A corporation has a new line of guitars that will generate sales of $380,000 per year. The variable cost rate for guitars amounts to 35.0% of revenue, while fixed costs are $110,000 per year. The capital investment for the factory was $800,000, depreciated straight line over 15 years. If the tax rate is 22.0%, what is the annual operating cash flow for this project?

Question

A corporation has a new line of guitars that will generate sales of $380,000 per year. The variable cost rate for guitars amounts to 35.0% of revenue, while fixed costs are $110,000 per year. The capital investment for the factory was $800,000, depreciated straight line over 15 years. If the tax rate is 22.0%, what is the annual operating cash flow for this project?

BlackTom AI · Accepted Answer

First, lay out the given data clearly: annual sales (revenue) = $380,000; variable cost rate = 35% of revenue; fixed costs = $110,000 per year; initial capital investment = $800,000 with straight‑line depreciation over 15 years; tax rate = 22%.
Next, compute the expenses that affect operating income: variable costs = 0.35 × 380,000 = $133,000. Subtracting variable costs from revenue leaves contribution before fixed costs: 380,000 − 133,000 = 247,000.
Then account for fixed costs: 247,000 − 110,000 = 137,000. This is the operating income before depreciation (often called EBIT before depreciation or operating contribution minus fixed costs). Now apply depreciation: annual depreciation = 800,000 / 15 = $53,333.33. Subtracting depreciation from the amount above gives EBIT (earnings before interest and taxes) = 137,000 − 53,333.33 = 83,666.67.
Compute taxes on EBIT: tax = 0.22 × 83,666.67 = 18,426.67. Therefore after-tax operating income (net income from operations) = 83,666.67 − 18,426.67 = 65,240.00.
Finally, determine operating cash flow (OCF): OCF = after-tax operating income + noncash depreciation back to cash = 65,240.00 + 53,333.33 = 118,573.33.
Now compare this result to each answer option:
- Option A: $127,860. This value is higher than the computed OCF. The discrepancy could come from using a different depreciation treatment or a miscalculation in taxes or margins, but with the given numbers the EBIT and tax flow do not align to this figure.
- Option B: $167,860. This is substantially larger than the computed OCF, implying much higher after-tax cash generation than allowed by the revenue, costs, depreciation, and tax inputs provided. It does not fit the arithmetic from the data.
- Option C: $81,060. This is closer to the after-tax portion before adding back depreciation, but omits depreciation, or treats it differently, and does not match the standard OCF formula when using the provided depreciation amount.
- Option D: $142,300. This is again inconsistent with the detailed stepwise calculation; it would require a different depreciation or tax treatment than the data indicates.
- Option E: None of the answer options here is correct. This would be the accurate choice if none of the numerical values above match the computed OCF exactly.
In summary, following the conventional approach for project OCF with straight-line depreciation, the calculated value is 118,573.33, which does not coincide with any of the specific dollar amounts listed in options A through D. The remaining option E reflects that mismatch.

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