Rock Haven has a proposed project that will generate sales of 1,740 units annually at a selling price of $24 each. The fixed costs are $13,900 and the variable costs per unit are $6.75. The project requires $29,200 of fixed assets that will be depreciated on a straight-line basis to a zero book value over the 4-year life of the project. The salvage value of the fixed assets is $7,300 and the tax rate is 21 percent. What is the operating cash flow?

Question

BlackTom AI · Accepted Answer

To evaluate the operating cash flow (OCF), start by laying out the given numbers and computing the key components.
1) Sales revenue: 1,740 units × $24 per unit = $41,760.
2) Variable costs: 1,740 units × $6.75 per unit = $11,745.
3) Contribution after variable costs: $41,760 − $11,745 = $30,015.
4) Fixed costs: $13,900.
5) Annual depreciation: $29,200 fixed assets ÷ 4 years = $7,300 per year (straight-line), reducing taxable income.
6) Earnings before tax (EBT) or EBIT in this setup is Sales − Variable − Fixed − Depreciation = $41,760 − $11,745 − $13,900 − $7,300 = $8,815.
7) Taxes: 21% of EBIT, so Taxes = 0.21 × $8,815 ≈ $1,851.15.
8) Net income: EBIT − Taxes = $8,815 − $1,851.15 ≈ $6,963.85.
9) Operating cash flow (OCF) is typically computed as Net income + Depreciation (since depreciation is a non-cash charge): $6,963.85 + $7,300 ≈ $14,263.85, which rounds to $14,264.

Now, evaluate each option against these calculations:
- Option A: $16,093. This would imply a higher OCF than our calculated NI + Depreciation, suggesting either a higher EBIT/taxes or additional cash items. If we worked backward, this would require either lower taxes on EBIT or higher non-cash additions to cash flow, neither of which align with the given numbers under standard OCF formulation.
- Option B: $21,349. Achieving this would require a substantial boost from tax shield or salvage-related adjustments within the year. Since salvage value is specified for the end of the project and is not included in annual OCF calculations, this value does not fit the standard OCF model here.
- Option C: $6,749. This is close to net income alone before adding back depreciation, which hints at omitting the non-cash depreciation add-back; however, OCF explicitly adds back depreciation, so this underestimates OCF.
- Option D: $9,366. This is noticeably lower than the computed NI + Depreciation; it would imply a much smaller net income or a smaller depreciation contribution, inconsistent with the data provided.
- Option E: $14,264. This matches the calculation NI + Depreciation: net income around $6,964 plus depreciation $7,300 equals about $14,264. Since OCF incorporates the tax effect on EBIT and adds back depreciation (a non-cash charge), this aligns with the standard approach for operating cash flow in a project with depreciation.

In summary, the only value that coherently arises from applying the typical OCF formula with the given sales, costs, depreciation, and tax rate is the one that equals approximately $14,264, which corresponds to the line of reasoning above and the arithmetic steps shown. The remaining options diverge from this calculation in ways such as overcounting taxes, omitting the depreciation add-back, or misapplying salvage considerations within annual OCF.

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