Valuation Approach Equivalence.
Conceptually, why should you expect a valuation based on dividends, a valuation based on the free cash flows for common equity shareholders, and a valuation based on residual income to yield equivalent value estimates for a given firm?
The earning-based valuation is a straightforward method which focuses on earnings by firms and the capital markets. All the people including board members, managers etc, are focusing on forecast data and reports. The performance of the firm is aligned more closely through earnings rather than dividends or free cash flows.
The free cash flow for common equity shareholders is the amount of cash which is generated by the firm. The value of the firm is determined by realizing it in cash flows. The residual income is used to help figure out the creditworthiness of a potential borrower. This amount of cash is available to be potentially distributed to shareholders.
It can be inferred that all the techniques are deployed to the value of the same company based on certain variables. In all these techniques, the same variables are used that affect the price of the stock. These variables include cash flows, sales, book value and so on. The only difference is the approach towards valuation.
The three mentioned valuation techniques should provide the same value estimates as the variables used in the valuation techniques are the same. There is only a difference in the perspective of valuation.