Valuation Techniques: Discounted Cash Flow, Earnings Quality, Measures of Value Added, and Real Options

A GENERAL DECAY MODEL

The preceding discussion was based on the special case of an immediate franchise plunge in a harshly competitive environment from an excess-return franchise to no franchise whatsoever. A more realistic (and more general) situation would be for the franchise to erode at some fixed pace in the course of time. The simplest approach to modeling such a situation would use a fixed annual decay rate, d, that takes the company’s earnings from its original level down to the ultimate fully competitive level, EQ. Thus, the earnings in the tth year would be expressed as

where D is the time required for the decay to reach the EQ level, EQ = E(1 − d)D, so

In the happy case in which Q is sufficiently large, this “decay orientation” would have to be expanded to include a margin that can grow at some annual rate until competitive equilibrium is attained.

At this point, a numerical example would probably be helpful: Suppose

Because all earnings are paid out in this single-phase model, there is no reinvestment, and the book value remains constant.

Under competition, the earnings are assumed to fall to the point at which the ROE equals

and the earnings are EQ = 9.

If the selected ...