To this point, we have utilized projections of future investments and returns to calculate the theoretical prospective P/E ratio at a single point in time. We now take a multiyear look at the time evolution of the relationship between realized earnings growth and realized P/E.

When estimating future earnings growth, historical earnings growth is the commonly used baseline around which an analyst will make some (typically modest) adjustments. Price appreciation is often assumed to follow the projected earnings growth with P/E remaining stable. In this way, investors tacitly elevate earnings growth to the central determinant of investment value.

Theoretically, stable P/Es are unlikely to be achieved, even under equilibrium conditions in which market returns and a company's long-term prospects remain stable. Rather there is a natural time-path of P/E evolution. This observation stands in stark contrast to the valuation methodology typically used to estimate the long-term potential of investment banking deals involving mergers, acquisitions and buyouts. In such valuations, growing earnings are projected along with a horizon P/E that is close to the current value. The combination of these growth and stability assumptions is likely to lead to excessively optimistic estimates of the IRR (internal rate of return) potential of such deals.

Given current P/E values, we ask how the P/E theoretically changes over subsequent years under varying earnings ...

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