Math Problem Statement

Marsha owns a manufacturing business that had sales of $2,000,000 last year. Its operating costs were $600,000 (excluding depreciation). The business has equipment that they bought for a total of $1,500,000 five years ago. The equipment is being depreciated straight-line to zero over 10 years. If the tax rate is 25%, what were the company's operating cash flows (OCF) last year?

Solution

To determine the Operating Cash Flows (OCF) for Marsha's business, we follow these steps:


1. Calculate Depreciation Expense:

The equipment cost is $1,500,000, and it is depreciated straight-line to zero over 10 years.

Depreciation Expense=Equipment CostUseful Life\text{Depreciation Expense} = \frac{\text{Equipment Cost}}{\text{Useful Life}} Depreciation Expense=1,500,00010=150,000\text{Depreciation Expense} = \frac{1,500,000}{10} = 150,000


2. Calculate Operating Income (EBIT):

Operating income is calculated as: EBIT=SalesOperating CostsDepreciation\text{EBIT} = \text{Sales} - \text{Operating Costs} - \text{Depreciation} EBIT=2,000,000600,000150,000=1,250,000\text{EBIT} = 2,000,000 - 600,000 - 150,000 = 1,250,000


3. Calculate Taxes:

Taxes are calculated on the EBIT: Taxes=EBIT×Tax Rate\text{Taxes} = \text{EBIT} \times \text{Tax Rate} Taxes=1,250,000×0.25=312,500\text{Taxes} = 1,250,000 \times 0.25 = 312,500


4. Net Income:

Net income is: Net Income=EBITTaxes\text{Net Income} = \text{EBIT} - \text{Taxes} Net Income=1,250,000312,500=937,500\text{Net Income} = 1,250,000 - 312,500 = 937,500


5. Add Back Depreciation to Compute OCF:

Operating cash flow is net income plus non-cash expenses (depreciation in this case): OCF=Net Income+Depreciation\text{OCF} = \text{Net Income} + \text{Depreciation} OCF=937,500+150,000=1,087,500\text{OCF} = 937,500 + 150,000 = 1,087,500


Final Answer:

The company's Operating Cash Flows (OCF) last year were $1,087,500.


Would you like a breakdown of any step?

Further Exploration:

  1. What are the implications of higher depreciation on cash flows?
  2. How would OCF change if the tax rate were reduced?
  3. What if the equipment was depreciated over 15 years instead?
  4. How does straight-line depreciation compare to accelerated depreciation in cash flow impact?
  5. Why is depreciation added back when calculating cash flow?

Tip: Always add back non-cash expenses (like depreciation) to EBIT when calculating cash flows, as they do not affect actual cash movement.

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Math Problem Analysis

Mathematical Concepts

Depreciation
Operating Income (EBIT)
Taxation
Net Income
Operating Cash Flow

Formulas

Depreciation Expense = Equipment Cost / Useful Life
EBIT = Sales - Operating Costs - Depreciation
Taxes = EBIT × Tax Rate
Net Income = EBIT - Taxes
OCF = Net Income + Depreciation

Theorems

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Suitable Grade Level

College/University (Business/Finance students)