Business Context

FinSight Analytics supports a public SaaS company that is evaluating whether a revised fixed-asset policy materially changes reported profitability. Finance wants a statistically grounded estimate of how a higher depreciation expense flows through net income and cash flow.

Problem Statement

Treat the accounting effect of a depreciation increase as a deterministic relationship with uncertainty coming from the firm's effective tax rate. You are given a sample of historical quarterly effective tax rates and asked to estimate the expected impact of a $10 increase in depreciation on the income statement, cash flow statement, and balance sheet.

Given Data

A $10 increase in depreciation is recorded in the current quarter.

Assume no change in revenue, capex, working capital, debt, or dividends during the quarter.

Requirements

1. Estimate the expected after-tax reduction in net income from the $10 depreciation increase.
2. Construct a 95% confidence interval for the after-tax net income impact using the sampled tax-rate uncertainty.
3. Show how the same $10 change affects cash from operations, ending cash, and PP&E / retained earnings.
4. State whether the cash impact is statistically distinguishable from zero.
5. Interpret the result in business terms: does higher depreciation hurt cash generation, or mainly reported earnings?

Assumptions

• Depreciation is a non-cash expense.
• The effective tax rate sample is approximately independent across quarters.
• The sample size is small, so use a t-distribution for inference on the mean tax rate.
• Taxes are paid in the same period and the tax shield equals depreciation multiplied by the effective tax rate.