In order to think about how returns impact on valuation, we need to understand the link between dividends, returns, and growth rates. Let's start by using our base calculation to remind ourselves how dividends link to changes in shareholders' equity and net income. So we know that opening shareholders' equity plus net income less dividends equals closing shareholders' equity. So if we have opening shareholders' equity, net income, and closing shareholders' equity, this can tell us the implied dividends. In this example, if we know that net income equals 200, opening shareholders' equity equals 1,000, and closing shareholders equity equals 1,060, we'll calculate that dividends are equal to 140. So dividends are equal to opening shareholders' equity plus net income, minus closing shareholders' equity, which is the same as being equal to net income less the increase in shareholder's equity. But what if we only know that net income is equal to 200? Return on equity is equal to 20%, and growth is equal to 6%. Is the information sufficient to imply what dividends are paid? Let's look at return on equity first. Remember, the return on equity is net income divided by opening shareholder's equity. So if we know return on equity and net income, we can calculate the opening shareholder's equity. In the example given, we know the return on equity is 20%, and net income is 200. Therefore, opening shareholder's equity must be 1,000. Now let's look at growth. The equity growth rate is calculated by taking the increase in shareholder's equity of 60, and dividing it by the opening shareholder's equity of 1,000. Rearranging this formula, we can see that the increase in shareholder's equity is equal to growth multiplied by opening shareholder's equity. In the example given, if we are told that growth equals 6%, and since we know that opening shareholder's equity is 1,000, we can establish that the increase in shareholder's equity must be 60. So we have now shown that using net income and return on equity, we can calculate opening shareholders' equity. And using growth, we can use this calculation to calculate the change in shareholders' equity. This should mean that we have all the ingredients for calculating dividends. Remember, from our base analysis, that dividends is equal to net income less the increase in shareholders' equity. Or we could say that dividends equals net income, minus growth multiplied by shareholders' equity. If we consider the return on equity is equal to net income divided by opening shareholders' equity, the inverse of this is one over return on equity, which is equal to opening shareholders' equity divided by net income. As a consequence, we could say that dividends equals net income multiplied by one minus growth, over return on equity. In our example, the dividends of 140 would be equal to 200 multiplied by one minus 6% over 20%. If we pop dividends back into our Gordon growth model, we now have equity value equals net income multiplied by one minus growth, divided by return on equity, all over the cost of equity minus growth. By dividing throughout by net income, we get the formula for PE. Or by dividing throughout by book value, we get the formula for price to book.
