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Simplified operating cash flow and a depreciation tax shield

When the stated deduction and immediate tax-use assumptions hold, cash margin after tax plus the modeled shield reconciles to operating cash flow.

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State the hypothetical tax model

Let receipts less operating cash costs be M, deductible depreciation D, and a constant tax fraction tau. Assume all deductions affect cash tax immediately at that rate. This is an educational model, not a statement about a jurisdiction’s tax rules or loss utilization.

Reconcile the two expressions

OCF=(M−D)(1−τ)+D=M(1−τ)+DτOCF=(M-D)(1-\tau)+D=M(1-\tau)+D\tau

The first form adds the noncash depreciation charge back to after-tax operating earnings; the second isolates the assumed tax effect.

Calculate a fictional period

With M = 200, D = 100 and tau = 25%, operating earnings after tax are 75. Adding back 100 gives cash flow 175. Equivalently, 200 × 0.75 + 100 × 0.25 = 175.

Separate the algebra from actual cash-tax timing

If deductions cannot be used now, the immediate shield assumption is not valid. Financial-report depreciation and tax deductions can also differ. Keep asset outlays and working-capital movements outside this operating identity until added at their own dates.

Further references