## See Chapters 4 8 9 and

1. For a given corporation with a fixed overall capitalization, a move to a higher debt-to-equity ratio will have two immediate effects. First, the earnings will be reduced by the amount of the debt service (after the appropriate tax impact), and second, the equity base will be reduced by the debt claim on the total book of assets. These effects lower both the numerator and the denominator of the P/E ratio, so that it is not immediately clear what the net impact would be, either in magnitude or direction. In fact, it turns out that, depending on the specific firm's characteristics, increasing leverage can move the P/E ratio either higher or lower. However, for the level of leverage typically encountered in nonfinancial firms (i.e., up to 50 to 60% of total capitalization), the P/E effect is quite modest, regardless of direction.

2. It is important to distinguish this very moderate bidirectional effect of leveraging a given company from the problem of an investor trying to evaluate a group of stocks that are similar apart from having varying degrees of leverage. From this market vantage point, comparable earnings and book values lead to roughly similar ROEs. However, for a given ROE, higher debt ratios imply lower returns on assets (ROAs). And since it is the ROA that basically determines a firm's enterprise value, it turns out that higher debt ratios can justify only lower P/E ratios. Thus, in contrast to the virtually negligible effect within the corporate finance framework described above, from this market viewpoint, increased leverage can have quite a significant dampening effect on the theoretical P/E ratio.

3. The interest rate sensitivity of equities (the so-called "equity duration") has long been a subject of much confusion. The DDMs treat a stock as a bond with a continually growing stream of dividend payouts. With so much of the cash flows back-ended into the future, such models display a very high sensitivity to any change in the discount rate. However, in practice, stocks have tended to display a much more moderate sensitivity to changing interest rates. This discrepancy leads to what is sometimes called the "duration paradox": Why should the equity market evidence such a low (and relatively unstable) duration when standard models suggest they should have a very high sensitivity to discount rates? The FV framework suggests several ways to resolve this paradox.

4. The first approach to the duration paradox is based on the role of inflation. Suppose a firm could immediately raise prices in response to an inflationary increase in its costs and in its discount rates. Such a firm would act as a pure inflation conduit, and changes in inflation would have no net effect on its intrinsic value or its P/E ratio. To the extent that interest rate shifts are determined solely by changes in inflation, this hypothetical stock would have a zero duration! However, in reality, business typically responds to inflationary shifts in a much more complex way and usually with significant lags. There is also a major difference in how the different components of firm value are likely to respond to changes in inflation levels. Future projects have greater pricing flexibility and adaptability than existing activities with their more rigid embedded price structure. Thus, the FV should be more inflation resistant than the TV. Since the total firm value is made up of both the FV and the TV, the sensitivity to inflation-driven interest rate changes will depend on the relative size of these two components. High P/E growth stocks with high FV/TV ratio should be relatively insensitive to inflation effects, while one should see greater sensitivity in low P/E value stocks with their lower FV/TV ratios. Taken together, this FV-based analysis provides a reasonable explanation for the far more modest duration effects that are actually seen in practice as contrasted with the superhigh durations implied by some of the standard DDMs.

5. In a common form of the standard DDM, the P/E ratio has, as the denominator, the difference between the COC and the earnings growth rate. It is typically assumed that the growth rate is indepen dent of the COC. Thus, as the COC decreases, from lower interest rate and/or from lower risk premiums, the COC moves closer to the growth rate, the denominator shrinks, resulting in sharply rising P/Es. Indeed, one periodically sees heroic forecasts of stellar P/Es (such as the Dow at 36,000), based on projections of a secular decline in the risk premium of equities. However, in the FV framework, the only growth that can affect a stock's price is that which is associated with a positive franchise spread. Any investment without such a positive spread may well grow the future book assets (and hence the future price), but it will not add to the firm's current value or price. It can therefore be argued that valuation models should only incorporate growth that reflects such positive-spread investment opportunities. With this approach, lower COCs will also reduce the rate of value-added growth. The theoretical P/E response to lower COCs will then be much more moderate than under the standard assumption of a fixed growth rate.

6. Indeed, without any need to assume an inflation flow-through effect, the equity duration in this spread-based growth model can be shown to just equal the P/E ratio itself! While not as low as the duration value derived from inflation flow-through (or seen empirically), these spread-based duration values can be up to 50 percent lower than the durations associated with the standard DDMs. One can further assume that the franchise spread itself is related to the magnitude of the COC. With this not-unreasonable assumption, the effective duration becomes even lower.

7. This focus on growth associated with a positive franchise spread leads to a strikingly simpler two-parameter form of the basic three-parameter DDM. In the basic DDM, the three basic parameters are the "gross" growth rate, the dividend payout ratio, and the discount rate. With the reasonable assumption that a firm invests only with the expectation of a positive franchise spread, it turns out that the standard "gross" growth rate can be transformed in a "net growth rate" that reflects the economic value added in each period. The standard DDM can then be expressed in a more compact form that makes use of only the discount rate together with this net growth rate. This simple two-parameter format is far more illuminating of the ultimate sources of firm value.

8. The fixed growth rate in the standard DDM also suggests that higher dividend payouts should lead to higher P/E ratios and higher ROEs. With a constant COC, these higher ROEs mean that the franchise spread should also be higher. However, such conclusions are rather hard for most analysts to accept. To the contrary, high dividend pay outs would generally be viewed as an indication of fewer opportunities for productive reinvestment. Most analysts would therefore expect to see these high payouts lead to lower P/E ratios, rather than the higher ones predicted by the standard DDMs. This unpalatable result can be corrected by embracing the concepts of a prescribed franchise spread and spread-based growth. A high payout ratio then implies, as it should, reduced opportunities for productive investment, and hence a lower P/E ratio. Thus, the concept of a fixed franchise spread and spread-based growth leads to a more reasonable relationship between the P/E and the payout behavior.

## The Debt Beater System

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