Depreciation tax saving with increasing inflation

From CFAI book:

“Inflation reduces the value of depreciation tax savings (unless the tax system adjusts depreciation for inflation). The effect of expected inflation is captured in the discounted cash flow analysis. If inflation is higher than expected, the profitability of the investment is correspondingly lower than expected.”

Can somebody plz show numerically how inflation reduces value of depreciation tax saving??

Suppose that your annual depreciation is straight-line: $2,000,000 per year.

In year 2, prices are costs are up by 5% because of inflation, but your depreciation expense is still $2,000,000. So everything else on your income statement increased by 5%, but your depreciation expense did not. Therefore, it’s (relatively) less valuable.

Here’s a simple example showing three scenarios:

  1. No inflation (i.e., inflation index of 100)

  2. Yes inflation + depreciation is NOT adjusted by inflation

  3. Yes inflation + depreciation IS adjusted by inflation

As you can see, when we look at cash flow after stripping the effect of inflation, we see that cash flow is lower in Case 2 (red-highlighted cell) as compared to Case 1 (blue cell) due to the fact that our depreciation tax shield does not keep pace with inflation.

In Case 3 (green cell), we see that cash flow in real terms is identical to Case 1 (blue cell).

Hope this helps.