Residual Income applications

Say you’re valuing a company and have 5 years of historical data and the current book value at the end of the five years is $2 million. Say you then look at what net income was the prior 5 years and apply an equity charge to each year to actually see what RI was and find out that RI each year was negative (implying ROE

Silly question, but why can’t a company grow even if it pays out 100% of earnings as dividends (therefore g=b x ROE = 0 bc nothing is being retained)? Why can’t earnings grow in that case ?

Say i wanted to come in and acquire fool control of this company, can i not include growth in my projections (thus assuming a different dividend policy then the prior regime) and therefore come up with a significantly higher equity value then an analyst who assumes no growth??

Just trying to run through different scenarios in my head, would appreciate anyones help. Thanks!!

If we assume a RoE, if all earnings are paid out, then next year’s earnings will be the same as this year’s earnings, at the given level of RoE (ie, there was no growth in earnings). You need last year’s earnings to compound to increase earnings for this year. If you don’t, then earnings can’t grow.

In the real world, you can grow a business that pays out all its earnings by some combination of 1) increasing sales, or 2) decreasing expenses. This has the effect or increasing gross/net profits, and thus earnings. In practice, a firm’s RoE isn’t the same from year-to-year, and thus can grow, even if it doesn’t retain any earnings.

I guess to the books point, that’s why they refer to it as SUSTAINABLE growth rate. Your point highlighted what i was thinking, bc growing sales/cutting costs can just as easily result in higher earnings than the prior year (ie growth) with out having had to retain any prior earnings to accomplish that growth. However, your sales will reach capacity at some point and you can only cut costs so much, so in order to grow there must be some reinvestment to build on. Same goes with raising equity and debt financing, no? While they can provide for growth in the short-term, you can’t continue to raise more and mroe debt and equity each year, it’s not sustainable.

Any one have thoughts on the first scenario?


Increasing sales, all else equal, increases earnings. Sure, that’s correct.

Assets = Liabilities + Equity

Every asset must be financed by an obligation or an ownership stake.

Sales increase, costs stay the same, earnings increase. Those earnings must either be retained or distributed.

If retained, equity increases, and assets increase by the same amount. The company has grown.

If distributed, equity does not increase, and so assets may not increase. The company cannot possibly grow if all earnings are distributed.

Sales are not tangible. They do not indicate a large or a small company. Assets do.

I see and agree with your general point, but i think it’s just a different way of thinking about growth, it is a vague term afterall. My impression was that, as discussed in the text, we’re talking about earnings growth. And growth occurs based on two inputs, ROE and the retention rate (b). Using this to determine growth, if all is paid out (ie b=o) then growth must equal zero (0=ROE x 0). However, in the short-term, even if all is paid out, earnings could still grow if either (i) sales increased (ii) costs are cut or (iii) both. So the g = ROE x b doesn’t necessarily hold all the time, that’s why it’s mainly applicable for sustainable growth and thus used in GGM.

To your point though, you say that a company cannot grow if all earnings are distributed, but what if it raises equity capital?? Assets/equity increase and thus the size of the company grows while earnings (at least prior to investment) have otherwise stayed the same.