Valuation: Measuring and Managing the Value of Companies, Fifth Edition

APPENDIX B

Discounted Economic Profit Equals Discounted Free Cash Flow

In this appendix, we provide a generalized proof of the equivalence between discounted cash flow and discounted economic profit. A less technical but specialized proof of equivalence is demonstrated using the key value driver formula in Appendix A.

To prove equivalence, start by computing the present value of a periodic stream of cash flow:

where

V = value of operations FCF_t = free cash flow in year t WACC = weighted average cost of capital

To this value, add and subtract the cumulative sum of all current and future amounts of invested capital (IC):

where IC_t = invested capital for year t

Next, adjust the preceding equation slightly to restate the same value using terms that can be canceled later. First, strip invested capital at time zero from the first cumulative sum. Then modify the second cumulative sum to t = 1 to infinity, changing each t inside the second cumulative sum to t - 1. This new representation is identical to the original representation but will allow us to cancel terms later. The new representation is as follows:

Multiply the second cumulative sum by (1 + WACC)/(1 + WACC). This action converts ...