# Appendix ADiscounted Economic Profit Equals Discounted Free Cash Flow

This appendix demonstrates algebraically the equivalence between discounted cash flow and discounted economic profit. In the first section, we convert the key value driver formula presented in Chapter 3 into a value driver formula based on economic profit. This formula is used in Chapter 10 to estimate continuing value in the economic-profit valuation. The second section of this appendix generalizes the proof to any set of cash flows.

## Proof Using Perpetuities

To convert the key value driver formula into an economic-profit-based formula, start with the growing cash flow perpetuity:

where

In Chapter 3, we convert the growing perpetuity into the key value driver formula:

where

The key value driver formula can be rearranged further into a formula based on economic profit. We do this to demonstrate that discounted cash flow is equivalent to the book value of invested capital plus the present value of future economic profit.

To begin, start with the key value driver formula, and replace NOPAT with invested ...

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