Math Problem Statement

Pink Industrial is evaluating a 4-year project that would require an initial investment in equipment of $695,000. The equipment would be depreciated to $107,000 over 7 years using straight-line depreciation. In year 4, the project is expected to have relevant revenue of $336,000 and relevant variable costs of $249,000. In addition, Pink Industrial would have one source of fixed costs associated with the project. Yesterday, Pink Industrial signed a deal with Diamond Marketing to develop an advertising campaign for the project. The terms of the deal require Pink Industrial to pay $56,000 to Diamond Marketing in 4 years. The tax rate is 40 percent. What is the operating cash flow for year 4 that Pink Industrial should use in its NPV analysis of the project?

Input instructions: Round your answer to the nearest dollar.

Solution

To calculate the operating cash flow (OCF) for year 4, we'll follow these steps:

  1. Calculate Depreciation Expense:
    The equipment is depreciated from an initial value of $695,000 to $107,000 over 7 years using straight-line depreciation.
    Depreciation per year=Initial CostSalvage ValueDepreciation Period\text{Depreciation per year} = \frac{\text{Initial Cost} - \text{Salvage Value}}{\text{Depreciation Period}} =695,000107,0007=84,000= \frac{695,000 - 107,000}{7} = 84,000

  2. Calculate Earnings Before Interest and Taxes (EBIT) for Year 4:

    • Revenue for Year 4: $336,000
    • Variable Costs for Year 4: $249,000
    • Depreciation Expense: $84,000

    EBIT=RevenueVariable CostsDepreciation\text{EBIT} = \text{Revenue} - \text{Variable Costs} - \text{Depreciation} =336,000249,00084,000=3,000= 336,000 - 249,000 - 84,000 = 3,000

  3. Calculate Taxes:
    The tax rate is 40%, so: Taxes=EBIT×Tax Rate=3,000×0.40=1,200\text{Taxes} = \text{EBIT} \times \text{Tax Rate} = 3,000 \times 0.40 = 1,200

  4. Calculate Net Income:
    Net Income=EBITTaxes=3,0001,200=1,800\text{Net Income} = \text{EBIT} - \text{Taxes} = 3,000 - 1,200 = 1,800

  5. Calculate Operating Cash Flow (OCF) for Year 4:
    OCF is given by: OCF=Net Income+Depreciation\text{OCF} = \text{Net Income} + \text{Depreciation} =1,800+84,000=85,800= 1,800 + 84,000 = 85,800

Thus, the operating cash flow for year 4 that Pink Industrial should use in its NPV analysis is $85,800.

Would you like more details or have questions on any part of this solution?

Here are some further questions you might consider:

  1. How would changing the depreciation method impact the OCF calculation?
  2. What would be the effect of a different tax rate on the operating cash flow?
  3. How would the OCF change if the project’s revenue or variable costs differed?
  4. How does straight-line depreciation differ from other depreciation methods?
  5. What role does the fixed cost play in this NPV analysis?

Tip: Always separate variable and fixed costs in project evaluations to clarify their impact on net income and cash flow.

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Math Problem Analysis

Mathematical Concepts

Depreciation
Operating Cash Flow
Net Income
Taxes
NPV Analysis

Formulas

Depreciation per year = (Initial Cost - Salvage Value) / Depreciation Period
EBIT = Revenue - Variable Costs - Depreciation
Taxes = EBIT × Tax Rate
Net Income = EBIT - Taxes
Operating Cash Flow = Net Income + Depreciation

Theorems

Straight-Line Depreciation
Tax Impact on Cash Flow

Suitable Grade Level

Grades 11-12