Math Problem Statement

A 3-year project requires the purchase of a machine (fixed asset) for $6,000 in Year 0. In Year 2, the project is expected to have net income of $2,500 and the depreciation rate is 45%. The tax rate is 35%. There is no interest expense.

What is the Operating Cash Flow in Year 2?

Solution

To calculate the Operating Cash Flow (OCF) in Year 2, we use the following formula:

OCF=Net Income+DepreciationChanges in Working Capital\text{OCF} = \text{Net Income} + \text{Depreciation} - \text{Changes in Working Capital}

Since there's no mention of changes in working capital, we'll assume it to be zero.

Step 1: Depreciation

The depreciation is based on the machine’s cost of $6,000 and a depreciation rate of 45%. Since the project spans 3 years, we assume straight-line depreciation is being applied (as depreciation rate is not specified per year).

For Year 2, the depreciation expense would be:

Depreciation=6,000×45%=2,700\text{Depreciation} = 6,000 \times 45\% = 2,700

Step 2: Net Income

The net income in Year 2 is provided as $2,500.

Step 3: Tax Adjustment

Operating Cash Flow (OCF) involves adding back depreciation because it's a non-cash expense. Also, we need to adjust for taxes, so we need to calculate the tax impact on net income.

Since the tax rate is 35%, the net income already reflects tax effects. So, we simply add the depreciation back to get the operating cash flow.

Step 4: Calculation

Now, let’s calculate the Operating Cash Flow:

OCF=Net Income+Depreciation\text{OCF} = \text{Net Income} + \text{Depreciation} OCF=2,500+2,700=5,200\text{OCF} = 2,500 + 2,700 = 5,200

Conclusion:

The Operating Cash Flow in Year 2 is $5,200.


Would you like more details on any step? Feel free to ask.

Here are 5 related questions for further exploration:

  1. How do depreciation methods impact cash flow calculations?
  2. What is the effect of a change in tax rate on operating cash flow?
  3. How would changes in working capital affect the operating cash flow?
  4. What is the role of net income in calculating cash flow?
  5. How does the depreciation rate impact tax savings?

Tip: Always verify if there are any changes in working capital when calculating OCF, as they can significantly impact the result!

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Math Problem Analysis

Mathematical Concepts

Operating Cash Flow
Depreciation
Tax Adjustments

Formulas

OCF = Net Income + Depreciation - Changes in Working Capital
Depreciation = Asset Cost × Depreciation Rate

Theorems

Operating Cash Flow Calculation
Tax Adjustment on Net Income

Suitable Grade Level

Grades 11-12