What is the formula for deflating a cash flow using an index?

The formula for deflating a cash flow using an index is designed to adjust future cash flows to their present value by taking into account the changes in the index, which usually reflects inflation or changes in purchasing power.

Using the option that is identified as correct, the rationale behind it is as follows: you take the cash flow amount from an earlier period and adjust it by the ratio of the index in that earlier period to the index in the later period. This helps account for how much purchasing power has changed over time due to inflation or other economic factors.

For instance, if you have a cash flow projected for a future year and you want to know its value in today's terms, you multiply the future cash flow by the index value from the earlier period, reflecting its value adjusted for inflation. This effectively deflates the cash flow to bring it into a common framework to make it relevant for present value analysis.

The other options do not align with the proper inflation adjustment mechanism. They may inaccurately represent the relationship between the indices or the cash flows in a way that does not effectively achieve the deflation to present values, hence not offering the correct approach to achieve the goal of the analysis.