## Appendix 7a

The basic franchise factor model (Leibowitz and Kogelman) decomposes a company's theoretical value, P, as follows:

where E = current normalized earnings k = the cost of capital r = the ROE on existing lines of business R = the ROE on new initiatives

G = the ratio of new capital investment (in present value terms) to

In Equation 7A.1, the first term, E/k, is the tangible value and the second term, [(R - k)/rk]GE, is the franchise value.

For the reader to appreciate the differential effects of the three types of employee claims (on current, net franchise, and gross franchise earnings), a discussion of how each acts independently to reduce firm value will be helpful. The effects are displayed separately in Figure 7A.1. (For Figure 7A.1, as in Figure 7.1, k = r = 12 percent and R = 18 percent.) By varying G, we can span a range of P/E values. For example, with G = 4.0, we obtain

current book value

Thus, the company's value prior to any franchise labor claim would be P = 8.33E + 16.67E = 25E. Now, if we assume that a 10 percent claim is exercised only against the current earnings (i.e., the first term in Equation FIGURE 7A.1 Separate Effect of Independent 10 Percent Franchise Labor Claims on Various Components of Earnings

7A.1), then the reduced value becomes P(L1 = 10 percent) and the percentage reduction, Z(L1 = 10 percent), is z(L = 10%) = P - P(Llp _ 10%)

To generalize this result, let P(L1) be the value resulting from an L1 claim on current earnings; then,

k kr with the resulting percentage reduction