When fully consistent assumptions are used to forecast earnings, cash flow, dividends, book value, and residual income through a full set of pro forma (projected) financial statements, and the same required rate of return on equity is used as the discount rate, the same estimate of value should result from a residual income, dividend discount, or free cash flow valuation. In practice, however, analysts may find one model easier to apply and possibly arrive at different valuations using the different models.
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Anthony, nice setup! To your question about the rental mortgages, you haven’t said what interest rate you are paying. As a start, if you are paying more than the risk free rate (Treasury bills) which you probably are, then a true apples to apples comparison would be yes, pay off the mortgage. But, if you are comfortable taking more risk, you have other options to invest in which you *hope* will yield you more over the coming years. You also didn’t say whether the rentals generate net income and if so, how much? What is the implied rate of return on the equity you have invested in them? If you pay the mortgages off, you’ll have even more equity tied up, will the extra net income make that worthwhile? Maybe you should use the money to buy more rentals instead, if purchase opportunities still exist in your town. … this is less of an answer than a framework to analyze the decision, hope it is helpful.
I guess I just don’t understand why the specific importance of focusing on “dividends” instead of focusing on the total return of your investment, including stock appreciation. I don’t really care if a company decides to issue a dividend or not; presumably, if they don’t issue a dividend, then they’re doing other things to increase the value of the company, which will be reflected in the stock price of the company. As an investor, I can make money by selling a percentage of my holdings or collecting dividends, and I don’t really care how that’s divided up – it’s an artificial distinction.

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Residual income is the amount of net income generated in excess of the minimum rate of return. Residual income concepts have been used in a number of contexts, including as a measurement of internal corporate performance whereby a company's management team evaluates the return generated relative to the company's minimum required return. Alternatively, in personal finance, residual income is the level of income that an individual has after the deduction of all personal debts and expenses have been paid.