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ine the value-relevance of recursion value which means capitalized earnings, on the condition that h book value is constant. The conditional density function are denoted for E by f(E,AV), and expanding model above for a fixed AV, and equity value is given by:

MV (E, AV) =+

Source: Burgstahler and Dichev (1997)

The limit of integration, AV/c, is the point of investors indifference where recursion value, that is, capitalized earning, equals adaptation value. For E>AV/c, investors prefer to continue to operate the company using the business technology at present, while for E

If rearranging the equation, it yields:

MV (E, AV) =AV +

Source: Burgstahler and Dichev (1997)

In this case, the equity value on a condition that the book value is constant can be explained as the sum of the adaptation value plus the value of an option on the recursion value. In a specific way, the integral term in this equation is a call option effectively, whose value is rising in the conditional way of expected future earnings.

The proposition below describes a testable implication of the conditional valuation function:

Proposition 1: On a condition of a given adaptation value, market value is an increasing, convex function of expected earnings.

In an intuitive sense, it follows because as the conditional mean of earnings increases in future, the value of the call option on earnings increases. In addition to that, the revision in market value is because a given improvement in expected future earnings is increasing in the level of expected earnings.

Figure 1 shows that market value of equity is a result of expected earnings for a fixed adaptation value. The horizontal line in the figure below means a fixed adaptation value, the upward sloping line means recursion value, which is increasing and linear in the level of expected earnings. The two lines cross at a point E = AV / c (E denotes expected future earnings using the firms current business technology, AV denotes adaptation value, c denotes capitalization factor of earnings).

The market value of equity curve is approaching the fixed adaptation value on the left of the point, and approaching capitalized expected earnings on the right of the point. For low expected future earnings, adaptation value does more contribution to market value of firm’s equity, and a revision in expected future earnings matters little for the valuation of a firm.

For high expected future earnings, however, recursion value does more contribution to market value of firm’s equity, and a revision of expected future earnings has a great impact on market value. For middle class of earnings, the market value is attributive to a more balanced combination of recursion and adaptation value. In this case, keeping adaptation value constant, the market value revision because of a change in the mean of expected future earnings depends on the level of the mean of expected earnings. The slope of the association between market value and expected earnings increases over the range of expected future earnings towards its limiting value, the earnings capitalization part.

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