What is the undiscounted cash flow in the final year of an investment, assuming $10,000 after-tax cash flows from operations, $1,000 from the sale of a fully depreciated machine, $2,000 initial requirement for additional working capital, and a 40% tax rate?[Fill in the blank]

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BlackTom AI · Accepted Answer

To solve this, we need to sum all the cash flows that occur in the final year of the project. Start by identifying each component:

Option analysis begins with the operating cash flow: the problem states $10,000 of after-tax cash flows from operations in the final year. Since this is after-tax cash flow, no further tax adjustments are needed for this component.

Next, consider the sale of the machine: the asset is fully depreciated, so its book value is $0. The sale price is $1,000, which creates a taxable gain of $1,000. With a 40% tax rate, tax on the gain is 0.40 × 1,000 = $400. Therefore, the after-tax cash inflow from the sale is $1,000 − $400 = $600.

Then, account for the working capital change: there is an initial requirement of $2,000 for additional working capital. In the final year, this working capital is recovered, producing a inflow of $2,000.

Now combine all pieces for the final-year undiscounted cash flow:
- Operating cash flow (after tax): $10,000
- After-tax proceeds from sale of asset: $600
- Recovery of additional working capital: $2,000
Sum: 10,000 + 600 + 2,000 = 12,600.

Why the other options are incorrect:
- Option a ($13,000): This would imply either not accounting for taxes on the sale, or adding the full $1,000 sale price without tax effect. Since tax on the $1,000 gain is due, the correct after-tax sale amount is $600, not $1,000.
- Option b ($12,400): This might reflect incorrectly applying tax, such as subtracting tax from the operating cash flow or miscounting the recovery of working capital. The after-tax operating cash flow is given as $10,000, and the correct after-tax sale is $600, so $12,400 would miss the $2,000 working-capital recovery.
- Option d ($9,000): This would ignore the $600 after-tax sale proceeds and the $2,000 working-capital recovery, focusing only on the operating cash flow, which is incomplete.

In summary, aggregating $10,000 from operations, $600 from the after-tax sale, and $2,000 from working-capital recovery yields the correct undiscounted final-year cash flow of $12,600.

What is the undiscounted cash flow in the final year of an investment, assuming $10,000 after-tax cash flows from operations, $1,000 from the sale of a fully depreciated machine, $2,000 initial requirement for additional working capital, and a 40% tax rate?[Fill in the blank]

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