,000 - $10,000) : (4 years)

    = ($20,000) : (4 years)

    = $62,500

    And the incremental after tax income is $75,000

    So, the net cash flow would equal to

    = $62,500 + $75,000

    = $137,500

    So, the payback period would be

    = $260,000 : $137,500

    = 1.89 years

    For second case

    The initial investment is $170,000

    And, the net cash flow is shown below:

    = Depreciation + incremental after tax income

    where,

    Depreciation equals to

    = (Original cost - residual value) : (useful life)

    = ($170,000 - $14,000) : (9 years)

    = ($156,000) : (9 years)

    = $17,333

    And the incremental after tax income is $41,000

    So, the net cash flow would equal to

    = $17,333 + $41,000

    = $58,333

    So, the payback period would be

    = $170,000 : $58,333

    = 2.91 years
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