Math Problem Statement

A new project will generate annual revenue of $310,000 and will entail operating expenses of $140,000. The annual depreciation and amortisation for the assets used in the project will equal $50,000. An annual capital expenditure of $10,000 will be required to offset wear and tear on the assets used in the project but no additions to working capital will be required. The company tax rate will be 35 percent. What is the incremental annual free cash flow for the project?

Solution

To determine the incremental annual free cash flow (FCF) for the project, we need to follow these steps:

  1. Calculate the Earnings Before Interest and Taxes (EBIT): EBIT=RevenueOperating ExpensesDepreciation and Amortisation\text{EBIT} = \text{Revenue} - \text{Operating Expenses} - \text{Depreciation and Amortisation}

  2. Calculate the Net Income: Net Income=EBIT×(1Tax Rate)\text{Net Income} = \text{EBIT} \times (1 - \text{Tax Rate})

  3. Calculate the Incremental Annual Free Cash Flow (FCF): FCF=Net Income+Depreciation and AmortisationCapital Expenditure\text{FCF} = \text{Net Income} + \text{Depreciation and Amortisation} - \text{Capital Expenditure}

Now, let’s plug in the numbers:

  1. Revenue: $310,000
  2. Operating Expenses: $140,000
  3. Depreciation and Amortisation: $50,000
  4. Capital Expenditure: $10,000
  5. Tax Rate: 35%

Step-by-Step Calculation:

  1. EBIT: EBIT=310,000140,00050,000=120,000\text{EBIT} = 310,000 - 140,000 - 50,000 = 120,000

  2. Net Income: Net Income=120,000×(10.35)=120,000×0.65=78,000\text{Net Income} = 120,000 \times (1 - 0.35) = 120,000 \times 0.65 = 78,000

  3. Free Cash Flow: FCF=78,000+50,00010,000=118,000\text{FCF} = 78,000 + 50,000 - 10,000 = 118,000

So, the incremental annual free cash flow for the project is $118,000.

Would you like any additional details or explanations? Here are some related questions:

  1. How would changes in the tax rate affect the FCF?
  2. What is the impact of increasing capital expenditure on the project’s cash flow?
  3. How would variations in operating expenses influence the overall FCF?
  4. Can FCF be negative, and what does that indicate about a project?
  5. What is the significance of including depreciation and amortization in cash flow calculations?

Tip: Understanding Free Cash Flow is crucial for evaluating the profitability and financial health of a project, as it shows the cash available to investors after accounting for capital expenditures.

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Math Problem Analysis

Mathematical Concepts

Free Cash Flow (FCF)
Tax Calculations
Depreciation and Amortization
Capital Expenditure

Formulas

EBIT = Revenue - Operating Expenses - Depreciation and Amortisation
Net Income = EBIT × (1 - Tax Rate)
FCF = Net Income + Depreciation and Amortisation - Capital Expenditure

Theorems

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Suitable Grade Level

Undergraduate - Finance or Business