Fundamental Determinants of Residual Income

Assumptions can be an analyst's best friend or worst nightmare. Just think about how McDonald's started out. It was a small burger restaurant in the middle of the United States. And if you assumed it would stay that way, you'd have missed out on lots of growth. Now think about how residual income would be calculated for such a new restaurant. Would it factor in that global growth?

Actually, no.

Exactly.

Residual income misses growth because it doesn't make assumptions about future earnings or dividends. It's just net income less the equity capital charge. So the initial calculation of residual income would just determine if that new restaurant is covering the cost of capital.

But what factors would help determine if a new business is positioned for growth? Well, think back to the residual income calculation. If constant earnings and dividend growth is assumed, then fundamental drivers of residual income growth can be determined. Take, for example, the price-to-book ratio. It can be broken down by using fundamentals, the Gordon growth model, and the sustainable growth rate equation. So when you put it all together, the growth rate and required rate of return will be used to calculate the justified price-to-book ratio. But net income also needs to be factored in. So what other ratio needs to be included?

That's it! Return on equity would also need to be included because it represents residual income as the net income return on equity. So, residual income can be represented through ROE. $$\displaystyle (ROE \times B_0) - (r \times B_0)$$ And that leads right into the justified price-to-book ratio (where _P_ equals the intrinsic value). $$\displaystyle \frac{P_0}{B_0} = \frac{ROE-g}{r-g}$$ So in a perfect world, the book value would equal the fair value of net assets and clean surplus accounting would prevail. And then residual income is a natural extension of the price-to-book ratio.

No. Debt to equity doesn't involve the net income return.

Not quite. Gross profit margin involves sales, but not net income.

So the determinants of a new restaurant's residual income can be easily identified from the price-to-book ratio. It's ROE, the growth rate, and the required rate of return. And when you think about it, it really makes sense. If residual income is the return to equity capital holders after an equity charge, then ROE would include the equity return. The growth rate would capture future value and the required rate of return represents the capital charge.

Another financial ratio that's closely connected to the justified price-to-book ratio and residual income is __Tobin's q__, which is the ratio of the market value of debt and equity to the replacement cost of total assets. So it has components of equity and a required rate of return via asset replacement. $$\displaystyle \mbox{Tobin's q} = \frac{\mbox{Market Value of Debt and Equity}}{\mbox{Replacement Cost of Total Assets}}$$ But it also has some differences. What's one difference you notice?

Yes! Actually, all three are differences. Tobin's q uses the market value of total capital in the numerator and uses total assets as the required rate of return; it values assets at replacement cost, not historical values. So there are some similarities and differences versus price-to-book ratios.

But how does Tobin's q impact valuation? Think of the purpose behind the Tobin's q measurement. If a new restaurant had a higher Tobin's q, what would its residual income be?

No. The market value of debt and equity wouldn't be lower.

That's not it. Tobin's q has an impact on residual income.

Yes! A higher Tobin's q value indicates that a business is using assets productively. That means that it's generating returns and the market value of debt and equity will capture those increased gains. And, naturally, residual income would also be higher through greater net income via that productivity. So Tobin's q can be another check on how strong residual income really is—but be careful. Since Tobin's q uses replacement costs, it can be hard to accurately measure.

To summarize: [[summary]]

No

Yes

ROE

Debt to equity

Gross profit margin

It includes the market value of total capital

Total assets are used as the required rate of return

Assets are valued at replacement cost, not historical cost

Lower

Higher

The same

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